Logical proof of SRT invalidity

[ozziemate]

There is no loss of time so no.
are you saying then that both cone diagrams woud end up regardless of travel and time dilation exactly the same... when superimposed on top of each other.

[Reality Check]

ozziemate: A web page with a good explanation of Simultaneity (http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm#simultaneity).

[Reality Check]

are you saying then that both cone diagrams woud end up regardless of travel and time dilation exactly the same... when superimposed on top of each other.
Yes - both cones will.

[ozziemate]

That they will end up like this:

http://bizzymate.com/uploads/images/physics/hsp02abcd.gif

[ozziemate]

if this is the case and we are talking about light cones how is the non simultaneousness demonstrated in a zero duration HSP that now has to accommodate both observers as the HSP's are sharing the same zero duration moment in between the the same future and past cones.

[Reality Check]

That they will end up like this:

http://bizzymate.com/uploads/images/physics/hsp02abcd.gif
Maybe

[ozziemate]

Maybe
why maybe? and not definitive?

[Reality Check]

idf this is the case and we are talking about light cones how is the non simultaneousness demonstrated in a zero duration HSP that now has to accommodate both observers as the HSP's are sharing the same moment in between the cones
Pardon?
Do you mean the standard derivations and illustrations of the relativity of simultaneity (http://en.wikipedia.org/wiki/Relativity_of_simultaneity) that abound on the web?

[Reality Check]

why maybe? and not definitive?
I mean that I guess that they do.
It is just the HSP is ignored in SRT and physics in general maybe because it is trivial.

[ozziemate]

I mean that I guess that they do.
It is just the HSP is ignored in SRT and physics in general maybe because it is trivial.
Surely the HSP isn't trivial when talking about non-simultaneity between two frames?
you are kidding?

So the rel.v. observers light cones are the same as the relative rest frame....hmmmmmm....

so both observers see the same identicle light info?
their only difference maybe their observed locations due to length conrtraction?

[ozziemate]

According to this image care/o wiki the horizontal green line is the cones sets zero duration hsp.

If that is the case regardless of angle of other lines we still have both events occuring in the same zero duration moment therefore simultaneous.

http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png

as shown by this construction:

http://bizzymate.com/uploads/images/physics/contruct01.jpg

[Reality Check]

Surely the HSP isn't trivial when talking about non-simultaneity between two frames?
you are kidding?

So the rel.v. observers light cones are the same as the relative rest frame....hmmmmmm....

so both observers see the same identicle light info?
their only difference maybe their observed locations due to length conrtraction?
No.
Consider 2 observers Alice and Bob. They meet at a point in spae and synchronize their identical clocks, let say to t=0.
Alice stays where she is and just watches her clock. It goes tick tock, tick tock, etc.
Bob accelerates to 0.5c and and watches his clock. It goes tick tock, tick tock, etc.
SRT states that Alice and Bob see their clocks tick at the same rate (first postulate). So after a million years

Alice's clock (and so her HSP time) = 1 million years.
Bob's clock (and so his HSP time) = 1 million years.
Thus their HSPs are the same.

[ozziemate]

No.
Consider 2 observers Alice and Bob. They meet at a point in spae and synchronize their identical clocks, let say to t=0.
Alice stays where she is and just watches her clock. It goes tick tock, tick tock, etc.
Bob accelerates to 0.5c and and watches his clock. It goes tick tock, tick tock, etc.
SRT states that Alice and Bob see their clocks tick at the same rate (first postulate). So after a million years

Alice's clock (and so her HSP time) = 1 million years.
Bob's clock (and so his HSP time) = 1 million years.
Thus their HSPs are the same.
but according to BOB he sees Alices HSP as different to what ALice see her own HSP and vica versa..yes?

[Reality Check]

According to this image care/o wiki the horizontal green line is the cones sets zero duration hsp.

