Is a finite, curved space universe only a mathematical abstraction?

[ynot]

I’ve been trying to gain a better understanding of the concept of a finite, curved space universe. The more I learn however the less sense it makes to me. My current “disbelief” is based mainly on the following . . .

Absolute zero is only a mathematical abstraction, and no part of actual existence can be factually measured or described as being absolute zero.

An absolute zero dimension is only a mathematical abstraction, and actual existence can never be less than 3-D (that actual existence is 3-D is self-evident).

A surface is only a mathematical abstraction, and can’t exist independently of the 3-D reality of actual existence.

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.

Explaining curved space by reducing 3-D to 2-D appears no more relevant than explaining a god by reducing reality to fantasy.

I love to learn new things so if anyone can prove me wrong on any of this I will not be displeased.

[fuelair]

I’ve been trying to gain a better understanding of the concept of a finite, curved space universe. The more I learn however the less sense it makes to me. My current “disbelief” is based mainly on the following . . .

Absolute zero is only a mathematical abstraction, and no part of actual existence can be factually measured or described as being absolute zero.

An absolute zero dimension is only a mathematical abstraction, and actual existence can never be less than 3-D (that actual existence is 3-D is self-evident).

A surface is only a mathematical abstraction, and can’t exist independently of the 3-D reality of actual existence.

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.

Explaining curved space by reducing 3-D to 2-D appears no more relevant than explaining a god by reducing reality to fantasy.

I love to learn new things so if anyone can prove me wrong on any of this I will not be displeased. I am unclear - the only absolute zero I am aware of is a temperature and it is quite provable - just not achievable (requires that universe be free of matter and energy). Any left and you are slightly above absolute zero. Otherwise cute - but is invalidated by actual A)experimentation and B) prediction. On the net, in books, feel free to look it up (the ab. zero thing too. Try Bose-Einstein condensates.

By the by - the way it works is you have to present evidence that you are correct which we then disprove or not as we choose - since you are making the argument it is incorrect without evidence but your decision that it isn't. No offense, that's just how it works here (and in pretty much all scientific arenas).

[ynot]

I am unclear - the only absolute zero I am aware of is a temperature and it is quite provable - just not achievable (requires that universe be free of matter and energy). Any left and you are slightly above absolute zero. Otherwise cute - but is invalidated by actual A)experimentation and B) prediction. On the net, in books, feel free to look it up (the ab. zero thing too. Try Bose-Einstein condensates.
By your own words, absolute zero as a temperature is "not achievable" (aka not possible). How do you prove that something that is not achievable/possible, is achievable/possible? Actual existence (the universe) is matter and energy and therefore must always have a temperature. If the universe was "free of matter and energy" it would have no actual existence. Absolute zero as a temperature is only "provable" therefore as a mathematical abstraction.

By the by - the way it works is you have to present evidence that you are correct which we then disprove or not as we choose - since you are making the argument it is incorrect without evidence but your decision that it isn't. No offense, that's just how it works here (and in pretty much all scientific arenas).
You want me to present evidence to disprove a negative? I'm not saying that I can provide evidence that the concept of a finite, curved space universe is incorrect (or that it is incorrect for that matter). I am saying that evidence (as mentioned) that others present for their concept of a finite, curved space universe appear to be based on mathematical abstractions. If this is so, I don't accept it as being valid evidence.

[Squishua]

I’ve been trying to gain a better understanding of the concept of a finite, curved space universe. The more I learn however the less sense it makes to me.
When you say it "doesn't make sense," do you mean you cannot comprehend it, or do you mean you find contradictions in it?

Curved space is not an easy thing to conceptualize. After all, we associate curves with lines and planes. Three dimensions is a bit harder to get your mind around. Try reading up on General Relativity.
My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.
What theories or research are you basing this conclusion on?

-Squish

[ynot]

When you say it "doesn't make sense," do you mean you cannot comprehend it, or do you mean you find contradictions in it?
The overall concept of a finite, curved space universe doesn't make sense to me, and I have many issues to discuss in this regard. This thread is not so much concerned with the overall concept however, but more with the validity of some of the evidence that's presented to support it. More specifically, evidence that appears to be based purely on mathematical abstractions.


Curved space is not an easy thing to conceptualize. After all, we associate curves with lines and planes. Three dimensions is a bit harder to get your mind around. Try reading up on General Relativity.

What theories or research are you basing this conclusion on?

-Squish
I find it somewhat condescending when people assume that not reaching the same (their) conclusion on a matter automatically means not knowing or understanding the matter. I have read (to some degree) Einstein (GR & SR), Feynman, Dawkins, Hawking, Walt Disney and others. I'm not an academic or scientist. I have an above average IQ (for what it's worth) and I believe my abilities to conceptualise are at least as good as anyone I've met. I am basing my conclusion on what I have mentioned above and many issues I have with the overall validity and viability of the concept.

[ynot]

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.
Perhaps this sentence is a result of suffering from premature articulation. "Conclusion" should perhaps read "thoughts", and "only" should read "predominately" or "mainly".

[fuelair]

I am getting a distinct coberst/liteislife/truthfreaker feel here. Just noting that your comprehension is no indicator of falsity - and did you miss the part about accurate predictability or did you not pick up scientific method?

[Dave1001]

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.

That's self evidently true. You're trying to model the universe in a 3 pound brain. We came up with a refined version of that model using a tiny subset of 60 billion brains over a tiny subset of about 5,000 years or so, plus external computing power that in total equals less than 2 human brains (according to Yadefsky (sp?)). If you get beyond abstractions, "mathematical" or otherwise, with those limited modeling resources, that would be one heck of hack. The (perhaps endless) question is how can we improve the model. Hopefully by something more concretely useful than saying "the universe is more complex than being finite and curved".

[Squishua]

I find it somewhat condescending when people assume that not reaching the same (their) conclusion on a matter automatically means not knowing or understanding the matter.
:confused:

I asked if there were particular theories or research that led you to your conclusion. I didn't say "I figured it out and you're a moron for not getting it."

You seem a bit defensive.

-Squish

[Ben Tilly]

Of course a finite curved space is only a mathematical abstraction. So is Newton's theory of gravity. So is Coulomb's Law.

The subject of science is about finding abstractions that seem to do a good job of describing the universe. Even after an apparent success, that doesn't change the fact that what we've created are abstractions.

Cheers,
Ben

[l0rca]

Of course a finite curved space is only a mathematical abstraction. So is Newton's theory of gravity. So is Coulomb's Law.

The subject of science is about finding abstractions that seem to do a good job of describing the universe. Even after an apparent success, that doesn't change the fact that what we've created are abstractions.

Cheers,
Ben

++

[baron]

I am unclear - the only absolute zero I am aware of is a temperature and it is quite provable - just not achievable (requires that universe be free of matter and energy).

Just energy, actually. Absolute zero is when molecules stop moving. The molecules are still there.

A temperature so close to AZ as to be AZ can, I understand, now be achieved by present day technology.

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.

The way I understand it is that the mathematics describe a reality that isn't intuitive to us and therefore we can't imagine.

[l0rca]

Speaking of mathematical abstractions...

http://www.tenthdimension.com/flash2.php

[ynot]

Of course a finite curved space is only a mathematical abstraction. So is Newton's theory of gravity. So is Coulomb's Law.

The subject of science is about finding abstractions that seem to do a good job of describing the universe. Even after an apparent success, that doesn't change the fact that what we've created are abstractions.

Cheers,
Ben
A theory of gravity may well be a mathematical abstraction, but gravity itself has actual existence (as witnessed by its observable effects). Don’t think I’ve every heard anyone deny the actual existence of gravity. Gravity existed well before the theory, and the theory is merely an attempt to explain the actual. With a finite, curved universe concept however, it seems (to me) that the theory precedes actual existence evidence.


I don't have the time to respond to other posts at present so will try to get back later.

[Zygar]

I’ve been trying to gain a better understanding of the concept of a finite, curved space universe. The more I learn however the less sense it makes to me. My current “disbelief” is based mainly on the following . . .

Absolute zero is only a mathematical abstraction, and no part of actual existence can be factually measured or described as being absolute zero.

What does absolute zero have to do with the curved space model? It is an unachievable (in the confines of earth) temperature which probably couldn't even be measured due to the fact that any measuring instruments would change the observed temperature. But, just because we can't create it on earth, and we think that it can't be measured, doesn't mean it doesn't exist.

An absolute zero dimension is only a mathematical abstraction, and actual existence can never be less than 3-D (that actual existence is 3-D is self-evident).

Zero dimensionality is an abstraction to represent a singularity. I doubt anyone would claim that a true singularity exists in 3-D reality. Even string theory doesn't claim that a true singularity is real.

A surface is only a mathematical abstraction, and can’t exist independently of the 3-D reality of actual existence.

What are you trying to say here?

My current conclusion is that the concept of a finite, curved space universe is only a mathematical abstraction.

Explaining curved space by reducing 3-D to 2-D appears no more relevant than explaining a god by reducing reality to fantasy.

Explaining curved space by reducing 3-D to 2-D is done only to help the human mind comprehend the idea of "spacetime curvature". This is an irrelevent statement.

Not that space-time curvature is real. Many theories posit this as a way of thinking about how spacetime works. It is intended to be an abstraction that helps the human mind comprehend it. I seriously doubt that spacetime is really curved like you see in those diagrams.

I love to learn new things so if anyone can prove me wrong on any of this I will not be displeased.

Prove what wrong? You haven't stated anything proveable.

[Zygar]

Of course a finite curved space is only a mathematical abstraction. So is Newton's theory of gravity. So is Coulomb's Law.

The subject of science is about finding abstractions that seem to do a good job of describing the universe. Even after an apparent success, that doesn't change the fact that what we've created are abstractions.

Cheers,
Ben

And? So we've created abstractions that represent the universe. Does that mean that reality doesn't work that way? What are you trying to say here?

[Ben Tilly]

And? So we've created abstractions that represent the universe. Does that mean that reality doesn't work that way? What are you trying to say here?

I'm saying that it is silly to dismiss ideas just because they are abstractions.

Incidentally reality actually doesn't work the way that the two abstractions that I brought up posit, though they are excellent approximations with great practical utility.

Cheers,
Ben

[Ben Tilly]

A theory of gravity may well be a mathematical abstraction, but gravity itself has actual existence (as witnessed by its observable effects). Don’t think I’ve every heard anyone deny the actual existence of gravity. Gravity existed well before the theory, and the theory is merely an attempt to explain the actual. With a finite, curved universe concept however, it seems (to me) that the theory precedes actual existence evidence.

A theory of gravity more describes than explains, actually. (That was one of the major complaints levied against Newton's theory.)

And you'd be amazed at how many scientific theories are created in advance of evidence for them. In fact this is often necessary. Only once one has a theory can one can design experiments to test it.

That said, I don't think the evidence that we actually live in a finite curved universe is very good. And even if we do, from our perspective the universe is still rather big.

Cheers,
Ben

[fuelair]

Just energy, actually. Absolute zero is when molecules stop moving. The molecules are still there.

A temperature so close to AZ as to be AZ can, I understand, now be achieved by present day technology.



The way I understand it is that the mathematics describe a reality that isn't intuitive to us and therefore we can't imagine.
Actually, the last time I hunted up current research on this(about 8 months ago) the research/calculations were different from that (which is the way I had originally learned it myself) According to the info at that time (which I found with data and a neat applet on Bose-Einstein condensates) said that current belief is that all matter & energy - at the heat death of the universe - will be evenly spread throughout the universe and will be at a temperature just above 0 K - and apparently (as a side note ) a bit lower than B-E Cs. Possibly 0 K will be achieved in a lab - but apparently not in Nature.

[ynot]

What does absolute zero have to do with the curved space model? It is an unachievable (in the confines of earth) temperature which probably couldn't even be measured due to the fact that any measuring instruments would change the observed temperature. But, just because we can't create it on earth, and we think that it can't be measured, doesn't mean it doesn't exist.
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Zero dimensionality is an abstraction to represent a singularity. I doubt anyone would claim that a true singularity exists in 3-D reality. Even string theory doesn't claim that a true singularity is real.



What are you trying to say here?



Explaining curved space by reducing 3-D to 2-D is done only to help the human mind comprehend the idea of "spacetime curvature". This is an irrelevent statement.

Not that space-time curvature is real. Many theories posit this as a way of thinking about how spacetime works. It is intended to be an abstraction that helps the human mind comprehend it. I seriously doubt that spacetime is really curved like you see in those diagrams.

[font=Verdana][size=2]

Prove what wrong? You haven't stated anything proveable.
I didn't mean absolute zero in terms of temperature, but in terms of existence. Using a 2-D scenario is saying that the third dimension is absolute zero (doesn't exist). Obviously a third dimension always does exist in reality. I don't think it's a very good scientific method to use an impossible scenario as an analogy. It wouldn't be acceptable if a person were to say that explaining a god is very hard in the reality of actual existence, so I will reduce reality to a fantasyland to make it easier.

"it can't be measured, doesn't mean it doesn't exist." But it does mean that it can't be proven to exist (IMO). So we can't say that it does or can actually exist.

Ben Tilly - "I'm saying that it is silly to dismiss ideas just because they are abstractions."
I'm not suggesting that any ideas should be dismissed.

[athon]

I don't get what you mean by 'just a mathematical abstraction'. To me, this is a significant indicator of how the rules of the universe operate.

There are many things which such mathematics predict that I can't fully conceptualize with my brain. Sub-atomic particles, for instance - I picture them as little buzzing balls, but they're not. They aren't physical little things; they're units of information. I can't 'conceptualize' a unit of information like that, so I imagine it as a little ball.

Absolute zero in energy states is a concept that might not exist per se in this universe, but so what? I can conceptualize it easily enough, and it's mathematically likely.

Curved space is slightly different. It does exist, in spite of our ability to conceptualize it.

So...well, I'm lost as to the point here.

Athon

[Zygar]

I'm saying that it is silly to dismiss ideas just because they are abstractions.

Incidentally reality actually doesn't work the way that the two abstractions that I brought up posit, though they are excellent approximations with great practical utility.

Cheers,
Ben

Thanks for the clarification. I agree with you completely. I just wanted to be able to understand your stance on this.

[Zygar]

I didn't mean absolute zero in terms of temperature, but in terms of existence. Using a 2-D scenario is saying that the third dimension is absolute zero (doesn't exist).

That is not a correct term. Absolute zero is a temperature, not a dimension of space.

Obviously a third dimension always does exist in reality. I don't think it's a very good scientific method to use an impossible scenario as an analogy. It wouldn't be acceptable if a person were to say that explaining a god is very hard in the reality of actual existence, so I will reduce reality to a fantasyland to make it easier.

"it can't be measured, doesn't mean it doesn't exist." But it does mean that it can't be proven to exist (IMO). So we can't say that it does or can actually exist.

Ben Tilly - "I'm saying that it is silly to dismiss ideas just because they are abstractions."
I'm not suggesting that any ideas should be dismissed.

This isn't how the actual math and models work. It is just a tool to show the concept to laymen because it is so very difficult to display a 3-D warped space (which effectively is a 3-D object in 4-D space) to the human brain. Try looking at a representation of a hypercube. It's a 4-D object, so our human brains have a great deal of trouble comprehending it. This has nothing to do with a concept like "god". It just has to do with the fact that our experience is 3-D and our brains think in 3-D. Your analogy is invalid.

[fuelair]

I didn't mean absolute zero in terms of temperature, but in terms of existence. Using a 2-D scenario is saying that the third dimension is absolute zero (doesn't exist). Obviously a third dimension always does exist in reality. I don't think it's a very good scientific method to use an impossible scenario as an analogy. It wouldn't be acceptable if a person were to say that explaining a god is very hard in the reality of actual existence, so I will reduce reality to a fantasyland to make it easier.

"it can't be measured, doesn't mean it doesn't exist." But it does mean that it can't be proven to exist (IMO). So we can't say that it does or can actually exist.

Ben Tilly - "I'm saying that it is silly to dismiss ideas just because they are abstractions."
I'm not suggesting that any ideas should be dismissed.

That is complete and abject silliness - not to mention it contradicts your first response to me.

[Rob Lister]

Just energy, actually. Absolute zero is when molecules stop moving. The molecules are still there.

A temperature so close to AZ as to be AZ can, I understand, now be achieved by present day technology.



The way I understand it is that the mathematics describe a reality that isn't intuitive to us and therefore we can't imagine.

Dude, this ain't horseshoes. Close not only doesn't count, and in fact is the bane, not the win.

BTW, I disagree with the OP but only because authorities whom I trust, and who are much, much smarter than I, have convinced me, and even almost made me understand, a closed universe. Still, this isn't horseshoes.

[ynot]

I don't get what you mean by 'just a mathematical abstraction'. To me, this is a significant indicator of how the rules of the universe operate
Math is a a very useful tool and I've nothing against it if it's used appropriately.

There are many things which such mathematics predict that I can't fully conceptualize with my brain. Sub-atomic particles, for instance - I picture them as little buzzing balls, but they're not. They aren't physical little things; they're units of information. I can't 'conceptualize' a unit of information like that, so I imagine it as a little ball.
Unfortunately my hand held magnifing glass doesn't provide me with any evidence of sub-atomic particles. I'm fairly happy to accept your claim that they exist however, as the concept that there's someting smaller than an atom seems reasonable. Wouldn't bet my life on it though. I don't think that the flatland 2-D scenarios are just used for abstract conceptual purposes.

Absolute zero in energy states is a concept that might not exist per se in this universe, but so what? I can conceptualize it easily enough, and it's mathematically likely.
I'm sorry that I've incorrectly used the term "absolute zero". In past discussions invoving zero it's been claimed that zero is the smallest possible incriment. I added the "absolute" to highlight my belief that zero is the absolute lack of any incriment. I don't think it really matters whether we're talking about zero in relation to temperature or existence. By definition, anything that has no existence, can't exist.

Curved space is slightly different. It does exist, in spite of our ability to conceptualize it.

So...well, I'm lost as to the point here.

Athon
Would appreciate your factual and conclusive evidence that curved space "does exist".

[Ben Tilly]

Would appreciate your factual and conclusive evidence that curved space "does exist".

If you wish to read the literature on tests of general relativity, be my guest. We have proof of effects that are predicted in general relativity as being due to curved space. For instance there is the Shapiro time delay, which predicts that it takes extra time to pass near a heavy object due to the time dilation from its gravity. This effect has been measured by the Cassini probe and the delay was within 0.002% of what general relativity predicts.

Be warned that it takes a lot of work to understand general relativity, and more still to understand exactly what these tests are testing. But all of the research is out there and published. If you have access to a local university, and a few years to spend learning, you can verify it in detail.

Cheers,
Ben

[baron]

Dude, this ain't horseshoes. Close not only doesn't count...

"Count" in what sense? Absolute zero cannot be achieved and even if it could, it could not be measured. The lowest temperature recorded is a few billionths of a K. At that temperature the behaviour of a system is essentially identical to that of a postulated system at 0K.

So in what way doesn't that "count"?

[69dodge]

Would appreciate your factual and conclusive evidence that curved space "does exist".Even if, in fact, it doesn't exist, that doesn't mean the very idea is nonsense, as you appear to think.

I think you're taking the word "curved" too literally. Forget about the word "curved". What do theories that supposedly involve "curved space" say about what we can actually observe? Is there anything nonsensical about these possible observations? Why is it impossible that we might observe what these theories say we should observe?

[ynot]

If you wish to read the literature on tests of general relativity, be my guest. We have proof of effects that are predicted in general relativity as being due to curved space. For instance there is the Shapiro time delay, which predicts that it takes extra time to pass near a heavy object due to the time dilation from its gravity. This effect has been measured by the Cassini probe and the delay was within 0.002% of what general relativity predicts.

Cheers,
Ben
Don't suppose it could be something simple like the gravity caused a "drag" effect? The GPS is an example usually given. Is the explaination below a valid alternative?


"The Global Positioning System (GPS) is nowadays considered as the prime example for the everyday importance of Relativity. It is claimed that without the relativistic corrections (which amount to 38 microseconds/day) the error in the determination of the position would accumulate quickly to values much larger then the observed accuracy. However, in reality the positions are actually not obtained by comparing the time signal received from the satellite with the receiver time, but by observing the difference between the time signals obtained from a number of different satellites.

Consider for simplicity a one dimensional problem where the receiver is located somewhere on the line connecting the two transmitters. In this case the signal from transmitter 1 reaches the receiver at time
(1) t1 = t0+ x1/c
and the signal from transmitter 2 reaches the receiver at time
(2) t2 = t0+ x2/c ,
where t0 is the time the signal is being sent out (assuming both transmitter clocks are synchronized), x1 is the distance of the receiver from transmitter 1, x2 the distance of the receiver from transmitter2, and c the speed of light.
Now if one subtracts Eqs.(1) and (2) one gets
(3) x1-x2 = c. [t1-t2].
One knows therefore the position of the receiver just by comparing the time signals from the two transmitters (the receiver clock is completely irrelevant).
If one assumes now that the transmitter clocks are running fast or slow by a relative factor (1+ε), one has instead:
(4) x1-x2 = c.[(1+ε).t1 -(1+ε).t2] = c.(1+ε).(t1-t2)
which means that the position will simply be wrong by a relative factor ε, but there is obviously no accumulation as the transmitter clocks run at the same rate relatively to each other.

Now the quoted relativistic correction of 38 microseconds/day corresponds to ε=4.4.10-10. As the satellites are at a distance of around 20000 km (=2.109 cm), the positional error due to relativity should actually only be 4.4.10-10 . 2.109 cm = 0.8 cm! This is even much less than the presently claimed accuracy of the GPS of a few meters, so the Relativity effect should actually not be relevant at all!"

[ynot]

Even if, in fact, it doesn't exist, that doesn't mean the very idea is nonsense, as you appear to think.
I don't think a god exists, but a god is still a good idea?

I think you're taking the word "curved" too literally. Forget about the word "curved". What do theories that supposedly involve "curved space" say about what we can actually observe? Is there anything nonsensical about these possible observations? Why is it impossible that we might observe what these theories say we should observe?
You could be right about me being too literal. But I think science should be quite literal (not that I represent science).

[ynot]

That is not a correct term. Absolute zero is a temperature, not a dimension of space.



This isn't how the actual math and models work. It is just a tool to show the concept to laymen because it is so very difficult to display a 3-D warped space (which effectively is a 3-D object in 4-D space) to the human brain. Try looking at a representation of a hypercube. It's a 4-D object, so our human brains have a great deal of trouble comprehending it. This has nothing to do with a concept like "god". It just has to do with the fact that our experience is 3-D and our brains think in 3-D. Your analogy is invalid.
Theists would also argue that the concept of a god is very difficult to display/explain to the human brain, and that the concept of a god doesn't match our experience. In this regard I think my analogy is valid.

[ynot]

BTW, I disagree with the OP but only because authorities whom I trust, and who are much, much smarter than I, have convinced me, and even almost made me understand, a closed universe. Still, this isn't horseshoes.
I get it now! - We should trust and be convinced by those that are much, much smarter than us - simple!. Oh . . . there goes a very, very smart theist that I might be able to trust. Maybe I should talk to him. :D

[LordoftheLeftHand]

Don't suppose it could be something simple like the gravity caused a "drag" effect? The GPS is an example usually given. Is the explaination below a valid alternative?


"The Global Positioning System (GPS) is nowadays considered as the prime example for the everyday importance of Relativity. It is claimed that without the relativistic corrections (which amount to 38 microseconds/day) the error in the determination of the position would accumulate quickly to values much larger then the observed accuracy. However, in reality the positions are actually not obtained by comparing the time signal received from the satellite with the receiver time, but by observing the difference between the time signals obtained from a number of different satellites.

Consider for simplicity a one dimensional problem where the receiver is located somewhere on the line connecting the two transmitters. In this case the signal from transmitter 1 reaches the receiver at time
(1) t1 = t0+ x1/c
and the signal from transmitter 2 reaches the receiver at time
(2) t2 = t0+ x2/c ,
where t0 is the time the signal is being sent out (assuming both transmitter clocks are synchronized), x1 is the distance of the receiver from transmitter 1, x2 the distance of the receiver from transmitter2, and c the speed of light.
Now if one subtracts Eqs.(1) and (2) one gets
(3) x1-x2 = c. [t1-t2].
One knows therefore the position of the receiver just by comparing the time signals from the two transmitters (the receiver clock is completely irrelevant).
If one assumes now that the transmitter clocks are running fast or slow by a relative factor (1+ε), one has instead:
(4) x1-x2 = c.[(1+ε).t1 -(1+ε).t2] = c.(1+ε).(t1-t2)
which means that the position will simply be wrong by a relative factor ε, but there is obviously no accumulation as the transmitter clocks run at the same rate relatively to each other.

Now the quoted relativistic correction of 38 microseconds/day corresponds to ε=4.4.10-10. As the satellites are at a distance of around 20000 km (=2.109 cm), the positional error due to relativity should actually only be 4.4.10-10 . 2.109 cm = 0.8 cm! This is even much less than the presently claimed accuracy of the GPS of a few meters, so the Relativity effect should actually not be relevant at all!"

If you are going to steal other peoples work, you should cite them at least.

I don't know the original source, but I doubt this is your work. An exact same posting was made below 2 years ago.

http://www.physicsforums.com/archive/index.php/t-55159.html

LLH

[Arkan_Wolfshade]

The finite, no-boundry model of the universe is a scientific theory; its validity can be judged by the same criteria as any other theory.

[ynot]

If you are going to steal other peoples work, you should cite them at least

Sorry - Didn't mean to imply it was my work (or that I even understand it). It came from - http://www.physicsmyths.org.uk/gps.htm

I don't know the original source, but I doubt this is your work. An exact same posting was made below 2 years ago.

http://www.physicsforums.com/archive/index.php/t-55159.html

LLH
"2 years ago"! - Boy you've got a great memory! Aint gonna tell you any lies.

[LordoftheLeftHand]

Sorry - Didn't mean to imply it was my work (or that I even understand it). It came from - http://www.physicsmyths.org.uk/gps.htm

If you don't understand it, why on earth are you posting it here, in vain support of one of your &$%^#* ideas?

LLH

[ynot]

If you don't understand it, why on earth are you posting it here, in vain support of one of your &$%^#* ideas?

LLH
Wasn't using it in support of my &$%^#* ideas. Not even sure that I have any &$%^#* ideas on this suject. I'm merely questioning your &$%^#* ideas on this subject. Was hoping that &$%^#* clever people like you could let me know if it was all &$%^#* or not.

[Ben Tilly]

Don't suppose it could be something simple like the gravity caused a "drag" effect? The GPS is an example usually given. Is the explaination below a valid alternative?

There is several decades of research into alternative theories, and tests between them. No simple alternative has been found. There are still, however, alternatives to general relativity which are under consideration. Also note that I was very careful in my wording. I said, We have proof of effects that are predicted in general relativity as being due to curved space. Note that I am very carefully not saying that space is actually curved. Effects which in general relativity are due to curvature may have other explanations in other theories.

Note that the explanation that you cut and pasted (which you did not understand) did not say that general relativity was not measured. It says that it is not relevant to GPS.

"The Global Positioning System (GPS) is nowadays considered as the prime example for the everyday importance of Relativity. It is claimed that without the relativistic corrections (which amount to 38 microseconds/day) the error in the determination of the position would accumulate quickly to values much larger then the observed accuracy. However, in reality the positions are actually not obtained by comparing the time signal received from the satellite with the receiver time, but by observing the difference between the time signals obtained from a number of different satellites.

The author of this piece misstated at least one basic fact. GPS is not the prime example for the everyday importance of relativity, but rather for general relativity. The special theory of relativity gives far greater corrections than 38 microseconds per day. 38 microseconds per day is the correction due to being slightly out of the gravity well of the Earth.

Secondly the author is right from the point of view of physics, but wrong from an engineering perspective. GPS units have their own internal clocks. It is true that in the end the difference between time signals is what drives the measurement. But what actually happens is that the GPS unit constantly corrects its own clock based on the information that it is getting from satellites, and then does measurements based on its clock. (The advantage of this is that you can get a measurement when only 3 satellites are visible.) Without the 38 microseconds per day adjustment, GPS units would have to be adjusting their clocks by 38 microseconds per day.

If you didn't have this adjustment made, then after being out of range for 15 minutes, after your unit spots 3 satellites, the resulting GPS measurement would be off by about 100 meters. (It would see the satellite as being 150 meters off from where it is. Assuming that the satellites are not directly overhead, the intersection would be off by less than that.) That's a pretty big discrepancy.

Cheers,
Ben

[ynot]

If the universe is infinite I don’t see that it would ever be possible to prove that it is. Obviously it would be possible to prove that it’s not infinite by proving that it’s finite. If it hasn’t been proven to be finite however, it should be assumed that it’s infinite (the default conclusion). As I don’t think it’s been proven to be finite, I must assume it’s infinite.

As I understand it, the curved-space universe concept claims that the universe is not only finite but also infinite in that it’s a singular, enclosed, circular system. A finite universe should have some form of outer edge. Perhaps it has and we haven‘t found it yet. Or perhaps curved-space will somehow always prevent us from finding it. There should also be something external to the edge that is either so significantly different from the universe that we can say “here is where the universe stops and the other thing starts”, or there is something that is nothing.

If we imagine a slug on the outer surface of a levitated sphere. The slug is deaf and blind and it can’t sense an atmosphere, so it’s only aware that the surface of the sphere and itself exists. It can only slither infinitely around the surface of the sphere and will never find an end to its journey. It experiences the sphere as being both finite and infinite. The slug is however merely deluded by its inability to observe the actual existence of a 3-D universe. If the sphere was made of a slug-edible substance, the slug could burrow in to the sphere and away from the surface. Alternatively, a bird could take the slug in its beak and fly it away from the sphere completely. In an actual existence 3-D universe, the surface of the sphere can never exist in isolation.

I think the finite, curved-space universe concept is clever, fascinating, entertaining, mind-bending, etc. But I don’t think it represents what is actual, factual or proven. But as always . . . I realise that I could be wrong.

[ynot]

There is several decades of research into alternative theories, and tests between them. No simple alternative has been found. There are still, however, alternatives to general relativity which are under consideration. Also note that I was very careful in my wording. I said, We have proof of effects that are predicted in general relativity as being due to curved space. Note that I am very carefully not saying that space is actually curved. Effects which in general relativity are due to curvature may have other explanations in other theories.

