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 a