If that is the case regardless of angle of other lines we still have both events occuring in the same zero duration moment therefore simultaneous.

http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png

as shown by this construction:

http://bizzymate.com/uploads/images/physics/contruct01.jpg
Now you are misquoting Wikipedia:

This picture illustrates the relativity of simultaneity (http://en.wikipedia.org/wiki/Relativity_of_simultaneity) in Lorentz transformations (http://en.wikipedia.org/wiki/Lorentz_transformations). The three colored reference frames are associated to three different observers in relative motion along the x axis. The y and z axis are perpendicular to the picture and aren't shown. They are identical for the three observers. Relative to the green observer, the red one is traveling at +0.28c and the blue one at approximately −0.52c.
Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame. The image becomes clearer once its RGB channels are viewed separately.
The upper highlighted area is A's future cone, consisting of the events which will occur after A in any reference frame. The lower highlighted area is A's past cone, consisting of the events which occurred before A in any frame. The interior consists of the events from which a massive particle could have reached A, or which can be reached by a massive particle starting at A. The surface is the light cone: the events which can be reached by a light ray starting at A, or from which a light ray reaching A could have originated. The black areas outside the double cone consist of the events whose temporal ordering with respect to A depends on the frame of reference.WP (http://en.wikipedia.org/wiki/Image:Relativity_of_simultaneity_(color).png)

No 'zero duration' or HSP mentioned. The green line is the frame of reference of the green observer.

[Reality Check]

but according to BOB he sees Alices HSP as different to what ALice see her own HSP and vica versa..yes?
Sort of - they see each other's clocks running at a lower rate. But they then deduce that the other has a different velocity to them, apply SRT and see that their HSP times are still synchronized.

[ozziemate]

Sort of - they see each other's clocks running at a lower rate. But they then deduce that the other has a different velocity to them, apply SRT and see that their HSP times are still synchronized.
well then it comes down to whether or not Bob can see the same light info using Alices perspective as Alice sees using her own

[ozziemate]

naah not right....going to bed..be back in 6

[Reality Check]

well then it comes down to whether or not Bob and Alice can see the same light info.
They cannot - they each have their own light cones. Remember that they are at different locations but have different HSP times. So that diagram that you have with the same HSP times is almost right - you just need to offset the light cones.
Then you have: 2 observers in SRT.

[Tubbythin]

I was going to mention the distance between the emitter and the receivers of the light gates as that would introduce a delay between when the beam was broken and when the receiver stops receiving photons (due to the speed of light). However the real problem would be your lack of a spatial reference (or origin) for the A frame or in other words even if you place the clock at the center of the path (within A) it will still take time for the signal (at the speed of light) from the light gate receivers to reach the clock to start and stop it. Not much of a consideration in our normal experience but quite relevant given the distances and velocity you present. You can not consider A’s spatial origin to be distributive along its entire length, you need some spatial origin (where its clock is) for A as is evident with B, otherwise it is very easy to misinterpret. You might consider placing the clock, emitters and receivers at the mid point along of the length, on the edge of A and have the A clock start and stop upon the return of the reflected laser beam off of B. this would minimize the signal travel time for the activation and deactivation of the A clock. However, that precise spatial location to the path of B would be quite relevant to the experiment. There are several such experiments already worked out, you might consider searching for, looking at them and presenting one of them for discussion, as these considerations would have already been, well, considered.

Unless I've completely misunderstood what you've just said (certainly not beyond the realms of possibility) then you seem to be making things unecessarily complicated. If A was at the start and knew the distance to the gate at the end then the correction for light travel time from one end to the other is trivial. It might take a long time before A knows how long it took B to get to the end but it doesn't matter. Its a thought experiment, nobody has to actually stand around and wait for a light signal to come back.

Ie:
*A and B start clocks at the time B leaves A and passes through first light gate.
*B passes through second light gate and stops his clock. At this time the gate releases a photon in the direction of A.
*A receives photon from second light gate and stops clock. He measures a time T on his clock.
*A concludes it took B a time of T-d/c to get from the first light clock to the second light clock (where d is the distance in his reference frame between the two gates).

[Fredrik]

According to this image care/o wiki the horizontal green line is the cones sets zero duration hsp.

If that is the case regardless of angle of other lines we still have both events occuring in the same zero duration moment therefore simultaneous.

http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png

as shown by this construction:

http://bizzymate.com/uploads/images/physics/contruct01.jpg
The horizontal green line is the HSP of the observer whose point of view this diagram represents. The events represented by the two dots are simultaneous in that inertial frame.