Note that the explanation that you cut and pasted (which you did not understand) did not say that general relativity was not measured. It says that it is not relevant to GPS.



The author of this piece misstated at least one basic fact. GPS is not the prime example for the everyday importance of relativity, but rather for general relativity. The special theory of relativity gives far greater corrections than 38 microseconds per day. 38 microseconds per day is the correction due to being slightly out of the gravity well of the Earth.

Secondly the author is right from the point of view of physics, but wrong from an engineering perspective. GPS units have their own internal clocks. It is true that in the end the difference between time signals is what drives the measurement. But what actually happens is that the GPS unit constantly corrects its own clock based on the information that it is getting from satellites, and then does measurements based on its clock. (The advantage of this is that you can get a measurement when only 3 satellites are visible.) Without the 38 microseconds per day adjustment, GPS units would have to be adjusting their clocks by 38 microseconds per day.

If you didn't have this adjustment made, then after being out of range for 15 minutes, after your unit spots 3 satellites, the resulting GPS measurement would be off by about 100 meters. (It would see the satellite as being 150 meters off from where it is. Assuming that the satellites are not directly overhead, the intersection would be off by less than that.) That's a pretty big discrepancy.

Cheers,
Ben
Thanks Ben - Please read my response to LLH to get my purpose in posting this piece of text ( you can ignore the &$%^#*s) :)

[fuelair]

I firmly believe I have a thorough idea of what "all &$%^#*" is from certain posts - all by the same person - on this very thread.

[Crazycowbob]

I think I see what you're getting at here, that the idea of a closed universe is not given by physical evidence, versus, say, atoms, which can be seen through a SEM, or sub-atomic particles, whose evidence of existance has been shown in particle accelerators.

The thing is, atoms, and sub-atomic particles were postulated by mathematical theorem long before we were able to prove their existance (or non existance, as the case could have been had the great minds been wrong :) ). Also, the reason a closed universe is the current theory is because the mathmatics needed to explain the workings of the known universe (that which we have direct evidence of), when extrapolated outward beyond what we currently know, indicate that such is the case.

Is our understanding wrong? Possibly, I'm of the opinion that we have barely dipped our toes into the ocean of understanding, however, I do think the current models give us a solid starting point, and may very well describe the things we can not yet see for ourselves.




Fry: Wow, so there are an infinite number of universes?
Prof. Farnsworth: No, just the two.

[ynot]

I firmly believe I have a thorough idea of what "all &$%^#*" is from certain posts - all by the same person - on this very thread.
Of course you have a thorough understanding of what "all &$%^#*" is. You invented it. It's your language. I assume that by "the same person" you are refering to me. Am I really such a vile, despicable, dangerously deluded piece of worthless slime that you can't refer to me directly by my forum name?

[ynot]

I think I see what you're getting at here, that the idea of a closed universe is not given by physical evidence, versus, say, atoms, which can be seen through a SEM, or sub-atomic particles, whose evidence of existance has been shown in particle accelerators.
When people start with "I think I see what you're getting at here" I'm never quite certain if it's genuine or sarcastic.

The thing is, atoms, and sub-atomic particles were postulated by mathematical theorem long before we were able to prove their existance (or non existance, as the case could have been had the great minds been wrong :) ). Also, the reason a closed universe is the current theory is because the mathmatics needed to explain the workings of the known universe (that which we have direct evidence of), when extrapolated outward beyond what we currently know, indicate that such is the case.
I'm not in any way against theories, educated guesses, brainstorming, etc. I'm against it if they are claimed to be proven before they are. There is also a danger that "proof" can be made to fit a preconceived conclusion. Of course I realise that a scientist wouldn't do this :D
Conclusion should follow observation, not the other way around.


Is our understanding wrong? Possibly, I'm of the opinion that we have barely dipped our toes into the ocean of understanding, however, I do think the current models give us a solid starting point, and may very well describe the things we can not yet see for ourselves.
Agree



Fry: Wow, so there are an infinite number of universes?
Prof. Farnsworth: No, just the two.
I like that show. Almost as good as Homer (J S) :D

[Ben Tilly]

If the universe is infinite I don’t see that it would ever be possible to prove that it is. Obviously it would be possible to prove that it’s not infinite by proving that it’s finite. If it hasn’t been proven to be finite however, it should be assumed that it’s infinite (the default conclusion). As I don’t think it’s been proven to be finite, I must assume it’s infinite.

There is some evidence that the universe might be finite. In particular a finite universe would constrain quantum fluctuations in the early universe and help cosmologists explain why we do not see larger fluctuations than we do. However recent measurements indicate that apparently fundamental constants may vary over time. For instance see http://arxiv.org/abs/astro-ph/0112323. Given direct evidence that our understanding of basic physics is wrong over cosmological time scales, I'm not inclined to worry that cosmologists are having trouble explaining basic features of our universe.

As I understand it, the curved-space universe concept claims that the universe is not only finite but also infinite in that it’s a singular, enclosed, circular system. A finite universe should have some form of outer edge. Perhaps it has and we haven‘t found it yet. Or perhaps curved-space will somehow always prevent us from finding it. There should also be something external to the edge that is either so significantly different from the universe that we can say “here is where the universe stops and the other thing starts”, or there is something that is nothing.

And here you show a basic lack of comprehension of the idea that you're criticizing. Your argument is exactly analogous to a flat Earther claiming that the world cannot be finite in extent because if it was finite it would have an edge. If you truly understand the concept of a finite curved space, then you'll understand how exact that comparison is.

If we imagine a slug on the outer surface of a levitated sphere. The slug is deaf and blind and it can’t sense an atmosphere, so it’s only aware that the surface of the sphere and itself exists. It can only slither infinitely around the surface of the sphere and will never find an end to its journey. It experiences the sphere as being both finite and infinite. The slug is however merely deluded by its inability to observe the actual existence of a 3-D universe. If the sphere was made of a slug-edible substance, the slug could burrow in to the sphere and away from the surface. Alternatively, a bird could take the slug in its beak and fly it away from the sphere completely. In an actual existence 3-D universe, the surface of the sphere can never exist in isolation.

Using a 2 dimensional shape embedded in a 3-dimensional Euclidean space is only meant as a visualization aid, not a description of what is really going on. General relativity describes an internally consistent mathematical structure for the geometry of space-time. It does not describe a mathematical structure embedded in some other structure, it describes a mathematical structure that exists and has certain properties.

I think the finite, curved-space universe concept is clever, fascinating, entertaining, mind-bending, etc. But I don’t think it represents what is actual, factual or proven. But as always . . . I realise that I could be wrong.

I agree that it is not proven. In fact I don't think the evidence for it is very convincing. However it is plausible enough that you should keep your mind open, and it shouldn't just be dismissed out of hand.

Cheers,
Ben

[Schneibster]

Mmmmfff. I freely admit that your suspicion that the shape of the universe is not a finite, curved space agrees with my own prejudice. I deliberately characterize it as a prejudice, because I cannot give fully convincing logical grounds for making it a conclusion. There is, however, a fair bit of evidence that supports it as a conclusion.

However, it seems to me that since you are characterizing it as a "mathematical abstraction," our opinions diverge. You are not maintaining that it is in reality not an accurate description of the geometry of spacetime, as I am, but that it is in principle impossible for spacetime to have this or any other such geometry, a position that I have evidence to deny, on the grounds that it is impossible to visualize such a geometry without using oversimplified geometrical models that depend on our own three-space-one-time dimensional experience. I contend that we know that space is more than three-dimensional, merely on the basis of the Lorentz-Fitzgerald contraction; we can observe anomalous effects on measured characteristics of moving objects that admit of no other explanation than that three-dimensional space is curved in a fourth dimension, and that fourth dimension is time. If there is another explanation of these effects, I am unaware of it. Let's examine precisely what I mean:

Suppose two objects are moving at the same velocity; that is, they appear motionless to one another. Now let us suppose that one object undergoes an acceleration such that it is moving away from the other. Next let us suppose that we are observing these two objects in a frame in which they are both moving originally in the same direction, which we will arbitrarily define as the "x" direction, at equal velocities, and that the acceleration results in the accelerated object having the same speed, but its velocity having a different direction, that is, a combination of movement in both the arbitrary "x" direction and in the rectilinear but other than that also arbitrary "y" direction.

Let's define the frames of these two objects such that their "x" (which we will call "x'," or "x-prime," for the first object's frame, and "x''", or "x-prime-prime," for the second object's frame) will correspond to the direction they are moving in our frame. Furthermore, both objects will have y' and y'' that is parallel to our own y. Now, what happens?

At the beginning, the direction of x, x', and x'' is the same. After the second object receives its acceleration, x and x' are still the same direction, but x'' is in a different direction; in our frame, and in that of the first object, x'' points in a direction that is intermediate between x (or x') and y (or y'). Now, in terms of the second object's speed in its own locally defined x, which we are calling x'', it is going the same speed as the first object; but in terms of our x, or the first object's x, which we call x', it now is going slower. Compensating for this, in terms of the first object's y, which we call y', or our own y, it now has a non-zero motion. In all three frames, the two objects are now moving apart; but in terms of the first object's x', and in terms of our x, it is moving slower in x, and faster in y. But what about from the second object's point of view? Is the first object moving slower, or faster, in x''?

Note that in fact, the second object sees the first as moving slower in x''. So both objects see the other as moving slower in x. And this is the result of a coordinate transform, of a type we call "rotation."

Not only that, but if the two objects were elongated along the direction of movement, and the second object were rotated along with its vector being rotated, then each object would observe the other to be shorter in x.

So, what do we see when an object is accelerated? We see that it is shorter, and we see that it moves more slowly in t, where t is the time dimension. And from the frame of that object, exactly the same thing happens to the unaccelerated object.

Finally, we see that the transform that is needed for this new type of rotation uses the same equations that the type we know about does; but it does not use it in the same geometrical environment. Because, you see, the geometry of space with respect to time is not circular; it is hyperbolic. So instead of using circular trigonometry to describe the effects of this rotation, as we do for a rotation in space, we have to use hyperbolic geometry to describe it; and hyperbolic geometry is very unusual in many ways. There are "angles" in hyperbolic geometry that cannot be considered to exist; there are no such angles in circular geometry. Rotation over an "angle" in hyperbolic geometry results in an apparent change in the size of the rotated object; this does not happen in circular geometry. As a result, we observe unambiguously that the relation of time to space implies that space is curved with respect to time, in a way that it is not curved with respect to itself; in other words, the three spatial dimensions are "flat" with respect to one another, but "curved" with respect to time. And this is an observable fact of our universe. We can measure it, and we cannot account for it in any other way.

With curvature as weird as this (not to mention as difficult, if not impossible, to visualize, as this) possible for the previously "obvious" geometry of space, along with obvious and inescapable observable consequences, I think it is impossible to maintain that curvature of space is a mathematical abstraction without real physical meaning.

[gnome]

A philosophical barrier, in my estimation... the problem in your question is not in the term "abstraction" but in the term "just".

Any description of physics is going to be a mathematical abstraction. The significance of them begins and ends with their ability to predict or explain real phenomena. It is a foregone conclusion that our abstractions are probably not an exhaustive description, as we constantly must modify our models of physics to take into account new information. But they keep getting better and better.

[Schneibster]

Again, mmmfff. Hmmmm. My position on the "actual reality" of the better-proven models we use in physics can be summarized by noting that, "If it looks like a duck, waddles like a duck, and quacks like a duck, is it only a model of a duck?" Quite frankly, if you get right down to it, you can't prove that any of this is real at all. You can't even prove you're real. So to my mind, there is a fuzzy line there somewhere, further on than the point where we note that the cardinal numbers are "real" because we can see the difference between one orange and two oranges, and not quite as far as the computer models of chaotic phenomena like turbulence and population ecology, where we stop talking about reality and start talking about models of reality. I think the further we get away from observables that we can define without instrumentation, the more "abstract" our models must become; but always, there are anomalous observables, and always, we find explanations of varying degrees of plausibility and varying degrees of connectedness to our experiences. Where one draws that line is a matter of subjective importance, not objective.

IMHO, of course. YMMV. :D

[athon]

Would appreciate your factual and conclusive evidence that curved space "does exist".

Ok, I think I grasp it now.

I sometimes think people can be divided into the 'defined reality = that which I can see' group and the 'defined reality = that which I can infer' group. The former find it difficult to see how we can use abstract mathematics to create some strong definitions of reality. The latter see reality as entire definable by mathematics, hence unimaginable, abstract conclusions are just as real as those which can be seen and conceptualised.

I don't know how one can be encouraged to move from the former group to the latter. Curved space exists to me in the same way that I know the Earth's core is solid -- nobody has ever 'seen' it, yet inferences from the mathematics of our surrounding universe indicate this is so, at least until contrary evidence is provided.

In short, either you understand how science works, or you don't.

Athon

[athon]

Again, mmmfff. Hmmmm. My position on the "actual reality" of the better-proven models we use in physics can be summarized by noting that, "If it looks like a duck, waddles like a duck, and quacks like a duck, is it only a model of a duck?" Quite frankly, if you get right down to it, you can't prove that any of this is real at all. You can't even prove you're real. So to my mind, there is a fuzzy line there somewhere, further on than the point where we note that the cardinal numbers are "real" because we can see the difference between one orange and two oranges, and not quite as far as the computer models of chaotic phenomena like turbulence and population ecology, where we stop talking about reality and start talking about models of reality. I think the further we get away from observables that we can define without instrumentation, the more "abstract" our models must become; but always, there are anomalous observables, and always, we find explanations of varying degrees of plausibility and varying degrees of connectedness to our experiences. Where one draws that line is a matter of subjective importance, not objective.

IMHO, of course. YMMV. :D

If it walks like a duck, quacks like a duck, looks like a duck...we call it a duck until it starts to go 'moo'.

Science describes things as models in which we place some confidence will predict some sort of universal phenomena. That's it, end of story. 'Reality' doesn't come into it -- that's a philosophical construct which has no place in science, as it becomes a circular reasoning.

'What does science describe?'
Reality
'What is reality?'
That which science describes

So, we create models which we place confidence in on account of our personal acceptance of a level of evidence. Therefore, it becomes a scale of acceptibility, rather than a defined level of proof which suddenly pops into being. Nothing is suddenly 'real' - we just either are confident that it works, or we're not so confident.

That's why a lot of people don't feel comfortable with science; it offers no certainty. On the other hand, it's the very reason why I am comfortable with it. I am allowed to change my mind when presented with new evidence or a new way of interpreting old evidence.

Athon

[ynot]

And here you show a basic lack of comprehension of the idea that you're criticizing. Your argument is exactly analogous to a flat Earther claiming that the world cannot be finite in extent because if it was finite it would have an edge. If you truly understand the concept of a finite curved space, then you'll understand how exact that comparison is.
I don't understand what you're saying here. The world does have an edge in the form of a surface (an outer edge). Are you saying that a finite curved-space universe wouldn't have an outer edge?


I agree that it is not proven. In fact I don't think the evidence for it is very convincing. However it is plausible enough that you should keep your mind open, and it shouldn't just be dismissed out of hand.
I don't dismiss it out of hand. I just don't think it's proven.

[ynot]

Mmmmfff. I freely admit that your suspicion that the shape of the universe is not a finite, curved space agrees with my own prejudice. I deliberately characterize it as a prejudice, because I cannot give fully convincing logical grounds for making it a conclusion. There is, however, a fair bit of evidence that supports it as a conclusion.

However, it seems to me that since you are characterizing it as a "mathematical abstraction," our opinions diverge. You are not maintaining that it is in reality not an accurate description of the geometry of spacetime, as I am, but that it is in principle impossible for spacetime to have this or any other such geometry, a position that I have evidence to deny, on the grounds that it is impossible to visualize such a geometry without using oversimplified geometrical models that depend on our own three-space-one-time dimensional experience. I contend that we know that space is more than three-dimensional, merely on the basis of the Lorentz-Fitzgerald contraction; we can observe anomalous effects on measured characteristics of moving objects that admit of no other explanation than that three-dimensional space is curved in a fourth dimension, and that fourth dimension is time. If there is another explanation of these effects, I am unaware of it. Let's examine precisely what I mean:

Suppose two objects are moving at the same velocity; that is, they appear motionless to one another. Now let us suppose that one object undergoes an acceleration such that it is moving away from the other. Next let us suppose that we are observing these two objects in a frame in which they are both moving originally in the same direction, which we will arbitrarily define as the "x" direction, at equal velocities, and that the acceleration results in the accelerated object having the same speed, but its velocity having a different direction, that is, a combination of movement in both the arbitrary "x" direction and in the rectilinear but other than that also arbitrary "y" direction.

Let's define the frames of these two objects such that their "x" (which we will call "x'," or "x-prime," for the first object's frame, and "x''", or "x-prime-prime," for the second object's frame) will correspond to the direction they are moving in our frame. Furthermore, both objects will have y' and y'' that is parallel to our own y. Now, what happens?

At the beginning, the direction of x, x', and x'' is the same. After the second object receives its acceleration, x and x' are still the same direction, but x'' is in a different direction; in our frame, and in that of the first object, x'' points in a direction that is intermediate between x (or x') and y (or y'). Now, in terms of the second object's speed in its own locally defined x, which we are calling x'', it is going the same speed as the first object; but in terms of our x, or the first object's x, which we call x', it now is going slower. Compensating for this, in terms of the first object's y, which we call y', or our own y, it now has a non-zero motion. In all three frames, the two objects are now moving apart; but in terms of the first object's x', and in terms of our x, it is moving slower in x, and faster in y. But what about from the second object's point of view? Is the first object moving slower, or faster, in x''?

Note that in fact, the second object sees the first as moving slower in x''. So both objects see the other as moving slower in x. And this is the result of a coordinate transform, of a type we call "rotation."

Not only that, but if the two objects were elongated along the direction of movement, and the second object were rotated along with its vector being rotated, then each object would observe the other to be shorter in x.

So, what do we see when an object is accelerated? We see that it is shorter, and we see that it moves more slowly in t, where t is the time dimension. And from the frame of that object, exactly the same thing happens to the unaccelerated object.

Finally, we see that the transform that is needed for this new type of rotation uses the same equations that the type we know about does; but it does not use it in the same geometrical environment. Because, you see, the geometry of space with respect to time is not circular; it is hyperbolic. So instead of using circular trigonometry to describe the effects of this rotation, as we do for a rotation in space, we have to use hyperbolic geometry to describe it; and hyperbolic geometry is very unusual in many ways. There are "angles" in hyperbolic geometry that cannot be considered to exist; there are no such angles in circular geometry. Rotation over an "angle" in hyperbolic geometry results in an apparent change in the size of the rotated object; this does not happen in circular geometry. As a result, we observe unambiguously that the relation of time to space implies that space is curved with respect to time, in a way that it is not curved with respect to itself; in other words, the three spatial dimensions are "flat" with respect to one another, but "curved" with respect to time. And this is an observable fact of our universe. We can measure it, and we cannot account for it in any other way.

With curvature as weird as this (not to mention as difficult, if not impossible, to visualize, as this) possible for the previously "obvious" geometry of space, along with obvious and inescapable observable consequences, I think it is impossible to maintain that curvature of space is a mathematical abstraction without real physical meaning.
This is going to take time (that I don't have at present) to digest. But thanks for the time and effort you have given.

[ynot]

IMHO, of course. YMMV. :D
OK - I'll bite, what does YMMV mean? (Your mind might vary?)

[Schneibster]

Your Mileage May Vary, IOW you might think that something that quacks like a duck, waddles like a duck, and looks like a duck is less than likely to be a duck.

[ynot]

Your Mileage May Vary, IOW you might think that something that quacks like a duck, waddles like a duck, and looks like a duck is less than likely to be a duck.
Thanks - I see you've stopped eating that dry biscuit (Mmmmfff) :D

[UserGoogol]

I think a nice way to picture curved space is to consider the classic arcade game Asteroids. Now, in Asteroids, if you move off screen, you appear on the other side. If you just shoot a straight line of bullets when there aren't any asteroids on screen, it wraps around the screen quite niftily. Now, it's not so hard to extrapolate this to 3D, simply replace the square of the screen with a cube, and have it so that if you ever move to one of the sides of the cube, you appear on the other side.

Now imagine that you are inside the game, sitting inside the spaceship. If you look off in the distance, you can see the back of your ship. Additionally, if you look to the left and the right, you can also see your spaceship. The effect is something like being in a square room where all the walls are mirrors.

I don't think that Physics thinks the universe is of this structure, (the technical term for this shape is a 3-torus, I believe) but I think that this is a good way to conceptualize a kind of curved spacetime without having the misconception that many people make when they hear people talking about curved spacetime, "curved in what?" The word curved is being used in somewhat of a technical sense in General Relativity; not referring to being shaped into a curly shape within some larger space (like the surface of the Earth in our 3D reality) but space itself exhibiting properties that differ from Euclidean geometry in ways that are analogous to curved surfaces in regular space.

[AgingYoung]

If you are going to steal other peoples work, you should cite them at least.

Common courtesy is to give a person credit for their work the first time you cite it. The second time you preface it with, 'I've heard it said...' . The third time you say, 'I have this fantastic idea!'

Gene

[69dodge]

As a result, we observe unambiguously that the relation of time to space implies that space is curved with respect to time, in a way that it is not curved with respect to itself; in other words, the three spatial dimensions are "flat" with respect to one another, but "curved" with respect to time. And this is an observable fact of our universe. We can measure it, and we cannot account for it in any other way.

With curvature as weird as this (not to mention as difficult, if not impossible, to visualize, as this) possible for the previously "obvious" geometry of space, along with obvious and inescapable observable consequences, I think it is impossible to maintain that curvature of space is a mathematical abstraction without real physical meaning.I guess this is just a matter of terminology, but I've always seen the geometry of special relativity described as flat---with a Minkowski metric rather than a Euclidean one, which admittedly is a big difference---but still flat. It's only in general relativity, which deals with gravity, that spacetime is curved.

[Schneibster]

I guess this is just a matter of terminology, but I've always seen the geometry of special relativity described as flat---with a Minkowski metric rather than a Euclidean one, which admittedly is a big difference---but still flat. It's only in general relativity, which deals with gravity, that spacetime is curved.If I understand correctly, Minkowskian spacetime is only a construct to help us understand the idea; the correct metric is Einsteinian, and that's what I'm describing. Most popular physics books use the Minkowski metric because it's supposed to be "easier to visualize;" I've always found it counter-intuitive, because my geometric sense has always told me that it was subtly wrong. I was never satisfied about this until I came across pieces that fit into the above explanation; I could "feel" the Minkowski recipe was wrong, but was never able to quite put my finger on why. Hyperbolic geometry, I suppose, is considered to be so difficult to understand that popular physics books just avoid dealing with it; I have not, however, found it so. Once one is already twisting space away from the Euclidean/Cartesian sort of flatness, it is of little moment (at least to my mind) to make it behave hyperbolically.

[Ben Tilly]

If I understand correctly, Minkowskian spacetime is only a construct to help us understand the idea; the correct metric is Einsteinian, and that's what I'm describing. Most popular physics books use the Minkowski metric because it's supposed to be "easier to visualize;" I've always found it counter-intuitive, because my geometric sense has always told me that it was subtly wrong. I was never satisfied about this until I came across pieces that fit into the above explanation; I could "feel" the Minkowski recipe was wrong, but was never able to quite put my finger on why. Hyperbolic geometry, I suppose, is considered to be so difficult to understand that popular physics books just avoid dealing with it; I have not, however, found it so. Once one is already twisting space away from the Euclidean/Cartesian sort of flatness, it is of little moment (at least to my mind) to make it behave hyperbolically.

You understand incorrectly. The Minkowski metric describes special relativity perfectly.

It does not immediately make all consequences obvious. But it is an accurately mathematical description of special relativity.

For general relativity one needs a different metric. Einstein's metric describes that. But locally that metric looks like the Minkowski metric.

Cheers,
Ben

[Schneibster]

Ahhh. Thank you for clarifying, Ben. But that brings a question: based on the fact that we can describe the Lorentz transform either using the widely-known formulae that utilize the root of one minus the velocity squared over the speed of light squared, or using hyperbolic trig functions in a manner that is not too surprisingly reminiscent of the manner we use circular trig functions to describe ordinary rotations, how can anyone be comfortable referring to Minkowski spacetime as "flat?"

[LordoftheLeftHand]

If the universe is infinite I don’t see that it would ever be possible to prove that it is. Obviously it would be possible to prove that it’s not infinite by proving that it’s finite. If it hasn’t been proven to be finite however, it should be assumed that it’s infinite (the default conclusion). As I don’t think it’s been proven to be finite, I must assume it’s infinite.

I do not see why an infinite universe would be the default conclusion. In my life I've never encountered an infinite amount of anything.

I'm not a scientist but a finite universe sounds very likely to me. Starting with a finite universe (around the time of the big bang) and injecting a certain amount of finite space since should produce a finite area. In my non-professional opinion a finite number + a finite number should = a finite number.

LLH

[Schneibster]

I do not see why an infinite universe would be the default conclusion. In my life I've never encountered an infinite amount of anything.See, here's the problem: if it's not infinite, where's the edge?

Now, in the case ynot makes, I suppose that there is some question as to whether we'd notice that we were looking at light from, say, here, X number of billions of years ago, but in that case- we'd see the same thing in every direction, unless the "size" of the universe were more than the distance we can see.

The other point to make here is that we can measure- or at least estimate- the curvature. In more than one way. And the best estimates we get say it's pretty close to zero; and that means it's pretty close to flat. Not only that, but the error bars all indicate that the curvature is negative, if it's not exactly zero. There's very little error bar on the positive side, and a lot on the negative. And if the curvature of the universe is zero, or negative, then the universe is infinite in either case. Only positive curvature yields a finite universe, unless you postulate an "edge."

So only by making gratuitous assumptions, like that the universe is just big enough that we can't see the same thing in all directions, or that there's an "edge" out there just beyond what we can see, do we wind up with a finite universe- and there is no evidence to support those assumptions. If we accept the evidence, and don't think that the place we are in the universe is somehow "special," then we wind up with an infinite universe. It's not just a guess.

[ynot]

I do not see why an infinite universe would be the default conclusion.
Default assumption would be a better term (I can't prove it so I can't conclude it).

In my life I've never encountered an infinite amount of anything.
Exactly, if infinity did exist it couldn't be encountered, experienced, observed or proved. Infinity can only be disproven. The calculation of Pi is assumed to be infinte, but how you infinitly test it to prove it.

I'm not a scientist but a finite universe sounds very likely to me. Starting with a finite universe (around the time of the big bang) and injecting a certain amount of finite space since should produce a finite area. In my non-professional opinion a finite number + a finite number should = a finite number.

LLH
Obviously nothing that's finite can become infinite. I'm one of those idiots that entertains the theory that perhaps the universe always has been infinite.

[Yllanes]

Exactly, if infinity did exist it couldn't be encountered, experienced, observed or proved. Infinity can only be disproven. The calculation of Pi is assumed to be infinte, but how you you infinitly test it to prove it.

The same mathematical axioms that allow us to define Pi allow us to prove its irrationality. The proof is a bit long but not hard and can be found in some elementary calculus books (a very nice example is Spivak's Calculus).

For the universe we have a theory, GR, which has had huge success. Assuming space is homogeneous and isotropic at large scales (experimentally true) we find that it can only be a 3 sphere, a 3 pseudosphere or a 3 plane (R^3). We can measure the curvature and decide between these possibilities. Our current measurements point at flat, with enough uncertainty that the other two are barely possible. Soon we will be able to decide.

Obviously nothing that's finite can become infinite. I'm one of those idiots that entertains the theory that perhaps the universe always has been infinite.
You are not an idiot for thinking that, you are right. If the universe is infinite now it has always been infinite (it has already been said in this thread that in the beginnings of time, only the visible universe was very small, not all the universe. Check this FAQ (http://www.astro.ucla.edu/~wright/infpoint.html)).


Ahhh. Thank you for clarifying, Ben. But that brings a question: based on the fact that we can describe the Lorentz transform either using the widely-known formulae that utilize the root of one minus the velocity squared over the speed of light squared, or using hyperbolic trig functions in a manner that is not too surprisingly reminiscent of the manner we use circular trig functions to describe ordinary rotations, how can anyone be comfortable referring to Minkowski spacetime as "flat?"

You can pass from a rest frame to a boosted one with hyperbolic rotations. You can also pass from one frame to a spatially rotated one with trigonometric rotations. The second sentence is also true in newtonian dynamics, yet I don't think you would say Euclidean space is not flat. The fact that rotations exist in a space does not mean that this space is curved. Curvature means that geodesics deviate, that the angles of a triangle do not sum 180º, that length:radius is not 2*pi. The surface of the Earth is curved (consider the triangle formed by the 0º meridian, the 90º meridian and the Equator: 270º in total). Yet locally it is flat, you look at a football field and do not see any curvature. In the same way spacetime is curved in general, but flat locally. Minkowski spacetime describes the neighbourhood of any point (except a singularity, of course) in the same way that Euclidean geometry describes the neighbourhood of any point on Earth.

I am afraid I don't have time for a lengthy or more convincing exaplanation of why Minkowski spacetime is flat. If you really are interested, I suggest that you read the first chapter (perhaps even the second one) of Misner, Thorne and Wheeler's Gravitation (the big black book that looks like a phone listing, I'm sure it has to be in most libraries). It is very easy to read, thoroughly explained and this chapters make use of very little mathematics, they are light reading. After that you will understand what curvature means in G, and many other nice stuff.

[ynot]

The same mathematical axioms that allow us to define Pi allow us to prove its irrationality. The proof is a bit long but not hard and can be found in some elementary calculus books (a very nice example is Spivak's Calculus).
Unfortunately (or fortunately) I'm one of those die-hard, sceptical people that can't accept math as being infallible. Still, by irrational I guess you also mean infinite? I can see a circle as being infinite in regards to a continuos motion, but not as a physical structure. Could curved-space change the properties of a circle so that Pi becomes rational?


ETA - Perhaps math is infallible, but our abilities to correctly use it aren't.

[Ben Tilly]

Ahhh. Thank you for clarifying, Ben. But that brings a question: based on the fact that we can describe the Lorentz transform either using the widely-known formulae that utilize the root of one minus the velocity squared over the speed of light squared, or using hyperbolic trig functions in a manner that is not too surprisingly reminiscent of the manner we use circular trig functions to describe ordinary rotations, how can anyone be comfortable referring to Minkowski spacetime as "flat?"