This diagram is actually a very good starting point for a discussion about simultaneity in SR. The almost vertical red line represents the motion of another observer. The almost horizontal red line represents the set of events that he considers simultaneous with the event at the origin of the diagram. (He's forced to consider them simultaneous because of the definition of simultaneity that I posted earlier).

There's actually a pretty intuitive way to see why it would have been wrong to draw the red simultaneity line horizontal:

Look at the line from the lower left to the upper right where gray meets black. It can be interpreted as the world line of a ray of light. Note that it's exactly half-way between the (green) t axis and the (green) x axis. That's how the fact that the speed of light is =c is represented. We are using units such that c=1 (e.g. "years" for time and "light-years" for distance), and velocity is "position change divided by time change". The world line of light has been drawn exactly half-way between the two axes to ensure that for any two points on it, the "position change divided by time change" is =1.

The almost vertical red line is the observer's world line, and therefore also the time axis of his coordinate system. We will call it the t' axis. The red simultaneity line is the x' axis. Suppose that we had drawn it horizontal instead. Then the world line of light wouldn't have been exactly half-way between the t' axis and the x' axis. It would have been much closer to the t' axis, and that would have made the speed of light >1 in the red frame!

This argument can be made more rigorous (by providing a few missing mathematical details), but basically this is how you prove the relativity of simultaneity: You note that if the almost horizontal red line is drawn so that the angle between it and the horizontal isn't the same as the angle between the almost vertical red line and the vertical, then the speed of light isn't the same in the red frame as in the green frame.

[ozziemate]

Unless I've completely misunderstood what you've just said (certainly not beyond the realms of possibility) then you seem to be making things unecessarily complicated. If A was at the start and knew the distance to the gate at the end then the correction for light travel time from one end to the other is trivial. It might take a long time before A knows how long it took B to get to the end but it doesn't matter. Its a thought experiment, nobody has to actually stand around and wait for a light signal to come back.

Ie:
*A and B start clocks at the time B leaves A and passes through first light gate.
*B passes through second light gate and stops his clock. At this time the gate releases a photon in the direction of A.
*A receives photon from second light gate and stops clock. He measures a time T on his clock.
*A concludes it took B a time of T-d/c to get from the first light clock to the second light clock (where d is the distance in his reference frame between the two gates).
I think Tubby is quite correct:
here is the image again:
http://bizzymate.com/uploads/images/physics/lightgate.gif


The thing that is of current interest to me is that the animation whilst not intended, shows that an observer traveling at rel.v. 0.5c can actually synchronise his clocks with observer A.
To do this we have an event at clock A1 that is simultaneous regarding both RF's. [ please correct me if I am wrong] t=0

When Observer B finally makes his way to light gate A2 again the event occurs that suggest simultaneity between RFs

If we had a only one light gate for the entire length of A's platform we would show that at all times A and B share the same event thus synchronisation.

So theoretically time dialtion in particular would be easilly recorded when comparig the two RFs.

Is it possible for someone to post what the ratio is for time dilation and also length contraction when rel.v. is a constant 0.5c?
or provide a link to an auto input table for lorenz derived SRT ratios?
[ I am not at all confident that my figures here are correct...]

[ozziemate]

FYI ,
Have found this site (http://www.4p8.com/eric.brasseur/erta.html) that has input form tables for all Basic SRT formulas.

[Reality Check]

FYI ,
Have found this site (http://www.4p8.com/eric.brasseur/erta.html) that has input form tables for all Basic SRT formulas.
So you can use that site to get the actual values for the figure. Not that you really need them:
Observer A's clock reads 0 at A1 when A reads it.
Observer B's clock reads 0 at A1 when B reads it.
Observer A's clock reads X at A2 when A reads it.
Observer B's clock reads X at A2 when B reads it.
If observer A can read B's clock at A2 then observer A will read a time dilated value of X.
If observer B can read A's clock at A2 then observer B will read a time dilated value of X.
Note that this is not really what the clocks read but rather what the observers determine to be the interval between the times at A1 and A2 according to the other observer.

[ozziemate]

So you can use that site to get the actual values for the figure. Not that you really need them:
Observer A's clock reads 0 at A1 when A reads it.
Observer B's clock reads 0 at A1 when B reads it.
Observer A's clock reads X at A2 when A reads it.
Observer B's clock reads X at A2 when B reads it.
If observer A can read B's clock at A2 then observer A will read a time dilated value of X.
If observer B can read A's clock at A2 then observer B will read a time dilated value of X.
Note that this is not really what the clocks read but rather what the observers determine to be the interval between the times at A1 and A2 according to the other observer.

this is actually interesting,
It means that the global HSP has non-simulatneity in a zero duration moment [ as no doubt you have been trying to say for ages.
Observer A will see simultaneity on his HSP and observer B will see simultaneity on his HSP which both share the same zero duration moment.
However a global HSP will see non-simultaneity between Observer A's events and observer B's events yet and this is the important bit maintain the zero duration of the HSP moment.

ahh Ok....

I would assume then that both obserers wil see the same light infomation in their respective HSP's, there for the contention of this thread is false.
and the photonsphere retains simultaneity.

fair enough.......wow thanks guys, been a hell of a journey.

Global HSP is non-simultaneous in a zero duration moment....hmmmmmm yet retains photon simultaneity.....ha

where's the Champers! or should I say beer!

[Fredrik]

here is the image again:
http://bizzymate.com/uploads/images/physics/lightgate.gif

You did this one pretty well. There's just one thing I'd like to comment: When B arrives at the second gate, he can't compare the time on his clock with the time on A's clock since they are a million light-years apart. What he can do is send a radio message back to A, saying "I'm there". A will get the message when his clock shows 3 million years, and since he knows the distance to the second gate and that radio signals travel at the speed of light, he knows that he should subtract 1 million years for the radio signal's travel time, and his conclusion is therefore that the trip took 2 million years. (Note that this is in A's frame, since it's A's clock we're talking about).


The thing that is of current interest to me is that the animation whilst not intended, shows that an observer traveling at rel.v. 0.5c can actually synchronise his clocks with observer A.
To do this we have an event at clock A1 that is simultaneous regarding both RF's. [ please correct me if I am wrong] t=0

Yes, the two observers can compare their clocks at a point where their world lines intersect, and if they want to, they can also set them to 0 at that event. It's usually convenient to have them do that. It's also convenient to have them measure all distances from that event too. So not only do we have t'=t=0 at that event, we also have x'=x=0, y'=y=0 and z'=z=0 .

I still wouldn't describe it as an event that's "simultaneous regarding both frames". The word "simultaneous" describes a property of two events in one frame, not one event in two frames.


When Observer B finally makes his way to light gate A2 again the event occurs that suggest simultaneity between RFs

In order to prove that the two frames agree about simultaneity, you have to show that B's clock is showing 2 million years at that event.


If we had a only one light gate for the entire length of A's platform we would show that at all times A and B share the same event thus synchronisation.

Did you forget what the point of the "light gate" was? It's just an object that's stationary in A's frame, so that the intersection of its world line with B's world line defines the event where B reaches his destination. If you make it bigger, its intersection with B's world line is no longer an event.


Is it possible for someone to post what the ratio is for time dilation and also length contraction when rel.v. is a constant 0.5c?

The change is always by a factor of

\gamma=\frac{1}{\sqrt{1-v^2/c^2}}

It can be difficult to remember if you should multiply or divide by this quantity, but if you know if the result is supposed to be bigger or smaller, you can just try both and see which one that works.

In this case, the time on B's clock when he reaches his destination is obtained by dividing 2 million years by gamma. The result is about 1.73 million years.

[Tubbythin]

\gamma=\frac{1}{sqrt{1-v^2/c^2}}

It can be difficult to remember if you should multiply or divide by this quantity, but if you know if the result is supposed to be bigger or smaller, you can just try both and see which one that works.



Or remember that \gamma is always greater than 1.

[ozziemate]

just a foot note:

What this means to me is that if we imagine that the entire universe including matter and mass was reduced down to it's fundamental energistic state in this I use the term photon, the universe is simultaneous and that it is only when you split the universe into energy and mass/matter that the temporal nature of matter and mass generates non-simulatneity.
I know this will probably make no sense at all but I thought I'd share it anyways.