There are several answers to that. The first is that I'd never bothered to consider the question previously, Minkowski spacetime is just Euclidean geometry with a slightly odd (but uniform) metric, which is something I think of as flat. Interesting distortions at relativistic speeds, but I think of it as flat. It seems natural to me to assume that the universe is pretty much flat.

However a more technical answer is that Minkowski spacetime is flat because it has no curvature. A technical definition of curvature is a bit involved, but essentially if I go a small distance in a straight line, turn 90 degrees and go the same distance, turn another 90 degrees and go the same distance, then turn another 90 degrees and go the same distance again, I wind up precisely where I started. On a curved space, like the surface of a sphere, this is not true. In Minkowski space it is.

Cheers,
Ben

[Yllanes]

Unfortunately (or fortunately) I'm one of those die-hard, sceptical people that can't accept math as being infallible. Still, by irrational I guess you also mean infinite?
Irrational means that it has an infinite non-repeating decimal expansion, so yes.

Maths may fail, but if it does then the concept of infinite/finite sinks with it. If the concept of infinity makes sense, it can be proven that several things fit the definition. Things can be actual infinities, not only potential ones. Proving that pi is irrational does not involve calculating an infinity of digits, which is clearly impossible.


Could curved-space change the properties of a circle so that Pi becomes rational?


If you define Pi as the ratio length:diameter the answer is yes. With enough curvature it can be 3 or 4. Usually we define Pi as the limit of some series or as

$$
\pi := \int_{-1}^{1} \sqrt{1-x^2}\ \mathrm{d}x
$$

and say that in a curved space length:diameter is not Pi. For example, there is a theorem that says:

On a curved surface with curvature K, the relation between area or length and radius is (for small radius):[1]

\begin{align*}
L(r)&=2\pi r - \frac13 \pi K(\vec x_0) r^3 + \dots\\
A(r)&=\pi r^2-\frac{1}{12}Kr^4+\dots
\end{align*}

With K=0 we recover L = 2 pi r and A = pi r^2. So we don't actually say that pi changes, rather than the ratio length:diameter is not pi. If you defined pi' as L(r)/2r, there is a certain value of K that will make it 3.5, for example.

___
[1] Actually: Let alpha(t) be a parameterisation such that a(0)=a(2pi) and that the length r of the geodesics that join alpha(t) with some point x0 of a surface M be independent of the parameter t (in other words: a circumference). Then, for small r, the length of alpha and the area enclosed are:

[Ben Tilly]

See, here's the problem: if it's not infinite, where's the edge?

There need not be an edge. Think about an Asteriods game. It has finite extent but no edge. (Our view of it has an edge, but the physics is the same at that "edge" as it is anywhere else.)

Now, in the case ynot makes, I suppose that there is some question as to whether we'd notice that we were looking at light from, say, here, X number of billions of years ago, but in that case- we'd see the same thing in every direction, unless the "size" of the universe were more than the distance we can see.

There are geometries which are very hard to recognize from looking for obvious symmetries. In particular I've seen proposals for a horn-shaped universe where there would be no easy to recognize symmetries. See http://www.newscientist.com/article.ns?id=dn4879 for a popularization of one of these proposals.

The other point to make here is that we can measure- or at least estimate- the curvature. In more than one way. And the best estimates we get say it's pretty close to zero; and that means it's pretty close to flat. Not only that, but the error bars all indicate that the curvature is negative, if it's not exactly zero. There's very little error bar on the positive side, and a lot on the negative. And if the curvature of the universe is zero, or negative, then the universe is infinite in either case. Only positive curvature yields a finite universe, unless you postulate an "edge."

So only by making gratuitous assumptions, like that the universe is just big enough that we can't see the same thing in all directions, or that there's an "edge" out there just beyond what we can see, do we wind up with a finite universe- and there is no evidence to support those assumptions. If we accept the evidence, and don't think that the place we are in the universe is somehow "special," then we wind up with an infinite universe. It's not just a guess.

Sorry, but no. It is possible to have a finite universe with zero or negative curvature.

If you're having trouble visualizing how that is possible, just think of it as an infinite universe with repeating symmetry. Go far enough and it is just like you're back where you started. For a 2-dimensional flat example, you can think of a piece of wallpaper. For a 2-dimensional example with negative curvature, think of one of Escher's famous circle-limit drawings. (With the right metric, his circle limit drawings really are symmetries of hyperbolic space.)

As for why people have proposed this, the big one is that it is easier to explain why there seems to be a size limit to fluctuations in the geometry of the Universe in a finite universe than in an infinite one. As I've commented before, though, there is enough uncertainty about the actual laws of physics at the critical time that I'm not worried about our trouble in explaining what we see.

Cheers,
Ben

[Schneibster]

You can pass from a rest frame to a boosted one with hyperbolic rotations. You can also pass from one frame to a spatially rotated one with trigonometric rotations. The second sentence is also true in newtonian dynamics, yet I don't think you would say Euclidean space is not flat. The fact that rotations exist in a space does not mean that this space is curved.
However a more technical answer is that Minkowski spacetime is flat because it has no curvature. A technical definition of curvature is a bit involved, but essentially if I go a small distance in a straight line, turn 90 degrees and go the same distance, turn another 90 degrees and go the same distance, then turn another 90 degrees and go the same distance again, I wind up precisely where I started. On a curved space, like the surface of a sphere, this is not true. In Minkowski space it is.
I think you both missed my point. My point is not that rotations imply it is not flat; my point is that circular trig functions being the accurate description of rotations in space imply that space is flat, but hyperbolic trig functions being the accurate description of rotations in spacetime (i.e., where we talk about boosts, rapidities, etc.) imply that spacetime is not flat. You are aware, I am sure, that hyperbolic trig functions are not continuous as circular trig functions are; for example, although at some values of the argument that for circular functions we would call "angle," their value is real, there are other values of that argument for which their value is non-real. This in turn implies that there is no way to continuously rotate an object to the non-real "angle," without engaging in an infinite rotation, and it is this characteristic of spacetime (which the hyperbolic functions accurately model) that accounts for the speed-of-light limit.

It's probably also worth mentioning that in my opinion, the fact that there are actually two regions in which the argument is real, one of which is positive and one negative, may, in my humble opinion, account for the fact that there is antimatter; and the fact that it is not possible to continuously rotate from one "direction" to the other may, also in my humble opinion, account for the fact that we cannot "travel back in time," whatever the heck that might mean.

Yllanes gets into the more technical aspects of it. I'll address those as well.

Curvature means that geodesics deviate, that the angles of a triangle do not sum 180º, that length:radius is not 2*pi. OK, so if I have to use hyperbolic trig to describe spacetime, I'll guarantee you that the sum of the angles of a triangle is not 180º; in fact, the very definition of "triangle" doesn't look much like what we normally think of as a "triangle." So, am I wrong to think of this as "curvature?"

I am afraid I don't have time for a lengthy or more convincing exaplanation of why Minkowski spacetime is flat. If you really are interested, I suggest that you read the first chapter (perhaps even the second one) of Misner, Thorne and Wheeler's Gravitation (the big black book that looks like a phone listing, I'm sure it has to be in most libraries). It is very easy to read, thoroughly explained and this chapters make use of very little mathematics, they are light reading. After that you will understand what curvature means in G, and many other nice stuff.I own it, have read a fair bit of it, and my sense of it is that there is confusion between "flat space," and "flat spacetime." I can see why they would look at things that way, and I see why both of you do- do you see why I look at things the way I do?

Thank you both for an interesting conversation. I suspect we'll go on with this a bit. It might even be worth starting a thread for.

[Yllanes]

Thank you both for an interesting conversation. I suspect we'll go on with this a bit. It might even be worth starting a thread for.

Please do, if you are interested. If we want to continue this and understand one another I think we need a reboot.

[Schneibster]

Ben, fascinating material. I was misquoting some ideas I got from a Heinz Pagels book called Perfect Symmetry; IIRC, he stated that other topologies were possible, but considered less than likely by many. The book was published some time ago, rather before string physics became popular (though not, I think, before it got started), so his statements might be rather dated, and my restatement of them obviously was incomplete.

Those alternate topologies lead to some pretty fascinating ideas. Are you familiar with a novel (or was it a novella?) by Samuel Delaney in which he has several characters that go "around the universe" and wind up back where they started, in some manner associated with such an unusual topology? I cannot for the life of me recall what the name of it was.

[Yllanes]

Just to add that it may benefit you to pick up a Differential Geometry book, rather than a GR one. There are plenty of good ones with a profound physical motivation and language, but still rigorous and well written.

One of them is Schutz's Geometrical Methods of Mathematical Physics. It's short, goes to the point and gives you a very good understanding of differential geometry and its applications (not only in GR). Schutz is a very famous specialist in GR, so his book is specially good if you want geometry as a tool to understand that.

Another one is Frankel's The Geometry of Physics. I love this book. It has everything: classical mechanics, thermodynamics, particle physics, GR, etc. It begins with the basics of differential geometry, then goes on to some technical points and treats many applications. Some of the things this rather thick book includes cannot be seen in other books at this level. The language is again physical and not too formal. It does not tell any lie, however, and does things properly, it is only not formal compared to some of the books on differential geometry you can see around (if you don't believe me, pick up Helgason's...)

[Schneibster]

Thanks for the references, Yllanes- we'll see if I get motivated enough to start that thread.

[Yllanes]

Thanks for the references, Yllanes- we'll see if I get motivated enough to start that thread.

No rush... we can always restrict ourselves to commenting the first couple of chapters of Gravitation, if you have that book at hand.

[Ben Tilly]

It's probably also worth mentioning that in my opinion, the fact that there are actually two regions in which the argument is real, one of which is positive and one negative, may, in my humble opinion, account for the fact that there is antimatter; and the fact that it is not possible to continuously rotate from one "direction" to the other may, also in my humble opinion, account for the fact that we cannot "travel back in time," whatever the heck that might mean.

Your opinion on anti-matter is shared by at Richard Feynman, and his view that anti-matter is just regular matter moving backwards through time was an essential part of his work on quantum electrodynamics that earned him a Nobel in physics. Physicists don't generally think about things that way, but they all agree that mathematically it works out.

I own it, have read a fair bit of it, and my sense of it is that there is confusion between "flat space," and "flat spacetime." I can see why they would look at things that way, and I see why both of you do- do you see why I look at things the way I do?

I do see why you look at things that way. I don't have strong opinions either way, but it is easier for you to change your nomenclature than to convince the rest of the world to change theirs. So if you know that the rest of the world calls it "flat", then you should call it "flat" as well.

Thank you both for an interesting conversation. I suspect we'll go on with this a bit. It might even be worth starting a thread for.

If you do start the thread, please send me a private message. I often miss the start of new threads because most of the time I just look for responses in my subscribed threads.

Cheers,
Ben

[Schneibster]

Your opinion on anti-matter is shared by at Richard Feynman, and his view that anti-matter is just regular matter moving backwards through time was an essential part of his work on quantum electrodynamics that earned him a Nobel in physics. Physicists don't generally think about things that way, but they all agree that mathematically it works out.And to give credit where credit is due, I got it first from Vincent Icke, who attributed it to him, and then from QED, which was written by him.

I do see why you look at things that way. I don't have strong opinions either way, but it is easier for you to change your nomenclature than to convince the rest of the world to change theirs. So if you know that the rest of the world calls it "flat", then you should call it "flat" as well.I'm not sure the rest of the world really does. Like I said, space is pretty flat, although we are discussing the shape of its curvature here on this thread, that's as you (I think it was you) pointed out large-scale, not small-scale, and I have no quibble with calling that "flat." It's spacetime that I don't think is flat, and I have heard Einstein quoted as talking about space curvature, and come across some discussion of it in Relativity, and I think this might have been what he meant, because he specifically separated that from gravity. I think where I saw the quote was in The Elegant Universe, and if it was not, it was in one of the "twistor" guy's books (Roger something, I'll probably dig that out and read it again pretty soon). I should probably look the quotes up, and if I get stoked up and start that thread, I probably will, because I'll probably need them.

If you do start the thread, please send me a private message. I often miss the start of new threads because most of the time I just look for responses in my subscribed threads.

Cheers,
BenSure, I'll keep that in mind. It might not be for a couple of days.

[Ben Tilly]

I'm not sure the rest of the world really does. Like I said, space is pretty flat, although we are discussing the shape of its curvature here on this thread, that's as you (I think it was you) pointed out large-scale, not small-scale, and I have no quibble with calling that "flat." It's spacetime that I don't think is flat, and I have heard Einstein quoted as talking about space curvature, and come across some discussion of it in Relativity, and I think this might have been what he meant, because he specifically separated that from gravity. I think where I saw the quote was in The Elegant Universe, and if it was not, it was in one of the "twistor" guy's books (Roger something, I'll probably dig that out and read it again pretty soon). I should probably look the quotes up, and if I get stoked up and start that thread, I probably will, because I'll probably need them.

Well every reference that I can recall about the curvature of space has been tied to distortions in the metric caused by gravity in general relativity. You're the first person that I've heard who thinks of special relativity as showing curvature.

FWIW, my background is that I took enough physics in college to take a course on general relativity (most of which I've forgotten), and then in graduate school I took a bunch of differential geometry (most of which I've also forgotten). So at one point I knew quite a bit about this stuff. But that point was a while ago...

Cheers,
Ben

[Schneibster]

Now I'm gonna HAVE to hunt those quotes up. Good thing I enjoy reading!

[Schneibster]

Just a tantalizing little something to chew on:

First, I'm sure you both recall the equivalence principle of GRT. This principle states that gravity and acceleration are indistinguishable by any blind experiment.

Second, I'm sure you both are also familiar with the Lorentz symmetry. Now, I'm not entirely certain that you're familiar with the difference between a global and a local application of this symmetry. If you apply the Lorentz symmetry locally, which you must if you will obey the speed-of-light limitation, the result of a Lorentz transform must be gravity. Now, what if Lorentz rotation (in other words, acceleration) is used as a local symmetry?

:D

That's enough to tantalize. I'll start that new thread soon.

[LordoftheLeftHand]

I'm one of those idiots that entertains the theory that perhaps the universe always has been infinite.

Are you still promoting that silly "tired light" idea?

LLH

[Schneibster]

Are you still promoting that silly "tired light" idea?

LLHOh, thanks- I hadn't caught that. I certainly hope not.

[69dodge]

Your opinion on anti-matter is shared by at Richard Feynman, and his view that anti-matter is just regular matter moving backwards through time was an essential part of his work on quantum electrodynamics that earned him a Nobel in physics. Physicists don't generally think about things that way, but they all agree that mathematically it works out.I've certainly seen the phrase "moving backwards through time" before, but I still don't know what it means.

If an object "moves through space", this means that its position is a function of time, and we can define a direction of movement through space based on where it is at earlier and later times. But what does it mean for an object to "move through time"? If you look at its worldline in spacetime, can you tell which way it "moved through time"? Its worldine just is; where is there any movement at all?

[Yllanes]

If an object "moves through space", this means that its position is a function of time, and we can define a direction of movement through space based on where it is at earlier and later times. But what does it mean for an object to "move through time"? If you look at its worldline in spacetime, can you tell which way it "moved through time"? Its worldine just is; where is there any movement at all?

'Going backwards in time' means that you take the equations that describe some particle, change t -> -t and see what happens. The worldline is the same one the 'forwards in time' particle has, but is followed in the opposite direction. In other words, is like having a video of the motion of a normal particle and playing it backwards.

I've certainly seen the phrase "moving backwards through time" before, but I still don't know what it means.


It's just a pictoric way of describing antiparticles, it shouldn't be taken too far. In the first days of relativistic quantum mechanics, Dirac showed that the positron had to exist and the concept of antiparticle arose. In quantum mechanics, the time evolution operator is exp[- i H t], where H is the hamiltonian (energy). When the concept of antiparticles was introduced, it was seen that some operators related to particles were associated with the 'correct' time evolution, exp[-i H t], while their correspondent operators for antiparticles were associated with exp[i H t]. This motivated the idea that the time evolution of antiparticles is opposite to that of particles.

RQM, however, is not a consistent theory, there are issues with the conservation of probability. Within the next step, relativistc quantum fields or quantum field theory, it is easily proven that the time evolution of particles and antiparticles is actually the same and the one consistent with QM: exp[- i H t], so the picture of antiparticles going bacwards in time is inaccurate from this point of view. However, the description popularised by Feynman that the positron is some kind of 'time inverted' electron is a good way to understand several things. In Feynman diagrams (graphic tools to represent complicated integrals) arrows associated with particles point one way and arrows associated with antiparticles point the other way.

[ynot]

Are you still promoting that silly "tired light" idea?

LLH
You either have a good memory or you spend a lot of time dredging through past posts looking for negative ammunition. We should all be responsible for our past, so I guess its OK. I never "promoted" the "tired light" idea. I suggested the idea of "degraded light" as one of several brainstorming ideas. I merely suggested that perhaps the immense distances that light travels before we receive it, may have something to do with the observed red-shift. I don't know this, I can't prove this and I don't promote this. It was just an idea, however "silly". Don't know why you (and some others) have such an "if you're not with us, you're against us" approach.

[Schneibster]

I think I can explain, ynot.

"Tired light" is a hypothesis developed by Young Earth Creationists to explain how the universe could be only 4,000 (or whatever that weird figure some monk or something in like the 16th century figured out from a chronology of the Bible is supposed to be) years old. From your response I conclude that you developed this hypothesis on your own (and by the way, it's not entirely unreasonable) without being aware of others who had developed it. It's actually one that a lot of people who think about these things come up with, and then discard in the face of the evidence against it.

Another noteworthy thing about YECs is they generally don't change their opinions, and since it's obvious you have changed yours, I'd say that's the end of that digression.

[Schneibster]

'Going backwards in time' means that you take the equations that describe some particle, change t -> -t and see what happens. The worldline is the same one the 'forwards in time' particle has, but is followed in the opposite direction. In other words, is like having a video of the motion of a normal particle and playing it backwards.Well, actually, it turns out there's more to it than that.

One of the important concepts that has come out in physics is the concept of a "symmetry." It means pretty much what you'd expect; it describes some property of things that doesn't change under a rotation, the way that (for example) a symmetric vase seems to have the same shape no matter how you turn it, around its axis of symmetry.

But the symmetries physicists talk about are much deeper. For example, physicists speak of the "symmetry of physical results over spatial rotation." What they mean is, if you do an experiment, and turn it, and do it again, you'll get the same results (at least in flat spacetime, absent any gravity fields, or electric fields, or pieces of matter that might get in the way). And one of the important symmetries is the symmetry of results over time. What that means is, if you do the experiment today, and do it again tomorrow, you'll get the same results (again, with those same caveats).

Now, it turns out that there is more to this time symmetry. There is also a symmetry of results over time direction, also known as "time-reversal symmetry." And this symmetry is very deeply embedded in physics; Newtonian physics, and the Hamiltonian and Lagrangian that spring from it, and even a great deal of quantum mechanics, is time-reversal symmetric. It turns out that gravity and electromagnetism, and the color (AKA strong) force as well (as far as we can tell) are all time-reversal symmetric; there is only one force that is not, and that is the weak nuclear force. But this asymmetry shows up only under very particular conditions.

From some pretty esoteric mathematical considerations, we know that each symmetry is associated with a conserved quantity. For example, the symmetry over space (results are the same from place to place), we know that momentum is conserved; from the symmetry over time location, we know that energy is conserved. The person who proved this was a physical mathematician named Emmy Noether, and since it is a mathematical proof, a "theorem," it is called "Noether's Theorem." Another important point to understand about the symmetries involved is that they are only continuous symmetries; that is, a symmetry that can involve continuous rotations. And if you've been paying attention, you'll note that while the time location symmetry is continuous, the time reversal symmetry is not; it is "discrete," in that there are only two directions in time, although there are an infinity of locations arbitrarily close to one another. So the time reversal symmetry is not a continuous symmetry, and is not associated (directly) with a conservation law.

Now, from relativity, we know that there is a symmetry called the Lorentz symmetry. But this symmetry is rather different from the others; it imposes a curious sort of symmetry over velocity, but only in certain very special ways. To understand precisely how, you need to understand a bit more about special relativity.

The basic idea here is that you can define a quantity that works the same way as distance works in space, over spacetime. This quantity is called the "interval," and just as the space distance follows the Pythagorean formula for finding distance, d² = x² + y² + z², the spacetime interval follows a prescription as well, the Minkowski formula, s² = x² + y² + z² - c²t², where d is the space distance, s is the spacetime interval, x, y, and z are the standard spatial dimensional distance components, t is the time component, and c is the speed of light. The Lorentz symmetry asserts that the interval remains constant over spacetime rotations. As I discussed earlier, a spacetime rotation is a change in velocity; to distinguish this from an acceleration, physicists call this type of rotation a "Lorentz boost." Now, note that the Lorentz symmetry is a continuous symmetry; therefore, it should be associated with a conserved quantity under Noether's Theorem. What is this conserved quantity?

It turns out that the conserved quantity is a combination of three quantities: charge, parity, and time direction. This conservation is often, confusingly, called "CPT symmetry." Before I go on, I should explain what is meant by "parity." Parity is a property of mirror imaging; in other words, the difference between an object and its mirror image is a difference in parity. What this means is that parity only applies in situations where something can be distinguished from its mirror image. And again, if you've been paying attention, you'll have noticed that both charge and parity are discrete quantities, just like time. So, basically what we're saying here is that charge, parity, and time direction are jointly conserved; what that means is that if one of these changes, and the other two change with it, then CPT is conserved; but if one of these changes and one or both of the others don't, then CPT conservation is violated.

OK, so what does this have to do with using time-reversed particles as antiparticles? Well, what precisely is an antiparticle? At the time Dirac proposed them, physicists thought they only had charge reversal; in other words, the proton was the antiparticle of the electron. But subtle consideration of Dirac's work showed that this could not be the case, because the mass of the antiparticle had to be the same as the mass of the particle. So that meant an "anti-electron." Not long after this, a particle physicist actually found an anti-electron; Dirac's theory was proven, and he won a Nobel Prize. But there's more to an anti-particle than just charge reversal and identical mass; looking into things, we find that we have this Lorentz symmetry, and it turns out that this symmetry is also a property of Dirac's theory. And that, as you'll no doubt see, means that the reversal cannot be of charge alone; it must also be of time direction and parity, for the Lorentz symmetry to be preserved. And when physicists were able to measure parity, which turned out to be possible by observing the direction that electrons emerged from neutron decays when the neutrons were all lined up by a magnetic field and kept very cold so that they wouldn't move around and destroy the ability of the experiment to observe their parity, it turned out that neutrons did have parity, and not only that, but antineutrons had the opposite parity. The only one left is time, and we cannot measure direction in time; but given proof of charge reversal, and proof of parity reversal, it's difficult to deny it.

This is what Feynman said. And although many physicists (like Yllanes, for example- although s/he has not said so, from the knowledge s/he displays, I would guess that s/he is at least a very, very serious student of physics, so if I compliment hir, I don't feel nervous doing so) believe that Feynman was crazy to maintain this, there are others, primarily those who do a lot of work with relativity, who think he was at least looking at something important, and possibly was completely right.

Now, Lorentz symmetry is a property of special relativity. And special relativity is a property of the Standard Model of particle physics. So what that means is that CPT conservation is also a property of the Standard Model. So this conservation, and this symmetry, and this interpretation of antimatter, must necessarily follow. Basically, in other words, you can interpret a particular world line as an antiparticle moving forward in time (whatever that means), or a particle moving backward in time (again, whatever that means). And similarly with a particle moving forward; it can also be interpreted as an antiparticle moving backward. And as for whether time can have a direction, there can be little question, in view of two obvious facts:

1. Time-direction conservation is an integral part of the conservation law that follows from Lorentz symmetry by Noether's theorem. Without it, you have only CP conservation, and this is mathematically inconsistent.
2. As can be seen from the fact that the well-known algebraic form of the Lorentz transformation can be restated using hyperbolic trigonometric functions, it is obvious that space is hyperbolically symmetric around the time dimension; but hyperbolic trig implies two distinguishable directions that have real number roots, one positive and one negative.

THIS is why I say what I do. The evidence is clear and fairly compelling. Without the possibility for time-reversal, and thus without any meaning for the phrase, "moving backward in time," we face violation of Lorentz symmetry, repudiation of the Special Theory of Relativity and questions about the General Theory that stem from that, particularly because Lorentz symmetry is a local symmetry under GRT, and we run into all sorts of trouble, predicting things that we simply do not see.

But there is more yet to the story. Now I will discuss details that Yllanes is also almost certainly aware of, that go beyond this, which may tend to at least indicate that there is more to the picture than I have told.

It turns out that there is CPT violation. It's observable in two interactions: the decay of the K-meson, and the decay of the B-meson. The details are extremely esoteric, and require a heck of a lot of particle physics, but the facts are undeniable. Now, these interactions are weak force interactions. And it turns out that there are other weak interactions that violate CPT conservation. For example, there is a magnetic current interaction with electrons that can only happen under very special circumstances that shows T-reversal symmetry violation. And there is reason to believe that these asymmetries are the result of the symmetry breaking between the weak and electromagnetic forces. Furthermore, it also turns out that these asymmetries may be responsible for the fact that our universe is matter-dominated. And finally, this symmetry breaking may be responsible, through the Higgs boson, for mass in our universe. How these things will play out over the next several years and decades will be very interesting indeed; the LHC (Large Hadron Collider, a new particle accelerator that is pretty much all built and is being tuned up at CERN in Switzerland) is expected to potentially produce the Higgs boson, and there are a considerable number of other things that we might find out when experiments using it begin. That is scheduled for next year. Now, note that starting with CPT violation, technically, we are talking about Lorentz violation; and that means, since the Standard Model is based on relativity, that we are beyond the Standard Model. Some physicists don't see it that way; I am on the fence (although I am no physicist). And I'll be very interested to see what happens.

For certain, whatever we see, it will be very small, very fast, or both; it may violate SR over very short distances and/or very short times. That appears to be what we have found so far.

Before I move on, I'm going to digress just a bit; I left a dangling tail back there where I was talking about the Pythagorean and Minkowski formulae.

You will have noted that there is a big difference between the two formulae. The Pythagorean formula uses only additions; but the Minkowski formula uses a subtraction, and furthermore, it multiplies the negative term by the speed of light. It is this that makes the geometry of spacetime hyperbolic. If that term were positive, then spacetime would be circularly symmetric; of course, if that were the case, the speed of light would be infinite. Worse yet, the speed at which time passes would therefore also be infinite; and this would be approximately equivalent to there being no time, or to all times being indistinguishable. If this were the case in our universe, it is entirely possible that life as we know it could not exist. Why this is the case is one of the great unsolved riddles of physics, albeit one that you don't hear mentioned much because thinking about it makes most peoples' heads spin.

It's just a pictoric way of describing antiparticles, it shouldn't be taken too far. See, I don't buy this; I hear it a lot, but Lorentz symmetry says I'm not "taking it too far," and neither was Feynman. I'd go a heck of a long way before I'd say someone who won a Nobel Prize didn't know what they were talking about. But maybe that's just me. And Yllanes does present a strong case:

In the first days of relativistic quantum mechanics, Dirac showed that the positron had to exist and the concept of antiparticle arose. In quantum mechanics, the time evolution operator is exp[- i H t], where H is the hamiltonian (energy). When the concept of antiparticles was introduced, it was seen that some operators related to particles were associated with the 'correct' time evolution, exp[-i H t], while their correspondent operators for antiparticles were associated with exp[i H t]. This motivated the idea that the time evolution of antiparticles is opposite to that of particles.

RQM, however, is not a consistent theory, there are issues with the conservation of probability. Within the next step, relativistc quantum fields or quantum field theory, it is easily proven that the time evolution of particles and antiparticles is actually the same and the one consistent with QM: exp[- i H t], so the picture of antiparticles going bacwards in time is inaccurate from this point of view. However, the description popularised by Feynman that the positron is some kind of 'time inverted' electron is a good way to understand several things. In Feynman diagrams (graphic tools to represent complicated integrals) arrows associated with particles point one way and arrows associated with antiparticles point the other way.Now, there is something more to be understood here. Remember, what Feynman said is, "you can interpret this worldline as either an antiparticle going forward in time, or a particle going 'backward in time,' whatever that means." So really all that those equations prove is that the first part of what Feynman said is right; they don't prove that the second part is wrong. They just appear to make it unnecessary. Not only that, but relativity is an integral part of the Standard Model, and also an integral part of CPT symmetry, which (other than for the weak interactions), appears to be a manifest symmetry of physics. I think and have long thought that there is some "missing piece" in QFT, and I am not alone in that thought. That thought is part of the raison d'etre of string physics (which some call string "theory," it is a theory only in the mathematical sense at this time IMHO, not the scientific sense, since it is not yet falsifiable- nevertheless, it appears to be a valid physics, just one we cannot currently connect to the physics we actually observe around us). Another, and in many eyes more important, part of that reason for existence is that gravity is specifically excluded from the Standard Model; we have no quantum theory of gravity, only a field theory, and it is the only force for which this is true. The reasons for this get into areas that are WELL beyond the scope of this thread (not that quite a bit of this post isn't already- sorry). But that's how I see things, anyway.

[Schneibster]

Oh, by the way, I looked through The Force of Symmetry and Relativity for the curvature reference I was talking about; I haven't found it so far. I'm narrowing down on The Elegant Universe and The Fabric of the Cosmos, but haven't quite finished looking at Relativity yet, though I'm now certain it's not in The Force of Symmetry.

Meanwhile, I also read the first chapter of Gravity, but it didn't tell me much I hadn't already seen; Yllanes, I think you might be misinterpreting what I'm talking about. Perhaps the previous long post will help clear things up.

ETA: I also misstated something earlier. No, with this "curvature of spacetime" thing, I'm not talking about GRT. I'm talking about SRT. That is probably already clear from the long post, but I wanted to be explicit about it.

[Yllanes]

One of the important concepts that has come out in physics is the concept of a "symmetry."
The most important concept in my opinion.