It means that absolute and relative [temporal] time co-exist at a fundamental level [ when trying to comprehend the universal constants, such as invariance and inertia and gravity.]
Gravity for example is a non-temporal phenonema therefore for Gravity Time is absolute and simultaneous universally. But once matter or mass is involved time becomes relative yet utilises the universal simultaneity of gravity as it's uhm....underpining background so to speak.
Magnetism for example is IMO polarised gravity. The polarisation is caused as gravity is changed via matter into a temporal state meaning that the magnetic poles are still simutaneous globally in the same way gravity is yet part of mass and matter that are non-simultaneous [ in the context of our discussion].

any ways just some thoughts...

[ozziemate]

You did this one pretty well. There's just one thing I'd like to comment: When B arrives at the second gate, he can't compare the time on his clock with the time on A's clock since they are a million light-years apart. What he can do is send a radio message back to A, saying "I'm there". A will get the message when his clock shows 3 million years, and since he knows the distance to the second gate and that radio signals travel at the speed of light, he knows that he should subtract 1 million years for the radio signal's travel time, and his conclusion is therefore that the trip took 2 million years. (Note that this is in A's frame, since it's A's clock we're talking about).


Yes, the two observers can compare their clocks at a point where their world lines intersect, and if they want to, they can also set them to 0 at that event. It's usually convenient to have them do that. It's also convenient to have them measure all distances from that event too. So not only do we have t'=t=0 at that event, we also have x'=x=0, y'=y=0 and z'=z=0 .

I still wouldn't describe it as an event that's "simultaneous regarding both frames". The word "simultaneous" describes a property of two events in one frame, not one event in two frames.


In order to prove that the two frames agree about simultaneity, you have to show that B's clock is showing 2 million years at that event.


Did you forget what the point of the "light gate" was? It's just an object that's stationary in A's frame, so that the intersection of its world line with B's world line defines the event where B reaches his destination. If you make it bigger, its intersection with B's world line is no longer an event.


The change is always by a factor of

\gamma=\frac{1}{\sqrt{1-v^2/c^2}}

It can be difficult to remember if you should multiply or divide by this quantity, but if you know if the result is supposed to be bigger or smaller, you can just try both and see which one that works.

In this case, the time on B's clock when he reaches his destination is obtained by dividing 2 million years by gamma. The result is about 1.73 million years.
Thanks for your help fredrik you have been most patient.

The need to focus on the HSP issue meant that eventually the issue of a universal or global zero duration HSP could be thoroughly thrashed out.
And it appears that we have done so...:)

[ozziemate]

I'll post the full version of the light gate gedanken just incase someone wants to use it for fun or training [ save as file]:

http://bizzymate.com/uploads/images/physics/lightgate01.gif

[Thabiguy]

The thing that is of current interest to me is that the animation whilst not intended, shows that an observer traveling at rel.v. 0.5c can actually synchronise his clocks with observer A.
To do this we have an event at clock A1 that is simultaneous regarding both RF's. [ please correct me if I am wrong] t=0

When Observer B finally makes his way to light gate A2 again the event occurs that suggest simultaneity between RFs

If we had a only one light gate for the entire length of A's platform we would show that at all times A and B share the same event thus synchronisation.

So theoretically time dialtion in particular would be easilly recorded when comparig the two RFs.

Well I don't know if you could all that "easy", but yes, time dilation can be observed without requiring any object to stop.

Yours is an interesting example, though. The result may be slightly different than one might expect it to be. And it indeed does show the relativity of simultaneity.

1. A1 and A2 synchronize their clocks using light pulses. As they're not moving relative to each other, that's easy to do. They now wait for B to come.

2. B passes A1 at 0.5c. Much cheering ensues. A1 tells B that the time is now T. B sets his clock so that it also shows T. Their time is synchronized, and B flies on.

3. Time passes. (Yawn.)

4. After 2 million years, B passes A2. A2's time is now T+2 million years (of course), and B says that the time on his clock is now T+1.73 million years. The time dilation prediction is confirmed, and there is great rejoicing.

Now let's rewind and see it from B's perspective.