This is what Feynman said. And although many physicists (like Yllanes, for example- although s/he has not said so, from the knowledge s/he displays, I would guess that s/he is at least a very, very serious student of physics, so if I compliment hir, I don't feel nervous doing so) believe that Feynman was crazy to maintain this,

No, no, no, no, I don't think he was crazy... Far from it (I'm a he by the way). To pass from an equation/term describing particles to another describing antiparticles you perform CPT inversion. This is completely true and nothing wrong with it. My post was crippled because I was having a lot of problems trying to connect to the forum, or post a reply once here. It seemed to have worked when I had a mutilated version on my screen... Anyway, the result was a mess.

You explained it very well and thoroughly, so I won't. The point with 'taking it too far' is about the actual sentence 'moving backwards in time', which can be misunderstood. Positrons don't travel back in time, they have the same time evolution as electrons. In the early days of RQM this was not realised and they had some exp[i H t] terms playing havoc with probability currents...


Basically, in other words, you can interpret a particular world line as an antiparticle moving forward in time (whatever that means), or a particle moving backward in time (again, whatever that means).

This is what I should have said and what Feynman meant, of course. An antiparticle going forwards in time looks like a particle going backwards. This is not the same as saying antiparticles themselves go backwards.


Meanwhile, I also read the first chapter of Gravity, but it didn't tell me much I hadn't already seen; Yllanes, I think you might be misinterpreting what I'm talking about. Perhaps the previous long post will help clear things up.

Probably. I think what you mean is correct, only not the usual way to look at the problem.

[Schneibster]

The most important concept in my opinion.I won't disagree; there's an excellent argument that favors that interpretation. ;)

No, no, no, no, I don't think he was crazy... Far from it. To pass from an equation/term describing particles to another describing antiparticles you perform CPT inversion. This is completely true and nothing wrong with it. My post was crippled because I was having a lot of problems trying to connect to the forum, or post a reply once here. It seemed to have worked when I had a mutilated version on my screen... Anyway, the result was a mess.Heh, they've had a lot of database problems recently apparently. I had trouble last night and today, and to top it all off my connection is going up-n-down due to a local windstorm. Thanks for clearing it up.

(I'm a he by the way)I try not to insult by assuming. So am I (male), BTW.

You explained it very well and thoroughly, so I won't. The point with 'taking it too far' is about the actual sentence 'moving backwards in time', which can be misunderstood. Absolutely. I'm careful to qualify it, and put quotes around it, and a lot of other stuff, and it still gets misinterpreted a lot. It's also very difficult to think about, and therefore easy to make a mistake when you're explaining it.

Positrons don't travel back in time, they have the same time evolution as electrons. In the early days of RQM this was not realised and they had some exp[i H t] terms playing havoc with probability currents...I'd put it that it is equally valid to interpret a worldline as a particle moving forward in time, or an antiparticle moving backward in time, whatever those mean (I almost want to say "thisaway" and "thataway" rather than characterize these "directions" which we cannot directly measure as "forward" or "backward," implying that our viewpoint has some sort of absolute meaning); part of what I'm arguing here is that although there is no absolute gauge, there is a preference in our universe for matter, and therefore a broken symmetry between the two directions- but that's not for this thread. I'm getting stoked, and probably will start the new thread very soon (especially since I can't work with all these power outages).

This is what I should have said and what Feynman meant, of course. An antiparticle going forwards in time looks like a particle going backwards. This is not the same as saying antiparticles themselves go backwards.Right. It is, however, a matter of "fixing a gauge" to choose one direction in time as "forward," and once you do so, you have decided for each worldline you evaluate whether you will see that worldline as matter or antimatter, except in the case of particles like the photon which are their own antiparticle. This gauge fixing also determines, of course, which charge and parity you will see the worldlines as having, which is equivalent to whether you will see them as matter or antimatter.

Probably. I think what you mean is correct, only not the usual way to look at the problem.Yes, I know it isn't. It leads to some interesting speculations, too, and we'll go there. Maybe I'm crazy; maybe I'm just unusual in my interpretation; or maybe I'm wrong. Or perhaps even there's no way to find out which. It'll be interesting, though, however it comes out.

[Pragmatist]

It turns out that there is CPT violation. It's observable in two interactions: the decay of the K-meson, and the decay of the B-meson.

This is wrong, unless there's some very recent result I'm unaware of. The neutral kaon decay exhibits CP violation and as far as I'm aware, although there is strong evidence for CP violation in B-meson decay, it hasn't been absolutely confirmed (but I'm probably out of date on the latter). In either case however I'm not aware of any proven CPT violation to date.

[Schneibster]

Terminology. This is what I meant when I said that referring to it as CPT symmetry is confusing.

CP violation means Lorentz symmetry violation. CPT symmetry is often used as a synonym for Lorentz symmetry as expressed in particle physics. Technically, you are correct- the violation involved is one of charge and parity, not one of time-reversal. However, you apparently also missed that weak interactions involved in the magnetic moment of electrons in cryogenic research (I didn't originally give that much detail, but that's what's involved) show T-reversal violation; and it is undeniable that all three violations (kaon, beon, and weak/magnetic) involve the weak nuclear force. Thus, we can see that weak interactions violate Lorentz symmetry's complementary conservation law- CPT conservation. As I said, CPT is conserved as long as all three change together- if one or two change, but the other(s) do not, CPT conservation is violated, and this is the technically correct way to speak of it.

I believe the beon decay CPT conservation violation has been confirmed to six sigma at SLAC, using their B-factory, but I could be wrong- could have misread a prediction that it would be by some date that is still in the future, or they could have found a problem in the data, or something like that.

[Pragmatist]

Terminology. This is what I meant when I said that referring to it as CPT symmetry is confusing.

CP violation means Lorentz symmetry violation. CPT symmetry is often used as a synonym for Lorentz symmetry as expressed in particle physics. Technically, you are correct- the violation involved is one of charge and parity, not one of time-reversal. However, you apparently also missed that weak interactions involved in the magnetic moment of electrons in cryogenic research (I didn't originally give that much detail, but that's what's involved) show T-reversal violation; and it is undeniable that all three violations (kaon, beon, and weak/magnetic) involve the weak nuclear force. Thus, we can see that weak interactions violate Lorentz symmetry's complementary conservation law- CPT conservation. As I said, CPT is conserved as long as all three change together- if one or two change, but the other(s) do not, CPT conservation is violated, and this is the technically correct way to speak of it.

I believe the beon decay CPT conservation violation has been confirmed to six sigma at SLAC, using their B-factory, but I could be wrong- could have misread a prediction that it would be by some date that is still in the future, or they could have found a problem in the data, or something like that.

No, I still disagree, it's not just a matter of terminology. Firstly a CP (as opposed to a CPT) violation does not imply a Lorentz symmetry violation - period.

As for CPT, a Lorentz transformation necessarily is CPT invariant and a CPT violation would lead necessarily to a Lorentz violation in local field theories. However the reverse is not true. A Lorentz violation does not necessarily imply a CPT violation, so the situation is not that simple. Although some people seem to informally use CPT as a synonym for Lorentz symmetry, it's obvious that it is not.

Violations of any individual or combination of C, P and T have been observed but it is fundamental to just about all of current physics that CPT are not violated simultaneously. A CPT violation wouldn't just break Lorentz symmetry, it would break Quantum Electrodynamics and Quantum field theory, not to mention the Standard Model itself as well as SR and GR, in fact, there's very little it wouldn't break!

CPT violation has a special and specific meaning. It is absolutely not correct to say that a CP violation and a separate T violation is equivalent to a CPT violation because it simply isn't, neither in terminology nor reality. No CPT violations have ever been observed to date, and if one were, it would be earth shattering news for all of physics because it would undermine most current physical theories.

It is also worth mentioning that C symmetry isn't just charge reversal it is a conjugation of all internal quantum numbers of a particle. And parity is not the same as a mirror image, parity is a complete reversal of all spacial dimensions, whereas a mirror image is only a reversal of 2 dimensions (in R3).

As for the beons, I checked and it appears that Belle at KEK are claiming 99.9% certainty of CP violation in beon decay, but they say they won't be 100% certain until they do some new experiments in 2007 (anything to up the research budget! :D). But I think we can take it as given that beons do exhibit CP violation.

By the way, here is an up to date summary of the state of play in conservation law tests: http://pdg.lbl.gov/2006/tables/conlaw.pdf

[Almo]

I think a nice way to picture curved space is to consider the classic arcade game Asteroids. Now, in Asteroids, if you move off screen, you appear on the other side. If you just shoot a straight line of bullets when there aren't any asteroids on screen, it wraps around the screen quite niftily. Now, it's not so hard to extrapolate this to 3D, simply replace the square of the screen with a cube, and have it so that if you ever move to one of the sides of the cube, you appear on the other side.

Actually, Asteroids functions as a torus. :duck:

[Schneibster]

No, I still disagree, it's not just a matter of terminology. Firstly a CP (as opposed to a CPT) violation does not imply a Lorentz symmetry violation - period. Dang it, you're right. It's been a while since I went into this stuff- a year or more.

CPT reversal symmetry is an exact symmetry, preserved in all interactions, and I got it backwards. CPT symmetry is preserved if we observe violations of any one of charge reversal, parity reversal, or time reversal symmetry; but violation of two of them implies violation of the third, because otherwise CPT symmetry would be violated. Thus, the neutral kaon and beon decays imply violation of time reversal symmetry, because they show violation of CP reversal symmetry. This is necessary to preserve CPT reversal symmetry.

In addition, I was wrong about the conservation law associated with the Lorentz symmetry. It is a complicated quantity involving the center of mass of the object being rotated. It actually breaks down into four symmetries and four associated conservation laws, one for each of x, y, z, and t.

There is no conservation law associated with any of C, P, T, or any combination because they are all discrete symmetries.

As for CPT, a Lorentz transformation necessarily is CPT invariant and a CPT violation would lead necessarily to a Lorentz violation in local field theories. However the reverse is not true. A Lorentz violation does not necessarily imply a CPT violation, so the situation is not that simple. Although some people seem to informally use CPT as a synonym for Lorentz symmetry, it's obvious that it is not.This also is correct. Lorentz symmetry along with other considerations results in CPT reversal symmetry, and a violation of CPT reversal symmetry would necessarily involve a violation of Lorentz symmetry, but there are other possible violations of Lorentz symmetry that would not require a violation of CPT reversal symmetry. For example, if we got different results in some experiment after a Lorentz boost and could thus violate the principle of relativity by performing some experiment that could tell us our absolute velocity, that would be a violation of the Lorentz symmetry that would not necessarily involve a CPT violation.

Violations of any individual or combination of C, P and T have been observed but it is fundamental to just about all of current physics that CPT are not violated simultaneously. A CPT violation wouldn't just break Lorentz symmetry, it would break Quantum Electrodynamics and Quantum field theory, not to mention the Standard Model itself as well as SR and GR, in fact, there's very little it wouldn't break!Hmmmm. Well, I think the situation is more complicated than that. In the Wikipedia article on CP violation, it says that violation of the CP symmetry implies violation of T symmetry. Based on what you say, I'm not sure how to interpret that. It sounds like if CP is violated in an interaction, then T must be violated in that interaction as well in order to preserve overall CPT symmetry. Have I got that right?

CPT violation has a special and specific meaning. It is absolutely not correct to say that a CP violation and a separate T violation is equivalent to a CPT violation because it simply isn't, neither in terminology nor reality. No CPT violations have ever been observed to date, and if one were, it would be earth shattering news for all of physics because it would undermine most current physical theories.I'm guessing this means that the answer to my question above is "yes."

It is also worth mentioning that C symmetry isn't just charge reversal it is a conjugation of all internal quantum numbers of a particle. And parity is not the same as a mirror image, parity is a complete reversal of all spacial dimensions, whereas a mirror image is only a reversal of 2 dimensions (in R3).Yes, I understood this about parity- but I'm pretty sure not many other people will understand the distinction. As far as the charge part goes, yes, I understood that as well, and again, I'm not sure that many others will- and I'll also point out that antimatter is both C and P reversed from matter. In other words, the internal quantum numbers and the spatial characteristics of an antiparticle are reversed from those of its corresponding particle. In the Wikipedia article on antiparticle, it says: "Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation (C), parity (P), and time reversal (T)." So I think that this means that all three are literally reversed for an antiparticle- and that means that antiparticles have -t instead of t. Whether this means that they are "moving backward in time" or not is unclear; particularly since it's unclear what "moving backward in time" might mean. But if the sense of t must be reversed, that does pretty unambiguously imply that if one fixes some gauge on the t dimension in order to call a particle "matter," that that gauge is opposite for that particle's antiparticle. If one wished to refer to that gauge as "forward in time," or "the future," then one would refer to the opposite gauge as "backward in time" or "the past." What this means in practical terms is nothing, because we do not know of a rotation that can change t into -t; we cannot make rotations that are not continuous, and any attempt to rotate continuously so that t becomes -t results in a non-permitted (i.e. non-real-number) degree of rotation in one or more of the x-t, y-t, z-t planes. In other words, acceleration not merely to the speed of light, but to infinity, a meaningless concept.

As for the beons, I checked and it appears that Belle at KEK are claiming 99.9% certainty of CP violation in beon decay, but they say they won't be 100% certain until they do some new experiments in 2007 (anything to up the research budget! :D). But I think we can take it as given that beons do exhibit CP violation.Thanks for looking this up.

By the way, here is an up to date summary of the state of play in conservation law tests: http://pdg.lbl.gov/2006/tables/conlaw.pdfAnd thanks for this also.

And finally, thanks for taking the time to clear all of this up.

[Pragmatist]

I'm going to rearrange your quotes a bit so I can answer in context, because there is a common error in your first and third response, and it'll be easier to answer those together.

This also is correct. Lorentz symmetry along with other considerations results in CPT reversal symmetry, and a violation of CPT reversal symmetry would necessarily involve a violation of Lorentz symmetry, but there are other possible violations of Lorentz symmetry that would not require a violation of CPT reversal symmetry. For example, if we got different results in some experiment after a Lorentz boost and could thus violate the principle of relativity by performing some experiment that could tell us our absolute velocity, that would be a violation of the Lorentz symmetry that would not necessarily involve a CPT violation.

Yes, this is correct.

Dang it, you're right. It's been a while since I went into this stuff- a year or more.

CPT reversal symmetry is an exact symmetry, preserved in all interactions, and I got it backwards. CPT symmetry is preserved if we observe violations of any one of charge reversal, parity reversal, or time reversal symmetry; but violation of two of them implies violation of the third, because otherwise CPT symmetry would be violated. Thus, the neutral kaon and beon decays imply violation of time reversal symmetry, because they show violation of CP reversal symmetry. This is necessary to preserve CPT reversal symmetry.

In addition, I was wrong about the conservation law associated with the Lorentz symmetry. It is a complicated quantity involving the center of mass of the object being rotated. It actually breaks down into four symmetries and four associated conservation laws, one for each of x, y, z, and t.

There is no conservation law associated with any of C, P, T, or any combination because they are all discrete symmetries.

Hmmmm. Well, I think the situation is more complicated than that. In the Wikipedia article on CP violation, it says that violation of the CP symmetry implies violation of T symmetry. Based on what you say, I'm not sure how to interpret that. It sounds like if CP is violated in an interaction, then T must be violated in that interaction as well in order to preserve overall CPT symmetry. Have I got that right?

I'm guessing this means that the answer to my question above is "yes."

Ah, I see where the error is now. You misunderstood something in the article. A CP violation does not imply a T violation, a CP violation can be considered equivalent to a T violation. Think of it this way: any symmetry operation represents a violation if there is a change in the net (total) symmetry after whatever process is being considered. So the aim of any conservation law is to make the net change in symmetry zero. Now, if CP is equivalent to T, and CP becomes not CP (i.e. if there is a violation) then "not CP" is equivalent to "not T". In which case the net result for CPT conservation is the product "not T" . T which is zero. T doesn't change, so no T violation is implied.

I also wouldn't rely on Wikipedia for critical information, I've found lots of errors in it in the past and it's quite unreliable IMO. There are plenty of other reliable sites like Hyperphysics for example. The article you linked to for example makes the mistake of saying that parity is just a mirror image which is obviously wrong.

Yes, I understood this about parity- but I'm pretty sure not many other people will understand the distinction. As far as the charge part goes, yes, I understood that as well, and again, I'm not sure that many others will- and I'll also point out that antimatter is both C and P reversed from matter. In other words, the internal quantum numbers and the spatial characteristics of an antiparticle are reversed from those of its corresponding particle. In the Wikipedia article on antiparticle, it says: "Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation (C), parity (P), and time reversal (T)." So I think that this means that all three are literally reversed for an antiparticle- and that means that antiparticles have -t instead of t. Whether this means that they are "moving backward in time" or not is unclear; particularly since it's unclear what "moving backward in time" might mean. But if the sense of t must be reversed, that does pretty unambiguously imply that if one fixes some gauge on the t dimension in order to call a particle "matter," that that gauge is opposite for that particle's antiparticle. If one wished to refer to that gauge as "forward in time," or "the future," then one would refer to the opposite gauge as "backward in time" or "the past." What this means in practical terms is nothing, because we do not know of a rotation that can change t into -t; we cannot make rotations that are not continuous, and any attempt to rotate continuously so that t becomes -t results in a non-permitted (i.e. non-real-number) degree of rotation in one or more of the x-t, y-t, z-t planes. In other words, acceleration not merely to the speed of light, but to infinity, a meaningless concept.

Well, the parity distinction is easy to explain, just think of a mirror image that is also upside down. The definition of an antiparticle only requires that it be charge conjugated, not necessarily that there is also a parity violation or a time reversal. Of course in actual anti-particle production there may be parity reversals depending on the process but it isn't a necessary condition.

Lots of people (even a few physicists!) seem to be confused about all this. The antiparticle prediction arises from Dirac's electron theory which gave two solutions for the electron, one involving normal energy and the other with "negative energy" states. Now, these negative energy states seemed to offend the sensibilities of many physicists so they sought explanations in which they could avoid the concept of things like "antimass". In order to straighten out the calculations, the concepts of negative energy and antimass were rejected and the mass (and energy) of antiparticles were defined as positive real quantities. Vectors that depended on mass (like momentum) could be negative because the direction could be reversed, but it was more problematic for scalars like energy. In the end, the only way to make these quantities come out positive whilst not destroying the integrity of the antiparticle solutions was to reverse the arrow of time. But it's important to realise that this doesn't necessarily imply actual motion backwards in time, it's just a mathematical device.

So an antiparticle travelling forward in time has negative energy, "antimass" and follows a normal forward time evolution. In order to treat it as though it were a normal particle, with positive energy and mass etc., it has to be defined as travelling backwards in time. The real question is whether there is really any need to do this aside from a simplification of the formal calculations (which require positive values). Personally, I find the idea of negative energy states and antimass quite interesting and I think physicists often do Dirac a disservice by rejecting such solutions. Dirac thought they were valid and important in their own right - and I personally tend to agree with him. Even more interesting is that Dirac later tried to show that these solutions required the existence of some sort of aether - but because aether is "politically incorrect" in physics most people have never even heard of this. I strongly recommend looking it up, it's very interesting.

Anyway, there is nothing about antiparticles that actually requires motion backward in time. Feynman and Wheeler played for a while with the literal idea but later abandoned it as unworkable. Feynman continued to use it as a mathematical convenience only.

Thanks for looking this up.

And thanks for this also.

And finally, thanks for taking the time to clear all of this up.

No problem, and you're welcome! :)

[Yllanes]

Well, the parity distinction is easy to explain, just think of a mirror image that is also upside down. The definition of an antiparticle only requires that it be charge conjugated, not necessarily that there is also a parity violation or a time reversal. Of course in actual anti-particle production there may be parity reversals depending on the process but it isn't a necessary condition.


The CPT conjugate of an electron with charge -e and helicity +1/2 is a positron with charge e and helicity -1/2. (Helicity is the projection of spin in the direction of momentum). This is a simple result in QFT.


So an antiparticle travelling forward in time has negative energy, "antimass" and follows a normal forward time evolution. In order to treat it as though it were a normal particle, with positive energy and mass etc., it has to be defined as travelling backwards in time. The real question is whether there is really any need to do this aside from a simplification of the formal calculations (which require positive values). Personally, I find the idea of negative energy states and antimass quite interesting and I think physicists often do Dirac a disservice by rejecting such solutions. Dirac thought they were valid and important in their own right - and I personally tend to agree with him. Even more interesting is that Dirac later tried to show that these solutions required the existence of some sort of aether - but because aether is "politically incorrect" in physics most people have never even heard of this. I strongly recommend looking it up, it's very interesting.
Dirac's sea is interesting, a great hypothesis that earned him the Nobel prize and its results for several things are correct. But it does not cease to be an ad hoc explanation and it does not lead to a consistent theory, which is why it is not used today. This is no criticism of Dirac, he proved the esxistence of the positron and started RQM. It is only that with QFT we have a more complete theory (which was possible in great part thanks to him).

If modern theoretical physicists accept things like lots of extra dimensions, discretisation of spacetime or even negative energy and pressure (in dark energy), I think they would also accept negative energy electrons if this led to a consistent theory. The problem is that negative energy electrons don't exist, we have positrons instead. This positrons have the same time evolution as electrons, so they don't move backwards in time.

[Pragmatist]

The CPT conjugate of an electron with charge -e and helicity +1/2 is a positron with charge e and helicity -1/2. (Helicity is the projection of spin in the direction of momentum). This is a simple result in QFT.

Yes, of course. I wasn't trying to imply that given pairs had identical parity, (I can see that my wording was ambiguous, sorry) I was more generally addressing something that Schneibster said:

and I'll also point out that antimatter is both C and P reversed from matter. In other words, the internal quantum numbers and the spatial characteristics of an antiparticle are reversed from those of its corresponding particle.

In other words, I was simply trying to point out that we can't consider all antimatter to be "left handed" and all matter "right handed" (or whatever), that both matter and anti matter come in all "flavours" so that the specific definition of an antiparticle says nothing about its parity - in general what distinguishes a (randomly selected) particle from an (equally randomly selected) anti-particle is charge conjugation alone, not the parity. The point may be obvious and redundant and I'm sure Schneibster realised it already, but I was being explicit for the benefit of any other readers who may not have fully understood it.

Dirac's sea is interesting, a great hypothesis that earned him the Nobel prize and its results for several things are correct. But it does not cease to be an ad hoc explanation and it does not lead to a consistent theory, which is why it is not used today. This is no criticism of Dirac, he proved the esxistence of the positron and started RQM. It is only that with QFT we have a more complete theory (which was possible in great part thanks to him).

If modern theoretical physicists accept things like lots of extra dimensions, discretisation of spacetime or even negative energy and pressure (in dark energy), I think they would also accept negative energy electrons if this led to a consistent theory. The problem is that negative energy electrons don't exist, we have positrons instead. This positrons have the same time evolution as electrons, so they don't move backwards in time.

My point here was more a philosophical one rather than any criticism of current methods. Dirac had a different and interesting approach, he didn't aim specifically for conformance with experimental results, he was more interested in following where the mathematics could lead. This approach was severely criticised by many (especially Heisenberg), and it is that criticism that I personally think was unjustified. Dirac's view was that if some theory did not match experimental predictions then it didn't necessarily imply that the theory was wrong, merely that it was incomplete - and on that basis it was worth following at least a little further because with further expansion it may end up being self consistent and in accordance with observations. As a corollary, Dirac once said that he thought the fact that a theory matched experimental observations didn't necessarily make it "right".

I agree that the electron sea seems ad-hoc. Although it's often difficult to distinguish a legitimate refinement of a theory from "ad-hoc", there's a fine balance and the final judgement often tends to be as much political or fashionable as anything else. I think part of the problem in the above case was the severe criticism that Dirac suffered when he announced his negative energy levels. He was immediately attacked quite strongly by numerous famous physicists including Heisenberg who immediately denounced it as "crap" and Pauli who (IIRC) announced that if this was what Quantum Mechanics had become he was going to give up the field in disgust! Under that pressure I think Dirac was rather forced to come up with some ad-hoc explanation that preserved the status quo just to quieten the detractors. Perhaps if he had experienced a less hostile reaction he may have come up with something better - although of course that's merely opinion and speculation on my part.

For what it's worth, modern theory is more consistent and complete because it's been rendered and presented that way, there are still aspects in current theory that make some physicists uncomfortable and some even consider that the problems have simply been disguised or swept under the carpet. Again, it's very much a matter of personal opinion and preference. It is undeniable that the mathematical basis of current theory seems on the face of it to be well founded and well justified. I wasn't saying that Dirac's earlier ideas were better per se, I was simply saying that it was a pity that they were not more widely accepted (provisionally at that time) and followed up to see where they led - if they had been, it is possible that they may have eventually led to an even better theory than the ones we have today. Whilst it may be true that the electron sea specifically would not lead to a consistent theory, I don't believe that very much effort was made in the past to see whether the basic ideas arising from some of Dirac's more unusual results could be developed further, because all too often they were summarily dismissed as outrageous and offensive on purely philosophical grounds.

Anyway, philosophy aside - I agree that anti-particles follow normal time evolution and no moving backwards in time is required, I already said as much earlier.

[Yllanes]

All very valid points.


Anyway, philosophy aside - I agree that anti-particles follow normal time evolution and no moving backwards in time is required, I already said as much earlier.

Yes, I got this from your other post. I was repeating it, however, for the benefit of the proverbial lurker (though I think most people have already run scared of this tangled thread). Reading about Dirac's sea is interesting and, indeed, perhaps the best way for a layman to think of antiparticles. The fact that it doesn't lead to a watertight theory is irrelevant for someone who isn't going to calculate anything but just wants to get an idea of the field. I only wanted to point out that this is not the formalism theoretical physicists use to think about antiparticles.

The problem with these threads is that sentences written in a summarised language to address a particular point sometimes give the idea that they are contradicting other posts. I was trying to point out this was not the case, not disagreeing with your post.

[ynot]

(though I think most people have already run scared of this tangled thread).
Not at all - Behind my desk, sitting upright, arms folded, looking, listening, learning, like a good little student :)

All very interesting stuff (however hard/impossible to keep up with).

[Pragmatist]

All very valid points.



Yes, I got this from your other post. I was repeating it, however, for the benefit of the proverbial lurker (though I think most people have already run scared of this tangled thread). Reading about Dirac's sea is interesting and, indeed, perhaps the best way for a layman to think of antiparticles. The fact that it doesn't lead to a watertight theory is irrelevant for someone who isn't going to calculate anything but just wants to get an idea of the field. I only wanted to point out that this is not the formalism theoretical physicists use to think about antiparticles.

The problem with these threads is that sentences written in a summarised language to address a particular point sometimes give the idea that they are contradicting other posts. I was trying to point out this was not the case, not disagreeing with your post.

O.K. and thanks!

[luchog]

(a bunch of stuff)

I've been trying this entire thread to understand what you're trying to say, and have come to the conclusion that it is "complete and utter and total absolute nonsense gibberish" based on a complete misuderstanding of mathematics and physics.

Mathematical model are a map. Visual approximations are a map. And (smeg, i am going to hate myself for using this phrase), the map is not the territory. Your problem is that you are looking at the map, and because you don't understand it or how it relates to the territory -- that is, you can't read the map -- you insist that the territory doesn't exist. The fact is the map provides a very useful guide to get from place to place, and the more we travel, the more detailed the map becomes. To simply discard the map because you don't have the skill to read it is pure, unadulterated pig-ignorance.

[Zygar]

I've been trying this entire thread to understand what you're trying to say, and have come to the conclusion that it is "complete and utter and total absolute nonsense gibberish" based on a complete misuderstanding of mathematics and physics.

Mathematical model are a map. Visual approximations are a map. And (smeg, i am going to hate myself for using this phrase), the map is not the territory. Your problem is that you are looking at the map, and because you don't understand it or how it relates to the territory -- that is, you can't read the map -- you insist that the territory doesn't exist. The fact is the map provides a very useful guide to get from place to place, and the more we travel, the more detailed the map becomes. To simply discard the map because you don't have the skill to read it is pure, unadulterated pig-ignorance.

That is an excellent analogy. I couldn't agree more.

[ynot]

Mmmmfff. I freely admit that your suspicion that the shape of the universe is not a finite, curved space agrees with my own prejudice. I deliberately characterize it as a prejudice, because I cannot give fully convincing logical grounds for making it a conclusion. There is, however, a fair bit of evidence that supports it as a conclusion.

However, it seems to me that since you are characterizing it as a "mathematical abstraction," our opinions diverge. You are not maintaining that it is in reality not an accurate description of the geometry of spacetime, as I am, but that it is in principle impossible for spacetime to have this or any other such geometry, a position that I have evidence to deny, on the grounds that it is impossible to visualize such a geometry without using oversimplified geometrical models that depend on our own three-space-one-time dimensional experience. I contend that we know that space is more than three-dimensional, merely on the basis of the Lorentz-Fitzgerald contraction; we can observe anomalous effects on measured characteristics of moving objects that admit of no other explanation than that three-dimensional space is curved in a fourth dimension, and that fourth dimension is time. If there is another explanation of these effects, I am unaware of it. Let's examine precisely what I mean:

Suppose two objects are moving at the same velocity; that is, they appear motionless to one another. Now let us suppose that one object undergoes an acceleration such that it is moving away from the other. Next let us suppose that we are observing these two objects in a frame in which they are both moving originally in the same direction, which we will arbitrarily define as the "x" direction, at equal velocities, and that the acceleration results in the accelerated object having the same speed, but its velocity having a different direction, that is, a combination of movement in both the arbitrary "x" direction and in the rectilinear but other than that also arbitrary "y" direction.

Let's define the frames of these two objects such that their "x" (which we will call "x'," or "x-prime," for the first object's frame, and "x''", or "x-prime-prime," for the second object's frame) will correspond to the direction they are moving in our frame. Furthermore, both objects will have y' and y'' that is parallel to our own y. Now, what happens?

At the beginning, the direction of x, x', and x'' is the same. After the second object receives its acceleration, x and x' are still the same direction, but x'' is in a different direction; in our frame, and in that of the first object, x'' points in a direction that is intermediate between x (or x') and y (or y'). Now, in terms of the second object's speed in its own locally defined x, which we are calling x'', it is going the same speed as the first object; but in terms of our x, or the first object's x, which we call x', it now is going slower. Compensating for this, in terms of the first object's y, which we call y', or our own y, it now has a non-zero motion. In all three frames, the two objects are now moving apart; but in terms of the first object's x', and in terms of our x, it is moving slower in x, and faster in y. But what about from the second object's point of view? Is the first object moving slower, or faster, in x''?

Note that in fact, the second object sees the first as moving slower in x''. So both objects see the other as moving slower in x. And this is the result of a coordinate transform, of a type we call "rotation."

Not only that, but if the two objects were elongated along the direction of movement, and the second object were rotated along with its vector being rotated, then each object would observe the other to be shorter in x.

So, what do we see when an object is accelerated? We see that it is shorter, and we see that it moves more slowly in t, where t is the time dimension. And from the frame of that object, exactly the same thing happens to the unaccelerated object.

Finally, we see that the transform that is needed for this new type of rotation uses the same equations that the type we know about does; but it does not use it in the same geometrical environment. Because, you see, the geometry of space with respect to time is not circular; it is hyperbolic. So instead of using circular trigonometry to describe the effects of this rotation, as we do for a rotation in space, we have to use hyperbolic geometry to describe it; and hyperbolic geometry is very unusual in many ways. There are "angles" in hyperbolic geometry that cannot be considered to exist; there are no such angles in circular geometry. Rotation over an "angle" in hyperbolic geometry results in an apparent change in the size of the rotated object; this does not happen in circular geometry. As a result, we observe unambiguously that the relation of time to space implies that space is curved with respect to time, in a way that it is not curved with respect to itself; in other words, the three spatial dimensions are "flat" with respect to one another, but "curved" with respect to time. And this is an observable fact of our universe. We can measure it, and we cannot account for it in any other way.

With curvature as weird as this (not to mention as difficult, if not impossible, to visualize, as this) possible for the previously "obvious" geometry of space, along with obvious and inescapable observable consequences, I think it is impossible to maintain that curvature of space is a mathematical abstraction without real physical meaning.

Two objects both move in the same direction at the same speed. One object then veers off to move in a new direction while retaining the original speed. Initially an observer sees the objects moving at the same speed. Then, when one object changes direction, the observer sees that they now move at different speeds. The reality is that the objects continue to travel at the same speed. The perception is that one has changed speed. The perception is an optical illusion that doesn‘t correctly represent reality. I think the statement “is going slower” (bolded above) is incorrect. It should be “appears to be going slower”. I don’t understand how an optical illusion becomes a reality. What am I missing?

This is how I see the scenario. Am I wrong?

Let’s call the objects A and B and the observer C.

For C to correctly observe that A and B are moving in the same direction and speed, A and B must always be equidistant from C to avoid any depth perception anomalies.

A continues to travel at the same speed as B, but now veers off in a different direction from B.

Whether C now perceives that A is now moving the same, faster or slower than B depends on both the angle of the original motion of A/B relative to C, and the new angle of motion of A relative to C.

If A and B continue to always remain equidistant from C, they will still be perceived as moving at the same speed, only now in different directions.

If the original A/B motion was angled away from C, and the new motion of A is now angled more toward C, then C would perceive that A had sped up compared to B.

If the original A/B motion was angled toward C, and the new motion of A is now angled more away from C, then C would perceive that A had slowed down compared to B.

[ynot]

I've been trying this entire thread to understand what you're trying to say, and have come to the conclusion that it is "complete and utter and total absolute nonsense gibberish" based on a complete misuderstanding of mathematics and physics.

Mathematical model are a map. Visual approximations are a map. And (smeg, i am going to hate myself for using this phrase), the map is not the territory. Your problem is that you are looking at the map, and because you don't understand it or how it relates to the territory -- that is, you can't read the map -- you insist that the territory doesn't exist. The fact is the map provides a very useful guide to get from place to place, and the more we travel, the more detailed the map becomes. To simply discard the map because you don't have the skill to read it is pure, unadulterated pig-ignorance.
I’ve never hidden the fact that my understanding of mathematics and physics is limited. I think “complete misunderstanding” is a little harsh however. Everyone’s understanding of everything is limited, so isn’t it simply a matter of degree. Perhaps you would like it better if the forum had a “learners” section that members couldn’t leave until they prove a certain level of competence that you agree with.

I don’t either “insist that the territory doesn't exist” or “discard the map”. That you think I do perhaps reflects an “if you’re not with us, you’re against us” attitude. Or perhaps my inability to express myself clearly. I’m not making any claims. I’m questioning the claims of others, and more specifically, the validity of the methods used to reach the conclusions that the claims are based on. Obviously I can only do this from the position of learning and understanding that I’m currently at. I could (and sometimes do) take it on faith that the claims of others are correct. It depends how the claims register on my personal “does this make sense” scale.

I wouldn’t automatically disregard the validity and usefulness of a map written in Chinese just because I couldn’t fully read/understand it. If I had the time (which unfortunately I don’t) I could learn Chinese and gain the ability to fully read/understand it. I may find however that the map makes spiritual claims that you can get from A to B by levitation or astral travel. Understanding doesn’t automatically result in acceptance and agreement as you seem to imply.

ETA - I guess if a person believes they are absolutely and utterly correct, then they would also believe that an absolute and utter understanding would result in an absolute and utter acceptance and agreement.

[ynot]

Sorry - Double post

[Schneibster]

I'm going to rearrange your quotes a bit so I can answer in context, because there is a common error in your first and third response, and it'll be easier to answer those together.No stress. Thanks for being thorough.

Ah, I see where the error is now. You misunderstood something in the article. A CP violation does not imply a T violation, a CP violation can be considered equivalent to a T violation. I see that, but I'd like to point out that technically, it's a violation of CP- (or T-) reversal symmetry, "CP-violation" is shorthand for this. In other words, CP-reversal symmetry states that if both charge and parity are reversed, the laws of physics will be unchanged, and a violation of this symmetry means that an observed interaction exhibits features that are not unchanged under reversal of charge and parity. This is equivalent to the statement that this interaction exhibits features that are not unchanged under reversal of time. Correct?

Think of it this way: any symmetry operation represents a violation if there is a change in the net (total) symmetry after whatever process is being considered. So the aim of any conservation law is to make the net change in symmetry zero. Now, if CP is equivalent to T, and CP becomes not CP (i.e. if there is a violation) then "not CP" is equivalent to "not T". In which case the net result for CPT conservation is the product "not T" . T which is zero. T doesn't change, so no T violation is implied.This ALMOST cleared it up, but then you get to the last sentence and it all goes out the window. ;) Let's discuss this some more, and I suggest that we make it clear whether we are talking about T-reversal symmetry, or T-symmetry, or time itself, or precisely what, and the same for C and P. That may be the root of the misunderstanding.

I also wouldn't rely on Wikipedia for critical information, I've found lots of errors in it in the past and it's quite unreliable IMO. There are plenty of other reliable sites like Hyperphysics for example. The article you linked to for example makes the mistake of saying that parity is just a mirror image which is obviously wrong. I agree, and almost pointed that out; it was not, however, the source of my error, although it contributed to it. I did and do know the difference, and merely neglected it for the benefit of simpler souls; in a technical discussion like this one was sure to become, that was probably a mistake.

Well, the parity distinction is easy to explain, just think of a mirror image that is also upside down. The definition of an antiparticle only requires that it be charge conjugated, not necessarily that there is also a parity violation or a time reversal. Of course in actual anti-particle production there may be parity reversals depending on the process but it isn't a necessary condition.I was not aware that there were any observed antiparticles of particles that show parity symmetry violations (such as neutrons, which violate parity in their weak decays because under the influence of a magnetic field, they can be lined up and shown to have a directional preference) in which the sense of the violation was not reversed. In other words, the antiparticles of particles with an interaction that breaks P-reversal symmetry also break it, but in the opposite sense. If I understand correctly. I am aware that just because the weak decays happen with a particular directional preference does not mean that they all happen in that direction; but my understanding was that the preference of the direction in the neutron was reversed in the antineutron. Is this correct? Are there examples in which the preference is not reversed for the antiparticle?

In a digression, I'll also point out that, at least for the neutron weak decay, the C(antimatter)P(directional preference)-reversal asymmetry is restored IF one considers the neutron and antineutron together as a single system. But I'm not sure if this is either valid under the SM, or generally recognized if it is.

Lots of people (even a few physicists!) seem to be confused about all this. The antiparticle prediction arises from Dirac's electron theory which gave two solutions for the electron, one involving normal energy and the other with "negative energy" states. Now, these negative energy states seemed to offend the sensibilities of many physicists so they sought explanations in which they could avoid the concept of things like "antimass". In order to straighten out the calculations, the concepts of negative energy and antimass were rejected and the mass (and energy) of antiparticles were defined as positive real quantities. Vectors that depended on mass (like momentum) could be negative because the direction could be reversed, but it was more problematic for scalars like energy. In the end, the only way to make these quantities come out positive whilst not destroying the integrity of the antiparticle solutions was to reverse the arrow of time. But it's important to realise that this doesn't necessarily imply actual motion backwards in time, it's just a mathematical device.Well, what I'm arguing here is that, because we are made of matter and not antimatter, we fix a gauge, many times without acknowledging or sometimes even realizing it; the time dimension itself has no preferred direction intrinsically, but the dominance of matter in our universe has fixed the same gauge we use. This gauge is fixed oppositely for antimatter, and if the universe were predominantly antimatter, that gauge would be fixed in the opposite direction, although one could only realize that was the case (either for the dominance or the direction of the gauge) by comparing it (the universe!) with another universe (whatever THAT might mean) with the opposite dominance and the opposite gauge. And that is, to my mind, an implication of the fact that under the time reversal operation, we must also swap the charge and parity of all the particles, making them antimatter, if we wish to continue to represent charge, and time direction, as positive, and energy and mass as positive. If we reverse time, and do not reverse charge and time direction accounting, then we again wind up with negative energy. And finally, THAT implies that (for example) positrons are actually electrons with the time direction gauge fixed in the opposite fashion from normal electrons. Does that make any sense?

So an antiparticle travelling forward in time has negative energy, "antimass" and follows a normal forward time evolution. In order to treat it as though it were a normal particle, with positive energy and mass etc., it has to be defined as travelling backwards in time. The real question is whether there is really any need to do this aside from a simplification of the formal calculations (which require positive values). I think the basic unreality of a negative of a scalar itself answers this question; to my mind, negative mass indicates you are doing something wrong, just as when you find yourself dividing by zero.

Personally, I find the idea of negative energy states and antimass quite interesting and I think physicists often do Dirac a disservice by rejecting such solutions. Dirac thought they were valid and important in their own right - and I personally tend to agree with him. Even more interesting is that Dirac later tried to show that these solutions required the existence of some sort of aether - but because aether is "politically incorrect" in physics most people have never even heard of this. I strongly recommend looking it up, it's very interesting.Wow! Now that I had not heard of. I will devote some time to looking into it- but it's going to take some convincing for me to accept the validity of the negative of an absolute value (which is the mathematical meaning of the negative of a scalar).

Anyway, there is nothing about antiparticles that actually requires motion backward in time. Feynman and Wheeler played for a while with the literal idea but later abandoned it as unworkable. Feynman continued to use it as a mathematical convenience only.I think it's the whole "moving in time" thing that gets everyone's back up. From the majority point of view, nothing is moving in time, either forward or backward- "particles" are actually "worms" (if you like that simile) through spacetime, with complete existence at each moment of time throughout their spacetime path from one interaction to another (quantum jitters aside). I've searched and searched for another way to describe this, and the best I've come up with is "reversed time gauge," which is difficult for anyone but a physicist (amateur or not) to follow, since most people don't know what a "gauge" is if you're not talking about the fuel in your car. ;) But if I had to pick a technical description of it, I'd have to say that's probably as unprejudicial as I've found so far.

[Schneibster]

I was simply trying to point out that we can't consider all antimatter to be "left handed" and all matter "right handed" (or whatever), that both matter and anti matter come in all "flavours" so that the specific definition of an antiparticle says nothing about its parity - in general what distinguishes a (randomly selected) particle from an (equally randomly selected) anti-particle is charge conjugation alone, not the parity. The point may be obvious and redundant and I'm sure Schneibster realised it already, but I was being explicit for the benefit of any other readers who may not have fully understood it.Yes, you're sure, and I think I made it clear. However, I think there's something you have overlooked, which is that the implication here is that statistically, neutrons are more likely to be (let's say) right handed. And conversely, antineutrons are more likely to be left-handed. And we have no real explanation of why this might be.

One of the more interesting (not fully developed) thoughts I've had recently is that this is reminiscent of the fact that individual interactions are unconstrained by the Second Law of Thermodynamics, but get enough of them together and you get that 2LOT, which is actually the manifestation of the Fluctuation Theorem. But the FT ALSO says that if you look at FEW enough interactions, the time reversal symmetry emerges (is restored? more speculation on my part) and shows that the underlying interactions are in fact time-reversal symmetric; not only that, but the derivation of the FT in fact REQUIRES that those underlying interactions be time-reversal symmetric, yet leads directly to time-reversal asymmetric statistical behavior! This, I think, needs more work. But it looks like a clue to me.

[Schneibster]

This is how I see the scenario. Am I wrong?I would hesitate to use "wrong," I think part of the problem you're experiencing has to do with the fact that not only am I analogizing a four-dimensional rotation into three dimensions, but I'm analogizing a four-dimensional rotation in a spatiotemporal geometry that is hyperbolic into a three-dimensional rotation in a spatial geometry that is circular (and by "hyperbolic" and "circular," I am referring to the type of geometry that one uses to mathematically describe rotation and translation operations in those geometries, nothing more). This is a problem of visualization, not one of incorrect conclusion. If you had practical experience dealing with spatial hyperbolic geometries, as you do dealing with circular ones, this would be clearer; however, it is also possible that in that case you would experience two time dimensions, since it is this distinction that appears to result in our observation of a "difference" between the spatial and temporal dimensions. What the heck that would mean, I have no idea.

[Schneibster]

Let me clarify something about hyperbolic geometry. Hyperbolic geometry is counter-intuitive, because operations that we intuitively deal with (rotation, specifically) operate in a manner that is essentially impossible to visualize: specifically, you can rotate to and "angle" that we define as "infinity" without ever reversing your direction. Reversal of direction by continuous rotation is mathematically impossible, and as far as we can tell, in the real world, it is physically impossible as well (in other words, it is impossible to reverse your direction in time by any continuous rotation in spacetime). This is completely the counter of our intuitive concept of rotation, governed by our experiences in space, in which a rotation to an opposite orientation is a trivial operation.

[Yllanes]

Personally, I find the idea of negative energy states and antimass quite interesting and I think physicists often do Dirac a disservice by rejecting such solutions. Dirac thought they were valid and important in their own right - and I personally tend to agree with him. Even more interesting is that Dirac later tried to show that these solutions required the existence of some sort of aether - but because aether is "politically incorrect" in physics most people have never even heard of this. I strongly recommend looking it up, it's very interesting.

Wow! Now that I had not heard of. I will devote some time to looking into it- but it's going to take some convincing for me to accept the validity of the negative of an absolute value (which is the mathematical meaning of the negative of a scalar).

I can briefly explain Dirac's sea if you want. When Dirac first sought to explain the seemingly negative energy solutions of his equation, he considered the vacuum with both negative energy and positive energy states. We are talking about electrons, so we have the Pauli exclusion principle and no two can have all the same quantum numbers. In Dirac's explanation, the negative energy states were all full, so any extra, physical electron would have positive energy. Now, in a similar way as the holes in solid state physics, if a photon excites a negative energy electron and turns it into a positive energy one, the hole it leaves behind is interpreted as a positron. We can get the energy and other physical magnitudes of this hole by considering the difference in the total energy before and after. Suppose we extract the fermion n0 and that M is any physical quantity for the whole system (me- the same physical quantity for a single electron).


\begin{align*}
\mathcal M_{\text{sea}}^{\text{full}}&=
\sum_n m_n^{e^-},&
\mathcal M_{\text{sea}}&=
\sum_{n\neq n_0} m_n^{e^-}.
\end{align*}


Now we see that the value Delta of me- for the hole (positron) is $\Delta=\mathcal M_{\text{sea}}-\mathcal M_{\text{sea}}^{\text{full}}=-m_{n_0}^{e^-}
$ the opposite of its value for the negative energy electron. Thus,


\begin{align*}
E:\quad \Delta&=-\left(-\sqrt{\vec p\,^2+m^2}\right)=\sqrt{\vec p\,^2+m^2},\\
Q:\quad \Delta&=-q_{e^-}=q_{e^+},\\
s:\quad \Delta&=-\tfrac12.
\end{align*}


As I said before, this is not the way physicists think of these things nowadays, but it is nice.

[lenny]

Your problem is that you are looking at the map, and because you don't understand it or how it relates to the territory -- that is, you can't read the map -- you insist that the territory doesn't exist..i think you miss the ynot's point.

i do NOT insist the territory does not exist (nor do i believe ynot so insists): but can you tell us what this territory is?

Is a finite, curved space universe only a mathematical abstraction?

yes. as is each Law of Physics.

they are an abstractions, like a maps. mathematicians and physicists play games on the map. the map exists, is well defined, and we can sometimes quantify distances between different, similar, maps.

but what exactly is the territory? and what is the correspondence between the two? there are a half a dozen very-alive alternative philosophies of science out there trying to make this connection, none very compelling to the physicist. why should a skeptic accept the naive realism of many (?most?) scientists?
The fact is the map provides a very useful guide to get from place to place, and the more we travel, the more detailed the map becomes. To simply discard the map because you don't have the skill to read it is pure, unadulterated pig-ignorance.
i've read a map or two, and i can move about in the game reading the map; while i rarely extend the map itself, i've told friends where to dig and they go off sometimes prove/publish interesting things nearby.

so perhaps you could explain to me what the map means? exactly how it is related to the territory? what metric you use to contrast two maps with the same target? and what the target really "is"?

[ynot]

I guess there are two main things I’m concerned with . . .

Firstly - It seems to me that the concept of curved space is represented purely by math, and no actual evidence exists. Given that some impossible concepts (such as zero) can also be represented by math, I’m reluctant to trust that math alone accurately represents curved space as an actual reality. Wonder if this is due to lack of learning or lack of faith.

Secondly - It seems to me that the math of perception anomalies (optical illusions) is being wrongly attributed to reality. Relative motions, distances and speeds of objects present perception anomalies to an observer. I don‘t see however that there is any evidence (that is non-math) that they have any affect on the actual objects. Once again, is this is due to lack of learning or lack of faith?

Apparently it’s difficult (if not impossible) to explain curved space in 3-D terms, so 2-D scenarios are often used as analogies. It doesn‘t seem to matter that they‘re impossible analogies. What starts out as “lets pretend” however, seems to become “it is so” and the math of 2-D impossibilities get attributed to 3-D realities.

The biggest problem I have with all this is that I don’t think most of the leading brains of the world are idiots, In other words, if were a betting man, I would have to bet against my own argument. Where am I wrong? What am I missing?

[ynot]

i think you miss the ynot's point.

i do NOT insist the territory does not exist (nor do i believe ynot so insists): but can you tell us what this territory is?

Is a finite, curved space universe only a mathematical abstraction?

yes. as is each Law of Physics.

they are an abstractions, like a maps. mathematicians and physicists play games on the map. the map exists, is well defined, and we can sometimes quantify distances between different, similar, maps.

but what exactly is the territory? and what is the correspondence between the two? there are a half a dozen very-alive alternative philosophies of science out there trying to make this connection, none very compelling to the physicist. why should a skeptic accept the naive realism of many (?most?) scientists?

i've read a map or two, and i can move about in the game reading the map; while i rarely extend the map itself, i've told friends where to dig and they go off sometimes prove/publish interesting things nearby.

so perhaps you could explain to me what the map means? exactly how it is related to the territory? what metric you use to contrast two maps with the same target? and what the target really "is"?
Good points - thanks

[Schneibster]

Firstly - It seems to me that the concept of curved space is represented purely by math, and no actual evidence exists. Ummmm, did you miss the whole thing about gravity? Let's say this again, in unambiguous terms: space is curved by gravity. It's also curved in a more interesting way with respect to time, as I pointed out, but that it is curved by the presence of mass is inarguable. Look, the math that describes it is just a map, a model- but for the model to work the way that space really works, it has to be representing curved space. So, if space isn't curved, then the model that represents it as curved wouldn't work- the fact that you have to use a model that represents it as curved isn't an abstraction. For example, to make a really properly accurate map of the Earth's surface, you have to draw it on a globe. Now, will you argue that that doesn't mean the Earth is a globe???? Granted, don't confuse the map with the territory, but ALSO don't confuse characteristics the map HAS to have to be an accurate map with something that doesn't have to be in the territory- if it has to be there, it's because the territory really is like that.

Given that some impossible concepts (such as zero)Wow, hey, man, I have zero pet tigers. What's impossible? Looks perfectly real to me. Are you sure you've got a firm grasp on this?

Secondly - It seems to me that the math of perception anomalies (optical illusions) is being wrongly attributed to reality. Ummmmm, it's not an optical illusion. In fact, you can't see space curvature- light is curved by it, so it looks straight. But you CAN measure it. We do it all the time. Just drop a rock. Does it stay where it is, or does it move apparently on its own? If it stays where it is, then you're in flat space. If it moves apparently on its own, you're in curved space. Just that simple.

Relative motions, distances and speeds of objects present perception anomalies to an observer. I don‘t see however that there is any evidence (that is non-math) that they have any affect on the actual objects. Once again, is this is due to lack of learning or lack of faith?You've misunderstood what relativity says. It says, wherever you're standing, and however fast you're going, if you're in flat space, your measurements are as good as anyone's. You can convert them one into another. In fact, even if you're in curved space, you can still convert them- it's just a little more complicated. But you can do it, and the theory of relativity tells how. What relativity says is, you can't point to some particular observer in some particular state of motion and say, "well, that observer's frame is BETTER." All frames are equally valid; none is special, that is, none is absolute. There is no absolute motion. But there IS absolute acceleration; you can always measure acceleration with a rock, as I described above. Note that you cannot determine the difference between acceleration and curved space; they are the same thing.

Apparently it’s difficult (if not impossible) to explain curved space in 3-D terms, so 2-D scenarios are often used as analogies. It doesn‘t seem to matter that they‘re impossible analogies. What starts out as “lets pretend” however, seems to become “it is so” and the math of 2-D impossibilities get attributed to 3-D realities.Here, you are most definitely confusing the map with the territory. You CANNOT, not EVER, completely and consistently explain 3D space curved in a fourth dimension using lower dimensionalities. It's just not possible. It can't ever be accurate. There always has to be a defect- IN THE DESCRIPTION, not in the reality. You might as well say there are no green birds because you've never seen one. In fact, you CANNOT visualize it, no one can. We live in a 3D world. We can't imagine 4D. All we can do is describe it with math. That's all we've got, it's all we ever will have.

The biggest problem I have with all this is that I don’t think most of the leading brains of the world are idiots, In other words, if were a betting man, I would have to bet against my own argument. Where am I wrong? What am I missing?You just need to accept that you are 3D. You can't visualize 4D. But you CAN describe it: using math. No other method works completely and consistently. ANY other description you try to use MUST be incomplete.

[Schneibster]

One more try: math is a language, and like all languages it describes things, it is not the things it describes. However, math has a unique ability to describe things that are outside our experience, that we cannot accurately imagine, and do so accurately. In no natural language is it possible to do this with accuracy, although it is generally possible. And some of the things math can describe are not just objects, but characteristics, for example, characteristics of space. When we use math to unambiguously (whether we can imagine it or not) describe characteristics of space such as its curvature, it is not abstract- no more so than saying I have two oranges is abstract. It is very concrete to state that I have two oranges- just as it is very concrete to state that space is curved a certain way at a certain location. The fact that you or I cannot visualize what that (curved space) might mean in any realistic terms makes no difference to its reality. It is a limitation of US, not a limitation of SPACE.

[ynot]

Ummmm, did you miss the whole thing about gravity? Let's say this again, in unambiguous terms: space is curved by gravity. It's also curved in a more interesting way with respect to time, as I pointed out, but that it is curved by the presence of mass is inarguable. Look, the math that describes it is just a map, a model- but for the model to work the way that space really works, it has to be representing curved space. So, if space isn't curved, then the model that represents it as curved wouldn't work- the fact that you have to use a model that represents it as curved isn't an abstraction. For example, to make a really properly accurate map of the Earth's surface, you have to draw it on a globe. Now, will you argue that that doesn't mean the Earth is a globe???? Granted, don't confuse the map with the territory, but ALSO don't confuse characteristics the map HAS to have to be an accurate map with something that doesn't have to be in the territory- if it has to be there, it's because the territory really is like that.
What is the non-math evidence that gravity curves space?

Wow, hey, man, I have zero pet tigers. What's impossible? Looks perfectly real to me. Are you sure you've got a firm grasp on this?
How can you have zero pet tigers? Zero pet tigers means you don't have pet tigers. Do you feed your zero pet tigers zero meat?

Ummmmm, it's not an optical illusion. In fact, you can't see space curvature- light is curved by it, so it looks straight. But you CAN measure it. We do it all the time. Just drop a rock. Does it stay where it is, or does it move apparently on its own? If it stays where it is, then you're in flat space. If it moves apparently on its own, you're in curved space. Just that simple.
I didn't saying space curvature is an illusion. I said "Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with the concept of curved space.

You've misunderstood what relativity says. It says, wherever you're standing, and however fast you're going, if you're in flat space, your measurements are as good as anyone's. You can convert them one into another. In fact, even if you're in curved space, you can still convert them- it's just a little more complicated. But you can do it, and the theory of relativity tells how. What relativity says is, you can't point to some particular observer in some particular state of motion and say, "well, that observer's frame is BETTER." All frames are equally valid; none is special, that is, none is absolute. There is no absolute motion. But there IS absolute acceleration; you can always measure acceleration with a rock, as I described above. Note that you cannot determine the difference between acceleration and curved space; they are the same thing.
I'm not considering the concept of "Einstein relativity". I am saying ""Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with "Einstein relativity".

Here, you are most definitely confusing the map with the territory. You CANNOT, not EVER, completely and consistently explain 3D space curved in a fourth dimension using lower dimensionalities. It's just not possible. It can't ever be accurate. There always has to be a defect- IN THE DESCRIPTION, not in the reality. You might as well say there are no green birds because you've never seen one. In fact, you CANNOT visualize it, no one can. We live in a 3D world. We can't imagine 4D. All we can do is describe it with math. That's all we've got, it's all we ever will have.
The point is not that you can't say there aren't green birds because you haven't seen one, but that you can't say that there are.

You just need to accept that you are 3D. You can't visualize 4D. But you CAN describe it: using math. No other method works completely and consistently. ANY other description you try to use MUST be incomplete.
Exactly, and being an eternal sceptic, I'm questioning the validity of the math in this case. I'm not trying to prove anything wrong, just don't think it's been proven right (for me).

[ynot]

What is the non-math evidence that gravity curves space?


How can you have zero pet tigers? Zero pet tigers means you don't have pet tigers. Do you feed your zero pet tigers zero meat?


I didn't saying space curvature is an illusion. I said "Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with the concept of curved space.


I'm not considering the concept of "Einstein relativity". I am saying ""Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with "Einstein relativity".


The point is not that you can't say there aren't green birds because you haven't seen one, but that you can't say that there are.


Exactly, and being an eternal sceptic, I'm questioning the validity of the math in this case. I'm not trying to prove anything wrong, just don't think it's been proven right (for me).

ETA - Actually it's not so much the validtity of the the math as the validiy of what the math is based on.

[Schneibster]

What is the non-math evidence that gravity curves space?Ummmm, how does "things fall" work for you?

How can you have zero pet tigers? Zero pet tigers means you don't have pet tigers. Do you feed your zero pet tigers zero meat? Yes.

I didn't saying space curvature is an illusion. I said "Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with the concept of curved space.Actually, you did. See your first reply in the post I'm responding to now.

I'm not considering the concept of "Einstein relativity". I am saying ""Relative motions, distances and speeds of objects present perception anomalies to an observer." Nothing to do with "Einstein relativity". But you're trying to prove they're ONLY perception anomalies, not REAL ones- and you're wrong, they ARE real.

The point is not that you can't say there aren't green birds because you haven't seen one, but that you can't say that there are. But I'm not saying there are because I HAVEN'T seen one, but because I HAVE. And if I HAVE, then that's proof (for me, at least- you may or may not choose to believe me, and you may or may not choose to believe your own eyes when you see one for yourself).

Exactly, and being an eternal sceptic, I'm questioning the validity of the math in this case. I'm not trying to prove anything wrong, just don't think it's been proven right (for me).Well, you can't really ever prove anything about reality, not even that it exists. You're going to have to settle for "good enough," or remain a solipsist. But if you DO settle for "good enough," then there's good enough proof that reality really is like that to satisfy anyone who does enough research to find it out.

[ynot]

One more try: math is a language, and like all languages it describes things, it is not the things it describes. However, math has a unique ability to describe things that are outside our experience, that we cannot accurately imagine, and do so accurately. In no natural language is it possible to do this with accuracy, although it is generally possible. And some of the things math can describe are not just objects, but characteristics, for example, characteristics of space. When we use math to unambiguously (whether we can imagine it or not) describe characteristics of space such as its curvature, it is not abstract- no more so than saying I have two oranges is abstract. It is very concrete to state that I have two oranges- just as it is very concrete to state that space is curved a certain way at a certain location. The fact that you or I cannot visualize what that (curved space) might mean in any realistic terms makes no difference to its reality. It is a limitation of US, not a limitation of SPACE.
So you believe that the use of math is always infallible and accurate and that saying saying "I have two oranges" is not abstract?

Hmmm - a conspiracy of those “not to be trusted” mathematicians :D

[Schneibster]

No. I OBSERVE that it is. Whether you have the wherewithal to test it or not, I do, and I use it every day of my life, for my work and for several of my hobbies, and for my finances, and in several other extremely important areas of my life. It hasn't been wrong yet, although I have.

Honestly, saying you don't "trust" mathematicians is like saying you don't "trust" the sky is blue. WALK OUTSIDE AND CHECK FOR YERSELF. Don't bother me with your conspiracy theories.

[ynot]

Ummmm, how does "things fall" work for you?
Proves gravity exists not curved space. Does the rock fall to the Earth or visa-versa?

Yes.
Cheap non-pets!

Actually, you did. See your first reply in the post I'm responding to now.
Then why quote from my last post? Threads can evolve can't they?

But you're trying to prove they're ONLY perception anomalies, not REAL ones- and you're wrong, they ARE real.
So sayest the math!

But I'm not saying there are because I HAVEN'T seen one, but because I HAVE. And if I HAVE, then that's proof (for me, at least- you may or may not choose to believe me, and you may or may not choose to believe your own eyes when you see one for yourself).
And I'm also not saying there aren't because I haven't seen one. If I have it would be proof enough for me too. But I haven't.

Well, you can't really ever prove anything about reality, not even that it exists. You're going to have to settle for "good enough," or remain a solipsist. But if you DO settle for "good enough," then there's good enough proof that reality really is like that to satisfy anyone who does enough research to find it out.
"good enough" is usually good enough for me, but solely using math as proof of curved space is not good enough.

[ynot]

No. I OBSERVE that it is. Whether you have the wherewithal to test it or not, I do, and I use it every day of my life, for my work and for several of my hobbies, and for my finances, and in several other extremely important areas of my life. It hasn't been wrong yet, although I have.
I did say "the use of the math' not the math itself. Don't get me wrong, I've got nothing against math. I find it very useful, exciting and even entertaining.

Honestly, saying you don't "trust" mathematicians is like saying you don't "trust" the sky is blue. WALK OUTSIDE AND CHECK FOR YERSELF. Don't bother me with your conspiracy theories.
Did you miss the :D ? It was meant to be a joke.

ETA - Just walked outside. Cloudy, overcast day. Sky not blue

[ynot]

Using GR and SR to explain curved space to a person that doesn’t accept GR and SR, is about as fruitless as a Theist using the Bible to explain a God to an Atheist that doesn‘t accept the Bible. I’ve often asked Theists to explain their belief without using the Bible. Unfortunately I’ve yet to meet one that can or will. I suspect the same might apply in the case of curved space, given that it seems to be totally founded on GR and SR. When considering the points I’m trying to make, I’m asking that you put aside all thoughts of GR and SR. Not abandon them forever, just put them aside briefly. Not so much to suspend you disbelief, but to suspend your belief (sorry, that should be knowledge of course). Without GR and SR, relative motions, distances and speeds of objects will still present perception anomalies to an observer, but in what way will they have any affect on the actual objects?

[UserGoogol]

I suppose that in a sense it is probably possible to construct a theory of physics which instead of saying that space is curved, merely says that all things move according to curved paths as if reality were curved, but that in fact it is perfectly euclidean. Of course, I also suppose that to say "there are two apples" is also a mathematical abstraction. It would perhaps be more accurate to say "there is a subset of reality to which the two-apple-pattern can be ascribed."

This really feels like it's more metaphysics than physics, though.

[Schneibster]

Proves gravity exists not curved space. Does the rock fall to the Earth or visa-versa?Neither. They move together, proving the existence of curved space, that of the Earth and that of the rock. Gravity is an illusion.

Then why quote from my last post? Threads can evolve can't they? You said it. Do you now disavow it?

So sayest the math! Which is the only complete and consistent description of the reality that our other languages cannot describe.

"good enough" is usually good enough for me, but solely using math as proof of curved space is not good enough.Like I said, how do falling objects grab you? You are welcome to attempt to explain them otherwise; while duplicating Newton's theory of universal gravitation would be an impressive feat, it's still not going to convince me.

[ynot]

Neither. They move together,
YAY!! something we agree on.

proving the existence of curved space, that of the Earth and that of the rock.
Not proof for me I'm afraid. Proof of some form of attraction of the Earth and rock.

Gravity is an illusion.
You said it. Do you now disavow it?
Now I'm not sure if you're being serious. You say that I said space curviture is an illusion, but I say there is no actual evidence of space curviture, so how can I say it's an illusion (would love to know the # of the post in which you say I said it). Now you say that gravity, the thing that has been holding me down all my life, is actually the illusion :confused: .

Which is the only complete and consistent description of the reality that our other languages cannot describe.
And that our senses can't observe. The "reality" or the theory?


Like I said, how do falling objects grab you? You are welcome to attempt to explain them otherwise; while duplicating Newton's theory of universal gravitation would be an impressive feat, it's still not going to convince me.
Must admit I find the whole gravity thing a bit puzzling. Every morning I get out of bed and it's just there. I can sort of understand one object having an attraction to another, and the bigger the object the stronger the attraction. Don't understand why the Moon is trapped in it's orbit around Earth. As it goes through its apogee and perigee why doesn't it escape Earth's gravity or plunge to Earth. Also why do the planets circle the Sun? They're all different distances from the Sun and they're of different sizes. A gravitational magnet-like force doesn't seem to explain it. But then again, to me, nor does the concept of curved space. A God doesn't work either. Guess it just has to go in to the "I don't know" basket for now.

[Schneibster]

Now I'm not sure if you're being serious. You say that I said space curviture is an illusion,

Firstly - It seems to me that the concept of curved space is represented purely by math, and no actual evidence exists.That should put an end to that. If not, I believe that I will conclude this conversation is over. Your choice.

And that our senses can't observe. The "reality" or the theory? Our senses are incapable of observing germs. Does that mean they don't exist?

Must admit I find the whole gravity thing a bit puzzling. Every morning I get out of bed and it's just there. I can sort of understand one object having an attraction to another, and the bigger the object the stronger the attraction. Don't understand why the Moon is trapped in it's orbit around Earth. As it goes through its apogee and perigee why doesn't it escape Earth's gravity or plunge to Earth. Also why do the planets circle the Sun? They're all different distances from the Sun and they're of different sizes. A gravitational magnet-like force doesn't seem to explain it. But then again, to me, nor does the concept of curved space. A God doesn't work either. Guess it just has to go in to the "I don't know" basket for now.You can't imagine magnetic orbits? Sounds like your imagination is out of whack.

[ynot]

That should put an end to that. If not, I believe that I will conclude this conversation is over. Your choice.
Don't see how that saying something doesn't exist is saying it's an illusion. Surely an illusion has to be observable, and therefore exist.

Our senses are incapable of observing germs. Does that mean they don't exist?
Our sense of sight can see germs with the aid of a microscope. We can see that they exist.

You can't imagine magnetic orbits? Sounds like your imagination is out of whack.
Would have thought that magnetic orbits would have had something to do with relative sizes and distances. It doesn't appear that they do. The Moon moves toward and away from the Earth over 50,000 km.

[Pragmatist]

I see that, but I'd like to point out that technically, it's a violation of CP- (or T-) reversal symmetry, "CP-violation" is shorthand for this. In other words, CP-reversal symmetry states that if both charge and parity are reversed, the laws of physics will be unchanged, and a violation of this symmetry means that an observed interaction exhibits features that are not unchanged under reversal of charge and parity. This is equivalent to the statement that this interaction exhibits features that are not unchanged under reversal of time. Correct?

O.K. yes, subject to what I will say next! :)


This ALMOST cleared it up, but then you get to the last sentence and it all goes out the window. ;) Let's discuss this some more, and I suggest that we make it clear whether we are talking about T-reversal symmetry, or T-symmetry, or time itself, or precisely what, and the same for C and P. That may be the root of the misunderstanding.

Sorry, my mistake, my initial explanation was correct, but the example was completely bass ackwards! :D

Some of the confusion is obviously due to us talking at cross purposes, so let me try and clear it up with some definitions that we can hopefully agree on. I think there is some confusion in the way each of us is using the term "violation".

Technically, the symmetry operations we are taking about are QM operators - they are not states, they are operations. Particles have states which undergo change under the action of these operators. Now, it is semantically meaningless to talk about "violation" of a state - states can change but only rules are violated. So a violation means that the operator does not give the expected result. If for example the charge conjugation operator is a black box and we feed "-" in, we expect "+" out. If the output has the same state as the input then the operator (the rule of the black box) has been violated.

Now, here is the confusing bit - we cannot violate a state, but we can change a rule. So change and violation are not synonymous.

Now with that in mind we can hopefully evaluate statements without getting our wires crossed!

CPT symmetry implies that all three rules are bound together. In other words, CPT is itself a "meta rule" or a composite operator. If C and P change, then T must also change if we want to maintain the symmetry of the CPT operator. This is a rule. A violation of "CPT symmetry" would imply that if C and P change, that T would not change correspondingly - like my backwards example. It is not the state of T which is violated, it is the rule that says essentially, "if X and Y then Z" that is violated.

CP symmetry implies that C and P are bound together into a composite CP operator and that if C changes then P must also change and vice versa in order to maintain the symmetry of that operator. A violation of CP symmetry would be if C changed (in a process) and P did not (or vice versa).

In the context of the discussion, and to sum up, CP violations have been observed, however no CPT violation has ever been observed. A CPT violation (should one occur) would also break the symmetry of Lorentz transformations, however a violation of Lorentz transformation symmetry wouldn't necessarily cause a CPT violation.

A CP violation can be "fixed" by a corresponding change in T, so to be strictly correct, a CP violation implies a change in T. It does not imply a violation of T (I know some physicists say that, but it's not semantically correct - because you're talking about the meta rule of CPT transformation, not the T operator itself) - remember that operators are sequential. The rule is, that if C and P change, then T must change, so there is no violation (of the CPT meta rule). The same applies in reverse - a T violation can be fixed by a change in both C and P. The operation is symmetrical overall so in that sense CP is equivalent to T (specifically under CPT symmetry - if CPT symmetry were to be violated then of course CP would no longer be equivalent to T.) And we can also say that a CP violation is equivalent to a T violation because either requires reversal of the whole of the CPT operator in order to maintain CPT symmetry.

"C symmetry" means that the models which describe the behaviour of the the system would still be valid if all the internal quantum numbers of the particle were reversed (and obviously it doesn't only mean charge, because neutral particles can undergo "charge" conjugation, i.e. the neutron and anti-neutron.

"P symmetry" means that the models which describe the behaviour of the the system would still be valid if we reversed all the spacial coordinates i.e. if we made a "left handed" upright system into a "right handed" upside down system.

"T symmetry" means that the models which describe the behaviour of the the system would still be valid if we could reverse the flow of time.

"Lorentz symmetry" means that the models which describe the behaviour of the the system would still be valid if we subjected the system to a Lorentz transformation.

T symmetry does not necessarily imply that time has actually reversed or that a system is travelling backwards in time, all it means is that the model we have for the system would continue to work if it were possible for us to run time backwards. Similarly, a T violation would mean that the model we have for the system would not continue to accurately describe the system if it were possible for us to run time backwards. Neither says anything about the actual possibility of running time backwards, or that it ever has in any particular instance. T symmetry is just a mathematical operator over the wavefunction.

Hopefully, that clears everything up!


I was not aware that there were any observed antiparticles of particles that show parity symmetry violations (such as neutrons, which violate parity in their weak decays because under the influence of a magnetic field, they can be lined up and shown to have a directional preference) in which the sense of the violation was not reversed. In other words, the antiparticles of particles with an interaction that breaks P-reversal symmetry also break it, but in the opposite sense. If I understand correctly. I am aware that just because the weak decays happen with a particular directional preference does not mean that they all happen in that direction; but my understanding was that the preference of the direction in the neutron was reversed in the antineutron. Is this correct? Are there examples in which the preference is not reversed for the antiparticle?

I don't understand what you mean by a P violation in the opposite sense. Spin is not affected by P reversal if that helps any.

In the case of the neutron (which is a fermion), the anti-neutron decay is opposite to the neutron decay - so yes, any directional preference will be reversed. But this is just CP symmetry, unless I completely misunderstand what you're trying to say. An example of an asymmetrical particle/antiparticle response would of course be a CP violation, and in that case the neutral Kaon and of course the Beon would fit.

In case we're talking past each other again, let me be more specific about what I meant when I said that antiparticles do not necessarily have to be P reversed from their corresponding particles. The simplest example is the difference between fermions and bosons. The antiparticle of any fermion is automatically parity reversed from the particle. But in the case of bosons, the antiparticle has matching parity with the corresponding particle. A good example of the latter is the "normal" pion (i.e. the pi minus) which has the same parity as the antipion (pi plus).

This is what I meant when I said that the difference between particles and antiparticles depends only on charge conjugation and not on parity reversal.


In a digression, I'll also point out that, at least for the neutron weak decay, the C(antimatter)P(directional preference)-reversal asymmetry is restored IF one considers the neutron and antineutron together as a single system. But I'm not sure if this is either valid under the SM, or generally recognized if it is.

Again, assuming I understand you correctly, there is no reason why that shouldn't be so under the standard model. In effect you are considering the neutron/antineutron wavefunction as a singlet state (i.e. they're entangled). The interesting thing is that the singlet of a fermion/antifermion like that would in effect have spin zero and therefore could be considered as some sort of "virtual boson" (i.e. the singlet wavefunction would be bosonic). And of course, as I mentioned above, bosons/antibosons have equal parity.


Well, what I'm arguing here is that, because we are made of matter and not antimatter, we fix a gauge, many times without acknowledging or sometimes even realizing it; the time dimension itself has no preferred direction intrinsically, but the dominance of matter in our universe has fixed the same gauge we use. This gauge is fixed oppositely for antimatter, and if the universe were predominantly antimatter, that gauge would be fixed in the opposite direction, although one could only realize that was the case (either for the dominance or the direction of the gauge) by comparing it (the universe!) with another universe (whatever THAT might mean) with the opposite dominance and the opposite gauge. And that is, to my mind, an implication of the fact that under the time reversal operation, we must also swap the charge and parity of all the particles, making them antimatter, if we wish to continue to represent charge, and time direction, as positive, and energy and mass as positive. If we reverse time, and do not reverse charge and time direction accounting, then we again wind up with negative energy. And finally, THAT implies that (for example) positrons are actually electrons with the time direction gauge fixed in the opposite fashion from normal electrons. Does that make any sense?

The current thinking as I understand it is that the arrow of time in our universe is what determined the predominance of matter, rather than the other way around! :) Yes, we can speculate that time would have to run backwards in an anti-matter universe, but the problem is that we have never experienced an instance of an anti-matter universe. So in the absence of any evidence for anti-matter universes we are literally obliged to believe that time direction is absolute. Also T symmetry (specifically T reversal symmetry) doesn't necessarily imply actual time reversal - which is I think one of the major points of contention here. And, as I already pointed out, you don't need to reverse the parity to perform matter/antimatter conjugation.


I think the basic unreality of a negative of a scalar itself answers this question; to my mind, negative mass indicates you are doing something wrong, just as when you find yourself dividing by zero.

But isn't that just "common sense" prejudice? I mean, we don't like the idea because it seems to fly in the face of "common sense", but we readily accept many things in QM and relativity that also do so. So why is this particular case any different? Look at it this way, electric charge is a scalar but we don't have any problem with accepting negative charge, do we? Also, in terms of parity transformations, pseudovectors (like angular momentum and magnetic field density) behave the same as scalars. Would we have any problem accepting negative angular momentum or negative magnetic field density?


Wow! Now that I had not heard of. I will devote some time to looking into it- but it's going to take some convincing for me to accept the validity of the negative of an absolute value (which is the mathematical meaning of the negative of a scalar).

See above.


I think it's the whole "moving in time" thing that gets everyone's back up. From the majority point of view, nothing is moving in time, either forward or backward- "particles" are actually "worms" (if you like that simile) through spacetime, with complete existence at each moment of time throughout their spacetime path from one interaction to another (quantum jitters aside). I've searched and searched for another way to describe this, and the best I've come up with is "reversed time gauge," which is difficult for anyone but a physicist (amateur or not) to follow, since most people don't know what a "gauge" is if you're not talking about the fuel in your car. ;) But if I had to pick a technical description of it, I'd have to say that's probably as unprejudicial as I've found so far.

One major part of the problem is that at the macroscopic scale, absolute temporal reversability would break many other things we consider inviolate - for example entropy.

[Schneibster]

Don't see how that saying something doesn't exist is saying it's an illusion. Surely an illusion has to be observable, and therefore exist.You mean like gravity?

Our sense of sight can see germs with the aid of a microscope. We can see that they exist.Our sense of sight can also see gravity's effects, and we can see with the aid of mathematics that they imply curvature of space. We can see it exists.

Would have thought that magnetic orbits would have had something to do with relative sizes and distances. It doesn't appear that they do.So you've never heard that the force varies as the square of the distance? Just like gravity?

The Moon moves toward and away from the Earth over 50,000 km.And...?

[ynot]

You mean like gravity?

Our sense of sight can also see gravity's effects, and we can see with the aid of mathematics that they imply curvature of space. We can see it exists.

Not sure what you're saying here. I never said that gravity was an illusion, you did. I've never disputed that gravity exists or that we can observe it's effects. I agree that math can imply curved space, but not prove it.

"We can see gravity's effects" - I agree.
"Math can imply curviture of space"- I agree.
"We can see it exists" - if you're talking about gravity's effects - I agree. If you're talking about curiture of space - I don't agree (imply ain't proof).

[Schneibster]

Not sure what you're saying here. Oh, I disagree- you understand it perfectly well, you just don't LIKE it.

I never said that gravity was an illusion, you did. I've never disputed that gravity exists or that we can observe it's effects. I agree that math can imply curved space, but not prove it. Account for it another way, or admit it's the only explanation we have that fits the facts.

[ynot]

Oh, I disagree- you understand it perfectly well, you just don't LIKE it.
LOL - "don't LIKE it". I accept many things that I don't necessarily like. About as valid as me saying that you only accept it because you "do LIKE it"

Account for it another way, or admit it's the only explanation we have that fits the facts.
Account for what in another way? Gravity or the concept of curved space? Don't see that not accepting something automatically obligates one to provide an alternative.

[Schneibster]

Some of the confusion is obviously due to us talking at cross purposes, so let me try and clear it up with some definitions that we can hopefully agree on. I think there is some confusion in the way each of us is using the term "violation".Well, a symmetry means that something stays the same over an operation; a violation of that symmetry means that it does not. When we talk about symmetries in this particular context, that of physical law, what we are discussing is the ways that physical law remains unchanged over some operation. In the case of C, P, and T, we're talking about symmetry over the reversal of these characteristics.

C-reversal symmetry implies that physical law remains unchanged over reversal of charge. Now, we know this is not the case; in order for physical law to remain unchanged if we reverse all charges, we must also reverse all parity, because of magnetism and angular momentum; and these same arguments militate against P-reversal symmetry. However, if both are reversed together, the objection disappears. This is CP-reversal symmetry. Until violations of CP-reversal symmetry were found in the neutral kaon decay, most physicists believed that CP-reversal symmetry was a manifest symmetry of nature.

Lorentz symmetry, as you state below, is still believed to be a manifest symmetry of all interactions. Any operation that can be described by a Lorentz transform does not result in any change to physical law. But it turns out that this symmetry has specific implications regarding charge, parity, and time reversal symmetries. It requires that all three of these symmetries be jointly met; in other words, it says that if all three of charge, parity, and time are reversed, then physical law remains unchanged for all interactions.

Now, this has further implications. Specifically, it implies that if a combination of two of the charge, parity, and time reversal symmetries are violated in conjunction in a single interaction, then the odd man out must also be violated to restore overall CPT-reversal symmetry. So this means that the CP-reversal symmetry violation of the kaon and beon decays implies T-reversal symmetry violation as well. In fact, it is equivalent because of this principle to state that kaon and beon decays violate CP-reversal symmetry, and that they violate T-reversal symmetry. But this also implies that these decays are CPT-reversal symmetric; the overall CPT-reversal symmetry that would be violated by CP-reversal asymmetry is restored by the violation of T-reversal symmetry. And this overall CPT-reversal symmetry also shows Lorentz symmetry, and is in fact necessary if Lorentz symmetry is to remain inviolate and a manifest symmetry of all interactions in nature.

I think I've finally got that right, and looking over what you've said, I believe we're saying the same thing- and that you're right, we were talking at cross-purposes (errors and oversights on both our parts aside).

Technically, the symmetry operations we are taking about are QM operators - they are not states, they are operations. Particles have states which undergo change under the action of these operators. Now, it is semantically meaningless to talk about "violation" of a state - states can change but only rules are violated. So a violation means that the operator does not give the expected result. If for example the charge conjugation operator is a black box and we feed "-" in, we expect "+" out. If the output has the same state as the input then the operator (the rule of the black box) has been violated.

Now, here is the confusing bit - we cannot violate a state, but we can change a rule. So change and violation are not synonymous.

Now with that in mind we can hopefully evaluate statements without getting our wires crossed!

CPT symmetry implies that all three rules are bound together. In other words, CPT is itself a "meta rule" or a composite operator. If C and P change, then T must also change if we want to maintain the symmetry of the CPT operator. This is a rule. A violation of "CPT symmetry" would imply that if C and P change, that T would not change correspondingly - like my backwards example. It is not the state of T which is violated, it is the rule that says essentially, "if X and Y then Z" that is violated.This is a bit different- but I think you're discussing specific interactions rather than classes of interactions, and I think it boils down to the same thing as I said, when you take it to the class level.

CP symmetry implies that C and P are bound together into a composite CP operator and that if C changes then P must also change and vice versa in order to maintain the symmetry of that operator. A violation of CP symmetry would be if C changed (in a process) and P did not (or vice versa).I think that's right- the operation over which the laws of physics are to remain unchanged therefore is the simultaneous reversal of charge and parity. And if this symmetry is manifest, it also allows us to conclude that the particular laws in question are also time-reversal symmetric.

In the context of the discussion, and to sum up, CP violations have been observed, however no CPT violation has ever been observed. A CPT violation (should one occur) would also break the symmetry of Lorentz transformations, however a violation of Lorentz transformation symmetry wouldn't necessarily cause a CPT violation.I believe all of this is correct.

A CP violation can be "fixed" by a corresponding change in T, so to be strictly correct, a CP violation implies a change in T. It does not imply a violation of T (I know some physicists say that, but it's not semantically correct - because you're talking about the meta rule of CPT transformation, not the T operator itself) - remember that operators are sequential. The rule is, that if C and P change, then T must change, so there is no violation (of the CPT meta rule). The same applies in reverse - a T violation can be fixed by a change in both C and P. The operation is symmetrical overall so in that sense CP is equivalent to T (specifically under CPT symmetry - if CPT symmetry were to be violated then of course CP would no longer be equivalent to T.) And we can also say that a CP violation is equivalent to a T violation because either requires reversal of the whole of the CPT operator in order to maintain CPT symmetry.The thing about these three operators is that they are not continuous transformations- they are reversals. That is, there are two charges, two parities, and two time directions. So when you say "change in T," you're talking specifically about the reversal of time direction, not just a change in location in time for an event. And this reversal must accompany a CP-reversal symmetry violating interaction, to "patch" it and maintain CPT-reversal symmetry. I'll talk about how this relates to the point I'm working on in a minute.

"C symmetry" means that the models which describe the behaviour of the the system would still be valid if all the internal quantum numbers of the particle were reversed (and obviously it doesn't only mean charge, because neutral particles can undergo "charge" conjugation, i.e. the neutron and anti-neutron.

"P symmetry" means that the models which describe the behaviour of the the system would still be valid if we reversed all the spacial coordinates i.e. if we made a "left handed" upright system into a "right handed" upside down system.

"T symmetry" means that the models which describe the behaviour of the the system would still be valid if we could reverse the flow of time.All three of these have discrete values, and technically you should be talking about C- or P- or T-reversal symmetries.

"Lorentz symmetry" means that the models which describe the behaviour of the the system would still be valid if we subjected the system to a Lorentz transformation.This is a continuous transformation, and thus not necessarily reversal symmetric; in other words, there are more transforms than simple reversal involved.

T symmetry does not necessarily imply that time has actually reversed or that a system is travelling backwards in time, all it means is that the model we have for the system would continue to work if it were possible for us to run time backwards. Similarly, a T violation would mean that the model we have for the system would not continue to accurately describe the system if it were possible for us to run time backwards. Neither says anything about the actual possibility of running time backwards, or that it ever has in any particular instance. T symmetry is just a mathematical operator over the wavefunction.Well, this is where I'm not so sure I agree. But it's tied up with the previous point on T-reversal and CP-reversal symmetry violation, and there's yet more material related to it below, so I'll wait again.

I don't understand what you mean by a P violation in the opposite sense. Spin is not affected by P reversal if that helps any.Now we start to get down to it. Here's what I mean:

For there to be a P-reversal symmetry violation in a particular interaction, there must be some feature of that interaction that is not spatially symmetric. When the parity is reversed, in other words, the reversed-parity interaction must be distinguishable from the normal-parity interaction for there to be a parity reversal symmetry violation. In the case of the weak decay of the neutron, this has been experimentally shown to be the case; there is a statistical preference for the electron and antineutrino produced by beta decay to go in a particular direction relative to the spin axis of the neutron. Weak decay in neutrons is therefore a P-reversal symmetry violating interaction. When I say that antineutrons show the P violation in the opposite sense, what I'm saying is that antineutrons also decay by a weak interaction, and if their spin axes are lined up, they show their P asymmetry in the opposite direction from the neutrons.

Now this is a particularly interesting case, because we cannot differentiate between neutrons and antineutrons by their charge- they are neutral. Thus, the only differentiating factor (other than their quark-vs.-antiquark makeup) is their parity. And reversal of that parity yields apparent conversion of the particle into the antiparticle, since the direction preference of their parity-violating interaction is reversed, and is among their only directly discernable characteristics.

In the case of the neutron (which is a fermion), the anti-neutron decay is opposite to the neutron decay - so yes, any directional preference will be reversed. Yes. We agree on this point, and that's what I meant by "P violation in the opposite sense."

But this is just CP symmetry, unless I completely misunderstand what you're trying to say. Well, since the neutron is two ups and a down, and the antineutron is two antiups and an antidown, I have to agree with you that it is a simultaneous reversal of charge and parity, but I also note that the two are asymmetric: one is matter, and one is antimatter. And the only way to "patch" the overall CPT-reversal symmetry is to reverse T as well.

Here's the really interesting part: how could we ever tell that T was reversed? The answer is, we can't, other than to note that C and P were reversed, and that CPT-reversal symmetry requires that T be reversed. What does this mean in real terms? Nothing, really- it just means that antiparticles can be interpreted as particles with their "directionality" in time reversed. It is our perception- based in thermodynamics- that causes us to see a "direction in which time increases," rather than a continuum of time coordinates with the particle occupying different positions in space- and this perception also causes us to perceive that particles and antiparticles are different, rather than the same thing with the gauge pointed thisaway or thataway.

Most illustrative is the fact that two different observers can see the same set of events as involving a particle, or an antiparticle, depending on their states of motion relative to the events. That this can happen at all is due to the uncertainty principle; because of the uncertainty of position and momentum, a particular particle can be observed by one observer to move just outside the light cone, or at least for there to be uncertainty whether it did or not, whereas for the other observer it is firmly within the light cone. This is only possible because of the conjunction of relativity and quantum uncertainty; thus, we can interpret this to mean that antiparticles are the result of the dual facts that our universe is relativistic, and our universe is quantum mechanical. And we finally observe that this T-reversal is accompanied by C- and P-reversal, thus preserving CPT-reversal symmetry, and Lorentz symmetry.

An example of an asymmetrical particle/antiparticle response would of course be a CP violation, and in that case the neutral Kaon and of course the Beon would fit.And in turn imply a T-reversal violation, or at least a time-reversed interaction that results in the CP-reversal violation.

In case we're talking past each other again, let me be more specific about what I meant when I said that antiparticles do not necessarily have to be P reversed from their corresponding particles. The simplest example is the difference between fermions and bosons. The antiparticle of any fermion is automatically parity reversed from the particle. But in the case of bosons, the antiparticle has matching parity with the corresponding particle. A good example of the latter is the "normal" pion (i.e. the pi minus) which has the same parity as the antipion (pi plus).I actually see this somewhat differently. In my opinion, the bosons are parity-reversed too; it's just that you can't distinguish a reversed parity boson from a normal parity boson, just as you can't distinguish a reversed time particle from a normal time antiparticle.

This indistinguishability in fact results in the laws of spin and statistics; because the normal and reversed parity bosons cannot be distinguished from one another, their spin amplitudes cannot annihilate if they are linearly superposed, and the two operators' amplitudes add to one another in the interference term, and increase the probability (gotten by squaring the amplitude, of course) of two bosons occupying the same quantum state; on the other hand, because the normal and reversed parity fermions CAN be distinguished, their spin amplitudes cancel one another out if they are linearly superposed, resulting in no interference term, and this would result in the annihilation (i.e. zero probability) of spin angular momentum (and violation of conservation of angular momentum) if they were to occupy the same state. Fermions therefore obey the exclusion principle, and form matter with discrete states and/or positions; whereas bosons collect together in the same state and position and form forces.

This is what I meant when I said that the difference between particles and antiparticles depends only on charge conjugation and not on parity reversal.I understand now why you said it, but because of the fact that it is impossible to distinguish even-parity spin angular momenta from their parity-reversed counterparts, I believe that you cannot prove it, and in fact that the laws of spin and statistics militate against this interpretation.

Again, assuming I understand you correctly, there is no reason why that shouldn't be so under the standard model. In effect you are considering the neutron/antineutron wavefunction as a singlet state (i.e. they're entangled). The interesting thing is that the singlet of a fermion/antifermion like that would in effect have spin zero and therefore could be considered as some sort of "virtual boson" (i.e. the singlet wavefunction would be bosonic). And of course, as I mentioned above, bosons/antibosons have equal parity.I don't insist on it. But it is interesting.

The current thinking as I understand it is that the arrow of time in our universe is what determined the predominance of matter, rather than the other way around! :) Yes, we can speculate that time would have to run backwards in an anti-matter universe, but the problem is that we have never experienced an instance of an anti-matter universe. So in the absence of any evidence for anti-matter universes we are literally obliged to believe that time direction is absolute. Well, certainly the "direction" we "experience time flowing" seems so; but that looks to be more a matter of thermodynamics, possibly due to initial conditions, than anything to do with the laws of physics, which seem pretty symmetric.

Also T symmetry (specifically T reversal symmetry) doesn't necessarily imply actual time reversal - which is I think one of the major points of contention here. And, as I already pointed out, you don't need to reverse the parity to perform matter/antimatter conjugation.Well, actually I question the ability to measure time reversal, and I question the ability to measure parity reversal in the instances you specify in arguing against it.

It's possible to get really turned around in this conversation, and wind up thinking that either it is possible that, or that I might be maintaining that it is possible that, time reversal is possible. In fact, I don't think it is; I think it would violate mass/energy conservation to be able to cause particles to reverse their "time gauge." In addition, the geometric (hyperbolic) interpretation of the Lorentz transform implies that such a rotation is impossible, because one would have to perform a timewise (i.e., x-t, y-t, z-t plane rotation, as opposed to our more familiar x-y, x-z, y-z rotation planes) rotation though an angle that, in hyperbolic geometry, would be infinite. The result of such a rotation would be a negative angle, which is equally meaningless.

But isn't that just "common sense" prejudice? I mean, we don't like the idea because it seems to fly in the face of "common sense", but we readily accept many things in QM and relativity that also do so. So why is this particular case any different? This isn't "common sense." The things in QM and SR and GR that contradict common sense, do not contradict how mathematics works. In fact, when you look closely enough what you discover is that common sense is what is contradicting math! Because of this, I feel that when I am told or read or find something that contradicts my experience, I'm more likely to believe it than I am to believe something that contradicts how math works. I've come across too many things that contradict my intuitive notions of how the universe works that were true, and too many things that contradict how mathematics works that were false, for this not to be the case.

Look at it this way, electric charge is a scalar but we don't have any problem with accepting negative charge, do we? That's because the electromagnetic force is represented by the unitary group of dimension one. Groups with odd dimensionality have anticharges; groups with even dimensionality do not (unless their symmetry is broken, as with the weak charge).

Also, in terms of parity transformations, pseudovectors (like angular momentum and magnetic field density) behave the same as scalars. Would we have any problem accepting negative angular momentum or negative magnetic field density?Negative angular momentum has acceptable physical meaning; I'm not so sure about negative magnetic field density. On the other hand, if gravity is mediated by a spin-two boson, it must be represented by a special unitary group of even dimension; and that would mean that it has no anticharge, rendering negative mass as meaningless as dividing by zero.

I'll guess that it is possible, if gravity turns out to either be the result of a broken symmetry, or turns out to be represented by a symmetry group of odd dimension; but I'm conservative, so not having seen any negative mass, or any sign of mesoscopic antigravity, I'll have to reserve judgement. Dark energy certainly has my attention, however.

One major part of the problem is that at the macroscopic scale, absolute temporal reversability would break many other things we consider inviolate - for example entropy.I agree- I don't think it's possible. I think that the rotation of the time gauge for a particle is impossible to perform. On the other hand, I think it's possible to create particles of either gauge, and that we see ones that share the majority gauge of the matter in our universe as "matter" and the ones that have the opposite gauge as "antimatter," and that all of the conservation laws and so forth dictate that when (for example) a matter particle with a positive electric charge is created, an antimatter particle with a negative charge must be created simultaneously, unless a matter particle with positive electric charge was destroyed. And so forth.

I'm pretty sure that none of what I speculate on (I'd hardly go so far as to say I believe it) contravenes any known laws of physics. As far as I know, the gravitational potential of antimatter has never been measured, either, so there's no reason for me to assert that your speculation about negative mass is out of order either, nor would I be out of order to suggest that negative mass might be a property of antimatter. I have more trouble with it, but as far as I know it doesn't contradict anything we have measured.

Last but not least, there is a final little twist to all of this. I did a lot of research into the CKM matrix and how the quarks convert into one another by the weak interaction (yes, I know it's quark superpositions converting to other superpositions, but you get the idea). As far as I can tell, and you might know different, the CKM matrix only specifies the amplitudes for the quark-converting weak interactions; not for the antiquark-converting weak interactions. If this is true, then it implies that there might be a CPT-reversed version of the neutral kaon decay; and if this is true, then the possibility exists that the beginning of the universe actually made two universes, one dominated by matter and the other by antimatter, which then evolved with opposite time gauges from that temporal location. If it is not, then that might indicate the existence of a true time reversal symmetry violation in physics, which would account for the existence of only one, matter-dominated universe. This might stem from a symmetry breaking in the early universe, which led to an imbalance between the quarks and the antiquarks; however, even the combination of neutral beon and neutral kaon aren't sufficient (unless someone's found something I haven't heard about) to create more than a few percent of the imbalance we see in the time we think there was. Conundrums therefore remain, in either case.

[Schneibster]

Account for what in another way? Gravity or the concept of curved space? Don't see that not accepting something automatically obligates one to provide an alternative.Gravity, of course. No, but if you don't I'm not going to bother with you any more.

[ynot]

Gravity, of course. No, but if you don't I'm not going to bother with you any more.
Gravity seems to be an attractive force that is inherent in all matter. The more matter, the stronger the force and the affect of gravity is diluted by distance.

However, since you have thrown out the challenge, let me brainstorm an alternative. Rather than being an attractive force, let’s consider gravity more as a repulsive force. Lets say that expanding space is the force behind gravity. Space is continuously expanding and exerting a pushing force on matter. Matter somehow weakens the pushing strength of space at a local level and causes a local weak area around the matter. The size of the weak area is related to the amount of matter. Any matter that enters the weak area of other matter is pushed in to that weak area by the force of expanding space. What do you think . . . too repulsive? (only represents 15mins brainstorming)

Whether you “bother” with me anymore is obviously your choice. As I’ve said in the past, I value and appreciate your contributions and have found them very informative and helpful. If you chose not to bother with me any more . . . have a nice New Year

[Ben Tilly]

Using GR and SR to explain curved space to a person that doesn’t accept GR and SR, is about as fruitless as a Theist using the Bible to explain a God to an Atheist that doesn‘t accept the Bible. I’ve often asked Theists to explain their belief without using the Bible. Unfortunately I’ve yet to meet one that can or will. I suspect the same might apply in the case of curved space, given that it seems to be totally founded on GR and SR. When considering the points I’m trying to make, I’m asking that you put aside all thoughts of GR and SR. Not abandon them forever, just put them aside briefly. Not so much to suspend you disbelief, but to suspend your belief (sorry, that should be knowledge of course). Without GR and SR, relative motions, distances and speeds of objects will still present perception anomalies to an observer, but in what way will they have any affect on the actual objects?

Saying that you wish to discuss complex relativistic effects while discounting all thoughts of GR and SR is like saying that you wish to discuss the budget but you're unwilling to use accounting to do it.

Well here is a simple effect. If you put 3 satellites around a heavy object and have them make a triangle with lasers, the sum of the angles will not add up to 180 degrees.

Within the context of the theory of relativity this implies that space is curved. Outside of that theory it is a fact of uncertain interpretation. This should be of no surprise - it is well-known that no fact can be interpreted except from within the context of a theory.

Now it may be that some day we come up with an explanation of gravity that accounts for all of the known facts and does not require curvature. I admit that this is possible. However our best current theories require curvature. And we have pretty good evidence for those theories. So my belief is that future theories will continue to involve curvature of some kind.

Like all of science, that is not certain. But it is the best we can do.

Cheers,
Ben

[ynot]

Saying that you wish to discuss complex relativistic effects while discounting all thoughts of GR and SR is like saying that you wish to discuss the budget but you're unwilling to use accounting to do it.
There are many different methods of accounting, I may use one method to discuss the budget but discount another. But you’re right, and so are the Theists. Just as their religion is based on the Bible, the concept of curved space is based on GR and SR, and it’s appropriate to discuss something on whatever it‘s based on. I guess what I’m trying to do by asking that GR and SR be put to one side for a moment is to go back to their roots. Relative motions, distances and speeds of objects have always presented perception anomalies to an observer, independently of GR and SR. I’m suggesting that perhaps, what is essentially an optical illusion, is being mistakenly interpreted as a reality.

I also said in post #114 “The biggest problem I have with all this is that I don’t think most of the leading brains of the world are idiots, In other words, if were a betting man, I would have to bet against my own argument.”

Well here is a simple effect. If you put 3 satellites around a heavy object and have them make a triangle with lasers, the sum of the angles will not add up to 180 degrees.

Within the context of the theory of relativity this implies that space is curved. Outside of that theory it is a fact of uncertain interpretation. This should be of no surprise - it is well-known that no fact can be interpreted except from within the context of a theory.
Gravity has an attractive effect on matter, why not also light? In other words, the trajectory of light is altered (curved) as it passes through gravity. Why does it have to be that space is curved?

Now it may be that some day we come up with an explanation of gravity that accounts for all of the known facts and does not require curvature. I admit that this is possible. However our best current theories require curvature. And we have pretty good evidence for those theories. So my belief is that future theories will continue to involve curvature of some kind.

Like all of science, that is not certain. But it is the best we can do.

Cheers,
Ben
That’s fine, but it’s not usually presented that way. More often seems to be “this is so, this is proven, this is actual, factual, etc”

Cheers back

[Schneibster]

There are many different methods of accounting, I may use one method to discuss the budget but discount another. Problem is, you dismissed mine, and when I asked you to provide another, you said:
Don't see that not accepting something automatically obligates one to provide an alternative.Now, I don't know of an alternative, and if you don't, then we can either discuss it in the framework of relativity, or we can NOT DISCUSS IT. Your choice, friend.

[ynot]

Problem is, you dismissed mine, and when I asked you to provide another, you said:
Now, I don't know of an alternative, and if you don't, then we can either discuss it in the framework of relativity, or we can NOT DISCUSS IT. Your choice, friend.
My intent or purpose is not annoy and frustrate you (or anyone else), and I‘m sorry that this seems to be the case. I’m not always very good at expressing my thoughts, and it sometimes takes me a while to define exactly what I’m on about, even to myself.

Did you read the text immediately following the bit you quote (“But you’re right . . .etc.”) where I conceded that it was unreasonable and inappropriate of me to expect people to discuss their belief without using and referring to whatever the belief is founded on? (if the word belief upsets you, replace it with knowledge).

Did you also read the text where I explained that what I’m questioning is the basis on which Relativity has been founded? In other words, is Relativity relevant? Seems to me the best way of doing this is to wipe the slate clean (suspend your current belief/knowledge) and start again from the beginning without prejudice. I suspect that you may have no interest in doing this, and that you’re very happy to accept that the building blocks of Relativity are strong and valid.

For anyone who might be interested - Perception anomalies have been around forever and can be observed, explained and understood without Relativity. It seems to me that the very seed of Relativity came from observed perception anomalies, and what is essentially an optical illusion, is being mistakenly interpreted as a reality. - Any comments?

[lenny]

However, math has a unique ability to describe things that are outside our experience, that we cannot accurately imagine, and do so accurately.

do you mean usefully? or accurately (as with mathematical precision)?

No. I OBSERVE that it is. ... Honestly, saying you don't "trust" mathematicians is like saying you don't "trust" the sky is blue. WALK OUTSIDE AND CHECK FOR YERSELF.

i think i could check that the sky was blue (it happens to be dark here); i have an empirically adequate means of seeing the sky as blue, sometimes white, currently black. but how do you suggest one might go about checking that Reality was described with mathematical precision by mathematics?

you argue like a physicist, taking resemblances to imply isomorphism; specific successes to imply general Truth, and diving into (interesting, fun, exciting) details of theory laden examples while overlooking the history of physics.

do you really believe mathematics governs/describes everything?

[ynot]

I’ve been trying to understand the “light clock” experiment where a blip of light bounces vertically between two mirrors, and I think it may be a good example of my “perception is wrongly being used as reality” theory.

The story as I understand it . . .
In the beginning, two synchronised light clocks have uniform motion (are stationary to each other), and each clock observes that the other always shows the same time. If the clocks are not in uniform motion however, and they are moving relative to each other (at a right angle to the bouncing blips), each clock will observe that the blip in the other clock is not only bouncing vertically between the mirrors, but it’s also moving horizontally to the bouncing motion. This means that each clock perceives that the blip in the other clock is moving in saw-toothed motion and that the distance that the blip has to travel from mirror to mirror is now longer. As the speed of the blip remains the same, it’s concluded that it must take the blip longer to reach the mirrors and consequently the clock must be running slower.

I think this conclusion is wrong. There are two separate and independent motions that are occurring simultaneously. Just as a blip can bounce vertically without moving horizontally, it can also move horizontally without bouncing vertically. Neither motion is dependant on the other and neither effects the other. To say that a combination the vertical and horizontal distances travelled by the blip is the distance between the mirrors is incorrect. The actual distance between the mirrors never changes and neither does the distance that the blip has to travel. Perception makes the mistake of combining the motions.

Imagine that clock A is spinning on a stationary axis, and that clock B is orbiting clock A on the same axis, and at exactly the same speed of the spin. If clock A was totally unaware that it was spinning, and that clock B was orbiting, it would incorrectly assume that they were both in uniform motion. Would clock A still perceive that clock B was running slower?

Lenny - Thanks for your comments

[Schneibster]

My intent or purpose is not annoy and frustrate you (or anyone else), and I‘m sorry that this seems to be the case. I’m not always very good at expressing my thoughts, and it sometimes takes me a while to define exactly what I’m on about, even to myself. Fair enough. Please note most carefully that to someone who has been studying this stuff for thirty or more years, frustration sets in when you make claims based on lack of knowledge about the underpinnings of the research. It would be very helpful if you'd do enough research yourself to find out that what's being claimed isn't being claimed baselessly- there are excellent reasons for using the theories we use. And a great deal of material, some of which you have seen here and some of which you have seen a link to, by the creator of this theory, that you can read for free.

Did you read the text immediately following the bit you quote (“But you’re right . . .etc.”) where I conceded that it was unreasonable and inappropriate of me to expect people to discuss their belief without using and referring to whatever the belief is founded on? (if the word belief upsets you, replace it with knowledge).I object to use of "belief" because I've taken the trouble to do the research so that I don't have to believe anything. Use of the word "belief" in this context denigrates the long-term effort I have made and continue to make to understand what the heck it is all them physicists are talkin about, and the further effort I've made to try to make this stuff more accessible for you. This isn't a belief system. It's all based on what we see, and any of it that doesn't accurately describe (and predict!) is discarded. As long as the current theory continues to hold sway, that means no one has found an experiment that contradicts it. Up to and including the Gravity Probe B mission, for which the data analysis should be available in the Spring of '07. That it is a current theory means that it explains or postdicts everything we see; no one has come up with a previous observation that contradicts it. That's what it means to be a theory of physics.

Did you also read the text where I explained that what I’m questioning is the basis on which Relativity has been founded? In other words, is Relativity relevant? Seems to me the best way of doing this is to wipe the slate clean (suspend your current belief/knowledge) and start again from the beginning without prejudice. I suspect that you may have no interest in doing this, and that you’re very happy to accept that the building blocks of Relativity are strong and valid.I accept them because:
a) They explain what we see. In detail. They have also repeatedly correctly predicted new observations that no one had ever bothered to make before.
b) No one has another explanation of the facts that explains as many of them, much less that has the predictive/prescriptive power of GR and SR.

You are treating this like these theories are isolated from reality somehow, like they don't dovetail with long-term, detailed, well-documented observation and experimentation. Let me say it again: there is no competing theory, that explains what relativity explains, that predicts what relativity predicts, and that doesn't conflict either with known experimental results or with other known facts. Relativity is what we have, and not only that but it is one of the two most successful scientific theories in the history of the world.

If you want to know what it says, then I'll do my best to tell you. If you want to propose it's wrong, and you don't have an alternative, I'm not really very interested. If you want to question whether the math it uses represents actual features of reality, I think that's valid- and I'm willing to discuss it. And that's what you said here. But when you refer to relativity, I think you need to have a much more realistic view of what it is you're talking about; hopefully the above will give you some idea of why so many people who know so much think so much of it. It's not because they "believe" it. It's because they USE it and it WORKS.

For anyone who might be interested - Perception anomalies have been around forever and can be observed, explained and understood without Relativity. It seems to me that the very seed of Relativity came from observed perception anomalies, and what is essentially an optical illusion, is being mistakenly interpreted as a reality. - Any comments?
Yes. "Perception anomalies" aren't explained by relativity. That's not what it's for. Relativity explains the reasons for MEASUREMENTS. It PREDICTS MEASUREMENTS that weren't made before, and does so correctly. It isn't about perception. It's about careful, thorough, detailed experimentation, and measurement of the results. If you haven't figured out yet that what you perceive is only about half right, and that half is only about a tenth of a percent of what's really going on, you need to pay more attention. So much for perception.

[Schneibster]

do you mean usefully? or accurately (as with mathematical precision)?What do you mean by "usefully?" When I say "accurately," I mean that when you calculate what's going to happen using relativity, then go measure it, that's what happens. Precision tells the amount of detail a measurement gives; accuracy is how close the prediction is to the measurement.

but how do you suggest one might go about checking that Reality was described with mathematical precision by mathematics?Simple. Do the math. Make a prediction. Run an experiment and measure the results. See how close they are to the prediction. If they are really close, then you've got an accurate theory. If not, then not.

you argue like a physicist, taking resemblances to imply isomorphism; specific successes to imply general Truth, and diving into (interesting, fun, exciting) details of theory laden examples while overlooking the history of physics.

do you really believe mathematics governs/describes everything?It describes everything we can measure with any precision. Accurately describes it, in fact. Much moreso than our perceptions do. And it describes things that we cannot perceive, and even things that we cannot either clearly and unambiguously imagine or describe with any other language. And it does so accurately. And we can measure the results. And friend, if you can't measure it, it ain't worth talkin about as far as physics goes.

Does it describe dreams? Subjective experiences? Acid trips? Probably not. We don't know enough about ourselves to use it that way. But physics, that is, the constitution, composition, and behavior of the world around us? You bet your sweet patootie it does- if you think not, you better go look your iPod over again. Works pretty good, huh? Now, how do you suppose that is? Magic?

[Schneibster]

I’ve been trying to understand the “light clock” experiment where a blip of light bounces vertically between two mirrors, and I think it may be a good example of my “perception is wrongly being used as reality” theory. It's not.

The story as I understand it . . .
In the beginning, two synchronised light clocks have uniform motion (are stationary to each other), and each clock observes that the other always shows the same time. If the clocks are not in uniform motion however, and they are moving relative to each other (at a right angle to the bouncing blips), each clock will observe that the blip in the other clock is not only bouncing vertically between the mirrors, but it’s also moving horizontally to the bouncing motion. This means that each clock perceives that the blip in the other clock is moving in saw-toothed motion and that the distance that the blip has to travel from mirror to mirror is now longer. As the speed of the blip remains the same, it’s concluded that it must take the blip longer to reach the mirrors and consequently the clock must be running slower.So far, so good. Before we go on, let me point something out:

Imagine you are standing on a platform, watching a train go by. The train has a floor-to-ceiling window in it, and standing in that window is a person holding a ball. Just when you can first see them, they drop the ball, and it falls to the floor.

What path do you see the ball take?

OK, now what path does the person who dropped it see it take?

OK, now the hard part: WHICH ONE IS RIGHT?

Get it?

I think this conclusion is wrong. There are two separate and independent motions that are occurring simultaneously. Just as a blip can bounce vertically without moving horizontally, it can also move horizontally without bouncing vertically. Neither motion is dependant on the other and neither effects the other. To say that a combination the vertical and horizontal distances travelled by the blip is the distance between the mirrors is incorrect. The actual distance between the mirrors never changes and neither does the distance that the blip has to travel. Perception makes the mistake of combining the motions. So explain that to the guy on the train who sees the ball fall to the floor in a straight line, just like every other ball he's ever dropped. And then tell me why you see that straight line as a parabola. Go ahead, I'm waiting.

And by the way, those two observations are PRECISELY what relativity predicts.

Imagine that clock A is spinning on a stationary axis, and that clock B is orbiting clock A on the same axis, and at exactly the same speed of the spin. If clock A was totally unaware that it was spinning, and that clock B was orbiting, it would incorrectly assume that they were both in uniform motion. Would clock A still perceive that clock B was running slower?Clock A cannot be unaware it is spinning. Spinning involves acceleration, constant acceleration in fact, and acceleration is absolute- the theory of relativity is misnamed, and Einstein himself said so- it should be the "theory of invariance." Many people who are unfamiliar with it misunderstand what it says. It says that UNACCELERATED motion is relative, but ACCELERATION is absolute. You can always tell if you are accelerating because you feel forces. In fact, BOTH clocks would feel acceleration, and as a result both would run more slowly than another clock that was stationary relative to the point clock A was revolving around, and clock B was rotating around. Which would run slower would depend on how much acceleration each was experiencing.

And again, all of this is precisely as relativity predicts.

[ynot]

Fair enough. Please note most carefully that to someone who has been studying this stuff for thirty or more years, frustration sets in when you make claims based on lack of knowledge about the underpinnings of the research. It would be very helpful if you'd do enough research yourself to find out that what's being claimed isn't being claimed baselessly- there are excellent reasons for using the theories we use. And a great deal of material, some of which you have seen here and some of which you have seen a link to, by the creator of this theory, that you can read for free.

I object to use of "belief" because I've taken the trouble to do the research so that I don't have to believe anything. Use of the word "belief" in this context denigrates the long-term effort I have made and continue to make to understand what the heck it is all them physicists are talkin about, and the further effort I've made to try to make this stuff more accessible for you. This isn't a belief system. It's all based on what we see, and any of it that doesn't accurately describe (and predict!) is discarded. As long as the current theory continues to hold sway, that means no one has found an experiment that contradicts it. Up to and including the Gravity Probe B mission, for which the data analysis should be available in the Spring of '07. That it is a current theory means that it explains or postdicts everything we see; no one has come up with a previous observation that contradicts it. That's what it means to be a theory of physics.

I accept them because:
a) They explain what we see. In detail. They have also repeatedly correctly predicted new observations that no one had ever bothered to make before.
b) No one has another explanation of the facts that explains as many of them, much less that has the predictive/prescriptive power of GR and SR.

You are treating this like these theories are isolated from reality somehow, like they don't dovetail with long-term, detailed, well-documented observation and experimentation. Let me say it again: there is no competing theory, that explains what relativity explains, that predicts what relativity predicts, and that doesn't conflict either with known experimental results or with other known facts. Relativity is what we have, and not only that but it is one of the two most successful scientific theories in the history of the world.

If you want to know what it says, then I'll do my best to tell you. If you want to propose it's wrong, and you don't have an alternative, I'm not really very interested. If you want to question whether the math it uses represents actual features of reality, I think that's valid- and I'm willing to discuss it. And that's what you said here. But when you refer to relativity, I think you need to have a much more realistic view of what it is you're talking about; hopefully the above will give you some idea of why so many people who know so much think so much of it. It's not because they "believe" it. It's because they USE it and it WORKS.

Yes. "Perception anomalies" aren't explained by relativity. That's not what it's for. Relativity explains the reasons for MEASUREMENTS. It PREDICTS MEASUREMENTS that weren't made before, and does so correctly. It isn't about perception. It's about careful, thorough, detailed experimentation, and measurement of the results. If you haven't figured out yet that what you perceive is only about half right, and that half is only about a tenth of a percent of what's really going on, you need to pay more attention. So much for perception.
Thanks - You (and some other members) should also note most carefully that this is not an academic forum per se. I’m sure many such forums exists and they may suit you better. Many JREF forum members are both chronologically and academically young. All one can hope to do is mature in both regards, but we are all what we are at the time. I suspect that many forum members think similar thoughts to those I express, but are hesitant to expose them on this forum due to the sometimes vitriolic and derogatory responses that are sometimes received. As far as I‘m concerned, this only applies to you very slightly, and overall I‘ve found your responses to be considerate and helpful.

I would prefer “limited knowledge“ rather than “lack of knowledge“. We all have limited knowledge, it’s just a matter of degree. You seem to imply that I haven’t put any time or effort at all in to learning about relativity. I have, but unfortunately I really don’t have much spare time to devote to it. In the mean time my mind doesn’t stop asking questions. I won’t waste our time by debating the semantics of “belief”. As I said, any time I use it, replace it with “knowledge“. My first hurdle with Relativity is to prove to myself that it‘s founded on a valid basis (I won’t accept it on faith). Until I do this, I don’t see that I can move on. Given the length of time the theory has been around, and the many clever minds that have scrutinised it, I expect that one day the penny will drop and I will go “AH-HA!”. Until that day arrives however, I have to go “Yeah But!“.

[Schneibster]

Thanks - You (and some other members) should also note most carefully that this is not an academic forum per se. I’m sure many such forums exists and they may suit you better. As a matter of fact, they are generally so far into it that they aren't worth it unless you're making a career out of it. I'm actually trying to practice at explaining things; the more I do it, the better I get, I find. So hopefully you'll get as much benefit from it as I do. Meanwhile, I certainly don't know it all, and I regularly meet up with folks who know more than I do both here on JREF and at some other places I hang out. I try to learn then.

Many JREF forum members are both chronologically and academically young. All one can hope to do is mature in both regards, but we are all what we are at the time. I suspect that many forum members think similar thoughts to those I express, but are hesitant to expose them on this forum due to the sometimes vitriolic and derogatory responses that are sometimes received. As far as I‘m concerned, this only applies to you very slightly, and overall I‘ve found your responses to be considerate and helpful. I'm glad to hear that. I am also grateful that I made the effort to edit before I posted. Trust me that you are too. :D

I don't mind sharing, and I don't mind going out of my way a fair bit; that has to be clear to you. Remember that the stupidest question is the one you didn't ask.

You get, by the way, a fair bit of cred from me for this post. It took some courage, and I compliment you.

I would prefer “limited knowledge“ rather than “lack of knowledge“. We all have limited knowledge, it’s just a matter of degree. It's not meant in a denigrating fashion; you can fix lack of knowledge just by going and getting some. Just like I did. What I was denigrating was your (to my perception) attempting to theorize about pretty much the most advanced area of science we have, without knowledge that I knew well before I entered secondary school. And a fair bit of that knowledge was in the basic science class that everyone had to pass to graduate.

You seem to imply that I haven’t put any time or effort at all in to learning about relativity. I have, but unfortunately I really don’t have much spare time to devote to it. Then pardon me; it doesn't seem to me that you have, that is of course a relative judgment.

I think my point got lost a little bit, too: it's that there is more to this stuff than it seems you have been exposed to before now. I think you would benefit enormously from taking the time to suck down a few really good books. I would encourage it. Strongly. If you can read a book in a month, you can be doing very well in a year. And I think you're wasting your mind if you don't; as I indicated elsewhere, your questions indicate a good mind with a pretty honed intuition of the right places to start asking questions. That the answers are obvious to someone like me doesn't make those questions stupid; what irritates is when you get an answer, and instead of trying to understand why that's the right answer, you reject it.

In the mean time my mind doesn’t stop asking questions. If you'll take my advice, you won't ever. I certainly never have.

I won’t waste our time by debating the semantics of “belief”. As I said, any time I use it, replace it with “knowledge“. The issue isn't the use of the term; it's the attitude that underlies it. It is a pervasive attitude in our culture, and one I find highly offensive (not to mention not merely arrogant but stupidly so). I do not assert that you in particular hold this attitude; but you should be aware that by using that term in this particular situation, you identify yourself as a member of a group the majority of whom do. I think this may start to show you some of the reasons why you got some of the responses from others a bit back that you did; my perception that you are capable of "being better than that," whatever that might mean, was why I defended you in that instance.

I think you might want to consider using a different term. It appears that I am by no means the only one to find it offensive in precisely that manner.

My first hurdle with Relativity is to prove to myself that it‘s founded on a valid basis (I won’t accept it on faith). Until I do this, I don’t see that I can move on. Given the length of time the theory has been around, and the many clever minds that have scrutinised it, I expect that one day the penny will drop and I will go “AH-HA!”. Until that day arrives however, I have to go “Yeah But!“. Here's a tip: it WORKS. Suppose you wanted to learn to fix electronics equipment. What would you do? Try to invent your own theory of how it works, or find a book, or a person, who can show you? Well, unless you wanna get zapped and burned a bunch, and burn up a lot of expensive stuff, with accompanying nasty smells and occasionally hair-raising personal risks, I'd kinda recommend the second course. Now, you have heard enough to know that relativity is the dominant paradigm just now, at least in terms of describing the shape of space and how gravity works and so forth. I suggest that you should go a fair bit further into it, as far as you can without math, before you conclude that you can't understand it.

And I'll tell you a secret (really, not much of one, but hey, whadda ya want?): people like me remember our "Ah-HA!" moments, treasure them in fact, and the only thing that comes close is watching someone else have one. That is not common. So don't think you're just wasting my time; if you wanna know, ask. But grow some gumption, too: do some reading.

[ynot]

What path do you see the ball take?.
I see a combination of both the horizontal motion of the ball travelling with the train and the vertical motion of the falling ball. I see a combination of two independent motions occurring simultaneously.

OK, now what path does the person who dropped it see it take?
The guy on the train sees the vertical motion of the ball falling.

OK, now the hard part: WHICH ONE IS RIGHT?
Both!

Get it?
I think so. But I wonder if you do.

So explain that to the guy on the train who sees the ball fall to the floor in a straight line, just like every other ball he's ever dropped. And then tell me why you see that straight line as a parabola. Go ahead, I'm waiting,
Because I see a combination of two independent motions occurring simultaneously, and he see only sees one motion.

And by the way, those two observations are PRECISELY what relativity predicts.
It's also what I would PRECISELY predict without Relativity.

Clock A cannot be unaware it is spinning. Spinning involves acceleration, constant acceleration in fact, and acceleration is absolute- the theory of relativity is misnamed, and Einstein himself said so- it should be the "theory of invariance." Many people who are unfamiliar with it misunderstand what it says. It says that UNACCELERATED motion is relative, but ACCELERATION is absolute. You can always tell if you are accelerating because you feel forces. In fact, BOTH clocks would feel acceleration, and as a result both would run more slowly than another clock that was stationary relative to the point clock A was revolving around, and clock B was rotating around. Which would run slower would depend on how much acceleration each was experiencing.

And again, all of this is precisely as relativity predicts.
Why do you insist on being so precise when I offer mind experiment analogies, but you don't seem to apply it to your own. Why not just say a clock can't be aware? It seems you're trying to win an argument rather than enter the spirit of understanding.

I can certainly imaging that I could be placed on a motor driven spinning chair that was so smooth that I couldn't perceive the spin by any vibration. I was unconscious when I was placed on the chair so I'm also unaware on any initial acceleration. The spin could also be slow enough that centrifugal forces were humanly undetectable.

[Schneibster]

I see a combination of both the horizontal motion of the ball travelling with the train and the vertical motion of the falling ball. I see a combination of two independent motions occurring simultaneously.

The guy on the train sees the vertical motion of the ball falling.

Both!

I think so. But I wonder if you do.All correct. See, that's not a "perception anomaly." That's WHAT'S REALLY HAPPENING. And what one person sees and what another sees, LOOKING AT THE SAME EVENT, need not necessarily be the same thing; they just have to be transformable into one another.

Now, that's a technical term: transform. What it means is, the set of laws, or equations, that you have to use to adjust one person's measurements into another's, when they are in different circumstances. And that isn't just something you do in relativity; you do it using Newton's laws too. And the transform for Newton's laws is called the "Galilean transform," because Galileo worked out the math for it before Newton made his Three Laws.

In relativity, the transform you use is called the "Lorentz transform." Because Lorentz worked it out, again before Einstein made his SR.

This is one of the more important concepts in physics; you see why I tell you you are asking good questions? When you get this figured out for Newtonian mechanics, you're ready to see why it's different in Einstein's theory.

Because I see a combination of two independent motions occurring simultaneously, and he see only sees one motion. Do you see why? Do you see that from his viewpoint, if YOU dropped the ball, HE'D see the parabola? Do you see that that means that his perception is just as good, just as true, as yours? Now, you are not moving, right? So do you see that there's no difference between his motion creating the parabola he sees in YOUR ball, and his motion creating the parabola you see in HIS? How can that be, if it's just perception? There's MOTION there, man. And that's not just perception; it's REAL.

It's also what I would PRECISELY predict without Relativity. But what you'd use to predict it (Newtonian mechanics) is only true if the speeds are very, very low; and even then, it's just a teeny bit off. At the normal speeds we deal with in our everyday life, Newton is "good enough." In fact, at the fastest speed any human has ever gone in a rocket, or for that matter the fastest any of the probes we've sent all over the Solar System have gone, it's STILL "good enough." You have to be in very precise circumstances to use what relativity can give you.

But it's not "good enough" to calculate the orbit of Mercury. You need relativity for that. Because when you get that close to the Sun, gravity gets stronger, and Newton's laws are just far enough from reality that they don't make the right prediction any more. And it's not "good enough" for GPS, either. Nowhere near, as another poster pointed out.

Why do you insist on being so precise when I offer mind experiment analogies, Because it's important. You'll miss the point otherwise.

but you don't seem to apply it to your own. Example, please? I am quite careful, I thought. I suspect a misunderstanding or something you have missed through- I'll be polite on your terms- limited knowledge. In any case, I do try to apply that level of precision to my own gedankenexperiments, and analogical explanations, but everyone makes mistakes.

Why not just say a clock can't be aware? It seems you're trying to win an argument rather than enter the spirit of understanding.I was accepting yours in the spirit it was offered. You seem to have misunderstood. I was using "aware" in the same sense you were. You have misunderstood the source of my criticism, I think. And that is probably because of limited knowledge of how things work. I tried to be as clear as I could. Where did you get lost?

I can certainly imaging that I could be placed on a motor driven spinning chair that was so smooth that I couldn't perceive the spin by any vibration. I was unconscious when I was placed on the chair so I'm also unaware on any initial acceleration. The spin could also be slow enough that centrifugal forces were humanly undetectable. Then the clock would have to be very, very precise to detect the acceleration; but the point I'm making is, IT CAN, no matter how small it might be. And whether the first one can or not, the second one can FOR SURE. Remember, it's at the end of a lever arm, and the force increases as the radius.

You also may not be aware that both rotating and revolving are forms of continuous acceleration. You can't do either without accelerating all the time, unless you are orbiting in a vacuum in a force field (gravity, magnetism, electricity will all do to provide the field- for that matter, in the absence of a force field, you could have a rocket sticking out the back of the second clock to keep it accelerating toward the first. But you will for sure have to have SOMETHING. Newton even tells us that something moving under the influence of zero forces is either still, or moving in a straight line).

Try it for yourself, the next time you're on the space station. :D

ETA: I think I finally understand what you're saying: "Why not just say that the clock can't feel the acceleration?" And my answer is, "because you can't move in a circle without accelerating. Period. That's the definition of moving in a circle, and you don't need relativity for that- Galileo and Newton say so."

Does that help?

[Schneibster]

And in case you doubt it, google "Newton's Bucket."

ETA: See? I TOLD you it was a good question.

[ynot]

All correct. See, that's not a "perception anomaly." That's WHAT'S REALLY HAPPENING. And what one person sees and what another sees, LOOKING AT THE SAME EVENT, need not necessarily be the same thing; they just have to be transformable into one another.

There is only one event, and it’s the same event for both people. There are not two events. The perception of the event is different for both people. There are two perceptions of the one event. The anomaly is in the perceptions. The perceptions see different events when there was only one. The two perceptions are not the reality of the one event, and the perceptions don’t change the reality of the event.

Do you see why?
Of course I do. It’s pretty simple stuff. So simple it’s easy to get it wrong :D .

Do you see that from his viewpoint, if YOU dropped the ball, HE'D see the parabola? Do you see that that means that his perception is just as good, just as true, as yours?
Just as false in my opinion. Neither person is accurately perceiving the actual event, they only perceive the event from the limitations of their particular perspective. Not sure if it’s possible to accurately perceive an event, You seem to be saying that two different perspectives of an event create two different actual events. There’s always only one ball, one train, etc.

Example, please? I am quite careful, I thought. I suspect a misunderstanding or something you have missed through- I'll be polite on your terms- limited knowledge. In any case, I do try to apply that level of precision to my own gedankenexperiments, and analogical explanations, but everyone makes mistakes.
Haven’t you used 2-D examples when explaining curved space?

I was accepting yours in the spirit it was offered. You seem to have misunderstood. I was using "aware" in the same sense you were. You have misunderstood the source of my criticism, I think. And that is probably because of limited knowledge of how things work. I tried to be as clear as I could. Where did you get lost?
So it’s all my mistake then. Do you ever consider for a split second that perhaps you might be wrong? Perhaps I didn't get lost, but you failed to find me. I was saying that clocks can’t be aware period. They don’t have any senses that I’m aware of. So I was saying that the whole scenario doesn’t make conventional sense. I was using it as a simplified analogy to demonstrate that perception doesn’t always (if ever) accurately represent reality. Not only did I deliberately not consider any effects of circular acceleration, i also didn't take account of the time light takes to go from clock to clock.

Then the clock would have to be very, very precise to detect the acceleration; but the point I'm making is, IT CAN, no matter how small it might be. And whether the first one can or not, the second one can FOR SURE. Remember, it's at the end of a lever arm, and the force increases as the radius.

You also may not be aware that both rotating and revolving are forms of continuous acceleration. You can't do either without accelerating all the time, unless you are orbiting in a vacuum in a force field (gravity, magnetism, electricity will all do to provide the field- for that matter, in the absence of a force field, you could have a rocket sticking out the back of the second clock to keep it accelerating toward the first. But you will for sure have to have SOMETHING. Newton even tells us that something moving under the influence of zero forces is either still, or moving in a straight line).

Try it for yourself, the next time you're on the space station. :D

ETA: I think I finally understand what you're saying: "Why not just say that the clock can't feel the acceleration?" And my answer is, "because you can't move in a circle without accelerating. Period. That's the definition of moving in a circle, and you don't need relativity for that- Galileo and Newton say so."

Does that help?
I’m certainly more up-to-speed on circular/angular motion than Relativity. I’ve enjoyed endless hours experimenting with gyroscopes and I’ve been trying to understand precession and nutations. By understand, I mean an actual mechanical knowledge of what is going on, not just the math that describes it. I’d be very happy if anyone can explain why precession occurs in one direction compared to the gyros spin and not the other.

[Schneibster]

There is only one event, and it’s the same event for both people. There are not two events. The perception of the event is different for both people. There are two perceptions of the event. The anomaly is in the perceptions. The perceptions see different events when there was only one. The two perceptions are not the reality of the one event, and the perceptions don’t change the reality of the event.OK, then, which is the CORRECT, ACCURATE description of this event?

Do you not see that this is the entire point of the conversation? There is no third perspective needed. These two are both completely accurate, completely correct, and need no further explication. They can, in fact, be transformed one into the other. There is no "underlying reality." What these two observers see is ALL THERE NEED BE. The viewpoint of any third observer can also be transformed into both of these. And there is no basis for declaring the viewpoint of ANY of these observers as "the truth" at the expense of the others; they are ALL "the truth."

THAT'S what relativity says; and Galilean relativity (and yes, there is such a thing) has acknowledged it from the beginning of the Enlightenment. Hundreds of years ago.

Just as false in my opinion. Neither person is accurately perceiving the actual event, they only perceive the event from the limitations of their particular perspective. Not sure if it’s possible to accurately perceive an event, You seem to be saying that two different perspectives of an event create two different actual events. There’s always only one ball, one train, etc.You're proposing an absolute frame of reference from which the "accurate" description can be made. This is a mistake; you cannot define such a frame. There is no basis for doing so. The two descriptions are equally accurate, and there is no "more accurate" description, even if a third, different perspective is added.

Haven’t you used 2-D examples when explaining curved space?And? Were you unclear that I was making analogies, and that there are inherent limitations based on our limited ability to visualize the reality in them? Did I not so state? If so, then I state it now: no 2D description can actually capture the reality of 4D spacetime. All we can do is show what it might be like, to the extent we can visualize it. And that extent is limited by our perceptions- but the reality is not so limited.

So it’s all my mistake then. Do you ever consider for a split second that perhaps you might be wrong? All the time. But the probability is vanishingly small- because of the observations that have been made, any later theory MUST include the majority of the elements of the current one. Just as relativity includes the majority of the elements of Newton's Laws. In fact, what relativity says is that Newton's Laws are approximately correct, and in all but the most critical situations, more accurate than our ability to measure the difference.

Perhaps I didn't get lost, but you failed to find me. I was saying that clocks can’t be aware period. They don’t have any senses that I’m aware of. So I was saying that the whole scenario doesn’t make conventional sense. I was using it as a simplified analogy to demonstrate that perception doesn’t always (if ever) accurately represent reality. Not only did I deliberately not consider any effects of circular acceleration, i also didn't take account of the time light takes to go from clock to clock.And I was (foolishly?) being polite and accepting the outward form of your analogy- and pointing out where it deviates from demonstrable characteristics of reality. Or would you prefer fantasy instead?

I’m certainly more up-to-speed on circular/angular motion than Relativity. I’ve enjoyed endless hours experimenting with gyroscopes and I’ve been trying to understand precession and nutations. By understand, I mean an actual mechanical knowledge of what is going on, not just the math that describes it. I’d be very happy if anyone can explain why precession occurs in one direction compared to the gyros spin and not the other. Precession occurs because the gyroscope cannot be perfectly balanced, and because of friction in the bearing.

Did you google Newton's Bucket like I told you?

Why are you so combative if your real agenda is to learn something?

[Kaylee]

you are standing on a platform, watching a train go by. The train has a floor-to-ceiling window in it, and standing in that window is a person holding a ball. Just when you can first see them, they drop the ball, and it falls to the floor.

What path do you see the ball take?

OK, now what path does the person who dropped it see it take?

OK, now the hard part: WHICH ONE IS RIGHT?




I see a combination of both the horizontal motion of the ball travelling with the train and the vertical motion of the falling ball. I see a combination of two independent motions occurring simultaneously.

The guy on the train sees the vertical motion of the ball falling.

Both!



All correct. See, that's not a "perception anomaly." That's WHAT'S REALLY HAPPENING. And what one person sees and what another sees, LOOKING AT THE SAME EVENT, need not necessarily be the same thing; they just have to be transformable into one another.


I like this example even better than the one Einstein himself gave! :D In his example, the train's passenger drops the stone out of the window, and the reader is instructed to disregard the effects of air resistance.

Does anyone happen to know if this scenario has ever been videotaped from the point of view of the two different people, and posted on a web site? If so, please post.

If I tried to recreate this with my friends, they would just think I'm nuts. And I may well be, but that's off topic. ;) :D

[ynot]

OK, then, which is the CORRECT, ACCURATE description of this event?

Do you not see that this is the entire point of the conversation? There is no third perspective needed. These two are both completely accurate, completely correct, and need no further explication. They can, in fact, be transformed one into the other. There is no "underlying reality." What these two observers see is ALL THERE NEED BE. The viewpoint of any third observer can also be transformed into both of these. And there is no basis for declaring the viewpoint of ANY of these observers as "the truth" at the expense of the others; they are ALL "the truth."

THAT'S what relativity says; and Galilean relativity (and yes, there is such a thing) has acknowledged it from the beginning of the Enlightenment. Hundreds of years ago.

You're proposing an absolute frame of reference from which the "accurate" description can be made. This is a mistake; you cannot define such a frame. There is no basis for doing so. The two descriptions are equally accurate, and there is no "more accurate" description, even if a third, different perspective is added.

And? Were you unclear that I was making analogies, and that there are inherent limitations based on our limited ability to visualize the reality in them? Did I not so state? If so, then I state it now: no 2D description can actually capture the reality of 4D spacetime. All we can do is show what it might be like, to the extent we can visualize it. And that extent is limited by our perceptions- but the reality is not so limited.

All the time. But the probability is vanishingly small- because of the observations that have been made, any later theory MUST include the majority of the elements of the current one. Just as relativity includes the majority of the elements of Newton's Laws. In fact, what relativity says is that Newton's Laws are approximately correct, and in all but the most critical situations, more accurate than our ability to measure the difference.

And I was (foolishly?) being polite and accepting the outward form of your analogy- and pointing out where it deviates from demonstrable characteristics of reality. Or would you prefer fantasy instead?

Precession occurs because the gyroscope cannot be perfectly balanced, and because of friction in the bearing.

Did you google Newton's Bucket like I told you?

Why are you so combative if your real agenda is to learn something?
Don’t know why you think I’m being “combative“. I don‘t think I am and I don't mean to be. Perhaps you expect me to learn passively by rote and not question or challenge anything you say? That ain’t gonna happen any time soon. I’m simply trying to get at the truth. And “the truth” from my perspective, is not necessarily “your truth”. I think in all communication there has to be a certain level of compromising and forgiving. Several times I’ve wanted to respond to the “tone” of what you have said rather than the content. But I have resisted for the sake of the communication. For instance you have just said “Did you google Newton's Bucket like I told you?” (my bolding). So you’re giving me orders now and telling me what to do? It would have been more user-friendly if you had said suggested or requested. I did Google Newton’s Bucket. Interesting, but I don’t think I have learnt anything substantially new from it.

Back to the train/ball scenario. As I said earlier, they are both correct and accurate, but only to the degree that their particular perspectives allow. So neither can be said to be totally correct and accurate. As I also said, I’m not sure if a totally correct and accurate perspective can ever be achieved. I guess I think that it’s a mistake to take a theoretical combination of two perspectives and call accurate and correct.

I would like to return to the light clock experiment because I think it contains a glaring flaw. It doesn’t seem to me that this experiment is comparing “apples with apples“. In the stationary clock, the light blip is fired vertically so that it bounces between the mirrors (no problem). If the mirrors were moved horizontally however, and the blip was still fired vertically, the light blip would miss the second mirror as light wouldn’t adopt the horizontal velocity of the mirrors. Therefore, the light blip would have to be fired at an angle (problem). The clocks are no longer the same. One is firing a blip between mirrors that are “x” apart, and the other is firing a blip between mirrors that are essentially “x+” apart. The experiment has nothing to do with moving mirrors and everything to do with distances between mirrors. In fact the mirrors don’t even need to be moving. Many stationary mirrors could be set up to bounce the angled blip in the saw-toothed motion. You could also just use two long mirrors for both clocks as shown below. All this experiment is proving is that a direct route is shorter, and therefore quicker, than an indirect route. Don’t see where Relativity comes in to it.

http://forums.randi.org/imagehosting/733545955e7a1a0e6.gif (http://forums.randi.org/vbimghost.php?do=displayimg&imgid=3388)
Essentially the experiment is comparing the two clocks below . . .

http://forums.randi.org/imagehosting/73354595622042f0c.gif (http://forums.randi.org/vbimghost.php?do=displayimg&imgid=3389)

[Molinaro]

Back to the train/ball scenario. As I said earlier, they are both correct and accurate, but only to the degree that their particular perspectives allow. So neither can be said to be totally correct and accurate. As I also said, I’m not sure if a totally correct and accurate perspective can ever be achieved. I guess I think that it’s a mistake to take a theoretical combination of two perspectives and call accurate and correct.

Yes, they both can be said to be totally correct and accurate.

If I tell you it is now 4pm EST, and someone else tells you that it is actualy 1pm PST does it mean that neither of us is totally correct and accurate?

You see, the situation that Schneibster is trying to make clear to you is that they are both equaly correct and accurate because translating from one perspective (eastern standard time) to another (pacific standard time) can be accomplished via a well defined mathematical procedure. Neither is any more or less accurate as far as the correct time is concerned, they are merely different perspectives.

The same is true for the scenario with the falling balls and moving trains and different observers. So long as they both make appropriate measurements and take into account all relative motions both answers will be equaly correct and accurate. And any other equaly correct and accurate answer can be calculated for any other perspective you may want to consider.

[ynot]

Yes, they both can be said to be totally correct and accurate.

If I tell you it is now 4pm EST, and someone else tells you that it is actualy 1pm PST does it mean that neither of us is totally correct and accurate?

You see, the situation that Schneibster is trying to make clear to you is that they are both equaly correct and accurate because translating from one perspective (eastern standard time) to another (pacific standard time) can be accomplished via a well defined mathematical procedure. Neither is any more or less accurate as far as the correct time is concerned, they are merely different perspectives.

The same is true for the scenario with the falling balls and moving trains and different observers. So long as they both make appropriate measurements and take into account all relative motions both answers will be equaly correct and accurate. And any other equaly correct and accurate answer can be calculated for any other perspective you may want to consider.
Thanks - I will think on what you have said. Do you think I have made a mistake in my interpretation of the light clock experiment?

[Molinaro]

I gave that part of your post a lot of thought, but have not come up with an appropriate answer as of yet.

My first thought is that any motion of the mirrors with be much slower than that of light, hence, the light won't miss. But, I don't think that is a proper explanation.

I've never much liked the light-clock explanation myself, but it does not make me question the idea it is trying to explain. I just think it is a bit oversimplyfied and leaves too much room for questioning the light-clock methodology.

I've always found the relativity and curved space ideas easiest to understand by realizing that the shape of space is not a property of space itself. It is the result of the contents of that space. And, any measurement of it's properties will necessarily, and entirely, depend on who is doing the measuring, where they are, how they are moving, etc...

I also like to think back to the timezone analogy whenever I find myself wanting to consider one answer 'more correct' than some other answer that actualy only differs by some well defined mathematical translation. Much the same way that 1+1 = 2 in decimal, and 1 + 1 = 10 in binary. Both are equaly correct.

[ynot]

Yes, they both can be said to be totally correct and accurate.

If I tell you it is now 4pm EST, and someone else tells you that it is actualy 1pm PST does it mean that neither of us is totally correct and accurate?

You see, the situation that Schneibster is trying to make clear to you is that they are both equaly correct and accurate because translating from one perspective (eastern standard time) to another (pacific standard time) can be accomplished via a well defined mathematical procedure. Neither is any more or less accurate as far as the correct time is concerned, they are merely different perspectives.

The same is true for the scenario with the falling balls and moving trains and different observers. So long as they both make appropriate measurements and take into account all relative motions both answers will be equaly correct and accurate. And any other equaly correct and accurate answer can be calculated for any other perspective you may want to consider.
I guess is comes down to what is meant by “totally”. 4pm EST is totally correct and accurate from the perspective of EST (and 1pm PST for PST). Neither are totally correct and accurate however for what might be called the “overall event time” or “universal time“. I accept and understand that one can be mathematically translated or transformed from one to the other. Not sure that it’s valid to compare an abstract event (a time system) with an actual event. The concern I have is not so much with the correctness and accuracy of perspective views of an event, but more with the way they’re combined and interpreted. Can’t clearly explain what I mean as yet.

[ynot]

I gave that part of your post a lot of thought, but have not come up with an appropriate answer as of yet.

My first thought is that any motion of the mirrors with be much slower than that of light, hence, the light won't miss. But, I don't think that is a proper explanation.
Imagine that the two horizontal mirrors are spinning discs, and the light blip is fired vertically. The movement of the mirrors would have no effect on the blip and the two clocks would run at the same speed.

ETA - The vertical light blip can only be moved horizontally if it's motion is angled from the vertical.

[Molinaro]

Actual events are in fact abstractions.

The observed motion of a ball is actualy an abstraction based on the motion of the elementary particles making up the ball, with each other, and with the elementary particles that make up the medium through which the motion takes place.

That makes it easy for me to discount the idea of any single one true motion for the ball. Whatever motion I decide to concider the actual motion will in fact be an abstraction based on my point of observation, and scale of observation.

[ynot]

Actual events are in fact abstractions.

The observed motion of a ball is actualy an abstraction based on the motion of the elementary particles making up the ball, with each other, and with the elementary particles that make up the medium through which the motion takes place.

That makes it easy for me to discount the idea of any single one true motion for the ball. Whatever motion I decide to concider the actual motion will in fact be an abstraction based on my point of observation, and scale of observation.
"Actual events are in fact abstractions." or observations of actual events are always abstractions because they can never be total?

[Schneibster]

The angled path of the photon works for the same reason that the falling ball's path looks like a parabola.

[Schneibster]

Does anyone happen to know if this scenario has ever been videotaped from the point of view of the two different people, and posted on a web site? If so, please post. I don't know about a web site, but when I was in school, we saw a movie one day in class where they had a little wheeled platform that ran on rails, and they ran it across on the rails and dropped a ball from a little scaffold on it, and traced the ball's location from one frame to the next, and showed it was a parabola. Then they did another shot where they moved the camera at the same rate as the platform and showed it was a straight line.

[Schneibster]

Don’t know why you think I’m being “combative“. I don‘t think I am and I don't mean to be.

Do you ever consider for a split second that perhaps you might be wrong?Uh-huh.

Perhaps you expect me to learn passively by rote and not question or challenge anything you say? That ain’t gonna happen any time soon. I’m simply trying to get at the truth. By postulating absolute motion. Uh-huh.

And “the truth” from my perspective, is not necessarily “your truth”. If you're talking about objective facts of mechanics, that everyone who measures the behavior of objects agrees are what happens every time, then there is no "my truth" or "your truth," there's only what everyone sees every time. And if you don't get why BOTH the straight line and the parabola are "what everyone sees every time," IOW why they are THE SAME THING, then I've basically been wasting my time talking to you.

I think in all communication there has to be a certain level of compromising and forgiving. I think that in communication, one has the obligation to stick to facts when facts are at issue. There is no compromise on the facts. I can't help it if they conflict with your pet theory. It's not my fault. Stop taking it out on me.

For instance you have just said “Did you google Newton's Bucket like I told you?” (my bolding). So you’re giving me orders now and telling me what to do? It would have been more user-friendly if you had said suggested or requested. I did Google Newton’s Bucket. Interesting, but I don’t think I have learnt anything substantially new from it. Then you didn't think about it very much. Albert Einstein learned from Newton's Bucket, and he thought about it for a very long time, while he was developing GR (after he'd already done the work that would eventually win him a Nobel Prize, and after he'd already completed SR). You'll pardon me if I observe that it's extremely unlikely that you're smarter than Albert Einstein. I wouldn't consider it insulting to have that said about me.

Back to the train/ball scenario. As I said earlier, they are both correct and accurate, but only to the degree that their particular perspectives allow. So neither can be said to be totally correct and accurate. Sorry, I'm gonna have to do that "not compromising" thing again. This is wrong. You've already been told why. BOTH are totally correct and accurate, to the limit of the precision of their respective measurements.

As I also said, I’m not sure if a totally correct and accurate perspective can ever be achieved. It can. They both are.

I guess I think that it’s a mistake to take a theoretical combination of two perspectives and call accurate and correct.I guess then that that's where we differ; unfortunately, it's also where you differ from the entire community of professional physicists, not to mention a large number of engineers.

And it's not a "combination." They are two different observations of the same event, and each is completely internally consistent, and completely consistent with the laws of physics. Finally, both observations are consistent with one another; the fact that they differ is no more important than the fact that a mountain looks bigger to someone standing closer than it does to someone standing farther away from it. And you should also see how both the behavior of the mountain, getting bigger when you get closer, and the behavior of the ball, falling in a straight line for one observer and a curve for another, influence the shape of space as perceived by different observers.

[ynot]

Schneibster tells me (in another thread) that I’m on his ignore list so I guess It’s pointless posting a response.

I’m really interested in getting some feedback on my comments regarding the light clock - Anyone?

[ynot]

Not sure anyone here is interested but I have solved my light clock misunderstanding (very quickly) on another forum where the members don’t have the superior, arrogant “teacher/tutor” attitude that I’ve experienced here.

The main flaw in my “logic” was that I was expecting the light blip travelling on the diagonal between the vertical and horizontal to have the sum of the vertical and horizontal speeds. This would have meant it would be travelling faster than c.

[Kaylee]

Not sure anyone here is interested but I have solved my light clock misunderstanding (very quickly) on another forum where the members don’t have the superior, arrogant “teacher/tutor” attitude that I’ve experienced here.


:confused: You have gotten some incredibly thoughtful responses to your questions, I wouldn't be surprised if the sum total of time it had taken to write theses responses added up into hours.

Well obviously you don't appreciate it, but I do. Its not often one can get spoonfed technical information in a very clear and understandable manner.

I think it would pay to look at the big picture here, instead of nitpicking on a few details. Whatever. Happy new year.

[Kaylee]

I don't know about a web site, but when I was in school, we saw a movie one day in class where they had a little wheeled platform that ran on rails, and they ran it across on the rails and dropped a ball from a little scaffold on it, and traced the ball's location from one frame to the next, and showed it was a parabola. Then they did another shot where they moved the camera at the same rate as the platform and showed it was a straight line.

Hmm, my first AND second response seems to have disappeared into cyberspace?!? Well, here's Take 3.

Thanks Schneibster, I'm glad this has been filmed. NYC has some great libraries including one that speicaizes in the sciences. Next time I'm there I'll ask a librarian if there have a similar movie on DVD.

[69dodge]

Without GR and SR, relative motions, distances and speeds of objects will still present perception anomalies to an observer, but in what way will they have any affect on the actual objects?http://en.wikipedia.org/wiki/Hafele-Keating_experiment

http://www.npl.co.uk/publications/metromnia/issue18/#article2

[69dodge]

Must admit I find the whole gravity thing a bit puzzling. Every morning I get out of bed and it's just there. I can sort of understand one object having an attraction to another, and the bigger the object the stronger the attraction. Don't understand why the Moon is trapped in it's orbit around Earth. As it goes through its apogee and perigee why doesn't it escape Earth's gravity or plunge to Earth.Why should it do either of those things?

If you throw a ball up, why doesn't it keep moving up?

It's true that a rocket can keep going up forever if it starts out moving fast enough away from the Earth. But the Moon isn't moving away from the Earth very fast. It's mainly just going around it.

The Moon doesn't hit the Earth even though the Earth's gravity pulls on it, because it's already moving sideways. To hit the Earth, it would have to stop moving sideways, or at least slow greatly, but it doesn't slow because nothing is pulling it backwards, just down.

See, e.g., http://galileoandeinstein.physics.virginia.edu/lectures/newton.html, especially the picture in the middle of the page.

Also why do the planets circle the Sun? They're all different distances from the Sun and they're of different sizes.What's the problem?

Their different sizes hardly matter to the way they orbit the Sun, for the same reason that, on Earth, big and little things fall the same way.

The planets are at different distances from the Sun, but also they circle it at different speeds. So, everything works out nicely.

A gravitational magnet-like force doesn't seem to explain it.Magnetism is probably not the best analogy: magnets have north and south poles, which attract and repel the poles of other magnets, but gravity just attracts.

[lenny]

Not sure anyone here is interested but I have solved my light clock misunderstanding (very quickly) on another forum where the members don’t have the superior, arrogant “teacher/tutor” attitude that I’ve experienced here. why not post a link to the explanation that worked for you? it might prove of value to others lurking here silently.

regret you did not like the attitude, but i think the information given (in terms of working within the theory) was pretty good. remember it is not alway easy to see what it is someone else is confused by.

but in any event, glad the theory now makes sense! are you also happy that it applies to reality now?

[Roboramma]

Hey ynot, just a little thought that may be of some help, take it or leave it.

I was reading through this thread and thought of my sig. The thought that struck me was basically this: The way that we determine that the earth is round is the same as the way that we determine that the universe is curved. We make observations and look for theories that can explain them. When we find a theory that explains our observations, we test it.
The theory that "the earth is round" (by the way, by round I mean curved here, not uniformly round or spherical), is well tested. There are plenty of good experimental results that confirm it - one nice one was magellan circumnavigating the globe, but the shape of the earth had been well understood long before that.
The theory that space is curved is similarly well tested.

Both theories, of course, are suceptible to new data. But as with the earth's shape, any new theory that has bearing on the curvature of space will still have to square with all the observations that support the current theory. And just as it's very unlikely that any new theory explaining the shape of the earth will tell us that it's actually flat, it's also very unlikely that any new theory of space-time will tell us that it is flat.

Note that I'm no expert and can't offer much but a little analogy (possibly poorly thought out) that might give you something to think about. As I said, take it or leave it.

[ynot]

People that know me usually describe me as being “emotionally constipated”. So why did I get a touch of emotional diarrhoea in this case? Perhaps it was something I ate. Perhaps I didn’t chew enough before swallowing. Did I forget to wash my hands before dinning? Were some of the condiments that I added tainted? Did those that prepared the food contaminate it somehow? In any event, the meal was substantial and nourishing, and those that provided it did so at no cost to myself, but at the cost of time and effort to themselves. I’m grateful and appreciative of the meal that was provided, and apologise for any nasty symptoms that resulted from my illness. Hopefully this illness is not repetitive or contagious.

I’m happy to report, that after consulting my homeopath, naturopath, faith healer, spiritualist, astrologer, tarot reader, iridologist, colour therapist, wellness facilitator and god, that my ailment appears to have all but cleared up, and I look forward to the possibility of dinning with you again in the future. :)

[Schneibster]

I'm sure ynot is starting to realize just how polite I was being earlier now. Thanks for driving the lesson home, folks.