2. A1 passes B at 0.5c, and they synchronize clocks. Then, A1 flies on, telling B that A2 is coming, a million light years behind.

3. B waits for A2 to come.

4. A2 approaches and passes, but not after 2 million years, but after 1.73 million years. This is because A1 and A2 are flying at 0.5c, so the distance between them has contracted to about 0.87 million light years. So B's clock indeed shows T+1.73 million years.

5. What about A2's clock? B figures that if A1 and A2 synchronized their clocks in advance, A2's clock should now show T+1.5 million years due to time dilation (A2 has been flying at 0.5c all this time). But lo and behold - A2's clock show T+2 million years...

6. "Idiots!" B mumbles under his breath. "They didn't even manage to synchronize their clocks properly!"

... And that is precisely what happened in B's reference frame. The time synchronization that A1 and A2 took in step 1 was invalid from his point of view. While A1 and A2 came to the conclusion that their clocks are now ticking and showing the same time simultaneously, in B's reference frame, A1's clock is half a million years behind A2's clock.

And that is the relativity of simultaneity.

[Reality Check]

this is actually interesting,
It means that the global HSP has non-simulatneity in a zero duration moment [ as no doubt you have been trying to say for ages.
Observer A will see simultaneity on his HSP and observer B will see simultaneity on his HSP which both share the same zero duration moment.
However a global HSP will see non-simultaneity between Observer A's events and observer B's events yet and this is the important bit maintain the zero duration of the HSP moment.

ahh Ok....

I would assume then that both obserers wil see the same light infomation in their respective HSP's, there for the contention of this thread is false.
and the photonsphere retains simultaneity.

fair enough.......wow thanks guys, been a hell of a journey.

Global HSP is non-simultaneous in a zero duration moment....hmmmmmm yet retains photon simultaneity.....ha

where's the Champers! or should I say beer!

Don't celebrate yet!
Just about every sentence in that post has something wrong:

There is no such thing as a 'global HSP'. There is only the HSP for each observer. Observers can agree to synchronize their clocks but they still have their own HSP.
Simultaneity only applies between events. There is no such thing as 'photon simultaneity'.
Observer A sees their own clock and observer B sees their own clock. If they have identical synchronized clocks then they will read the same time. That is true only in the situation where the observers have synchronized their clocks. SRT deals with more general situations.
As for the 'zero duration of the HSP moment': that is your quite reasonable assumption.
Others may disagree.
Mathematicians would say correct for an ideal observer (who can observe events in zero time).
Philosophers would say it is obvious since there is no time between the Past and the Future.
Physicists would say that the minimum time for an observation is the Planck time and that quantum mechanics would make the minimum larger.
Your 'assume then that both obserers wil see the same light infomation in their respective HSP's' is wrong.
Each observer has their own light cone and they see the light information in those light cones.

[ozziemate]

Don't celebrate yet!
Just about every sentence in that post has something wrong:

There is no such thing as a 'global HSP'. There is only the HSP for each observer. Observers can agree to synchronize their clocks but they still have their own HSP.
Simultaneity only applies between events. There is no such thing as 'photon simultaneity'.
Observer A sees their own clock and observer B sees their own clock. If they have identical synchronized clocks then they will read the same time. That is true only in the situation where the observers have synchronized their clocks. SRT deals with more general situations.
As for the 'zero duration of the HSP moment': that is your quite reasonable assumption.
Others may disagree.
Mathematicians would say correct for an ideal observer (who can observe events in zero time).
Philosophers would say it is obvious since there is no time between the Past and the Future.
Physicists would say that the minimum time for an observation is the Planck time and that quantum mechanics would make the minimum larger.
Your 'assume then that both obserers wil see the same light infomation in their respective HSP's' is wrong.
Each observer has their own light cone and they see the light information in those light cones.



awww Reality Check I thought you'd be pleased that the threads "logical proof that invalidates SRT" has been proven incorrect, that this threads topic has been proven false and that SRTstands as valid.:confused::)

[Acleron]

awww Reality Check I thought you'd be pleased that the threads "logical proof that invalidates SRT" has been proven incorrect, that this threads topic has been proven false and that SRTstands as valid.:confused::)

Usually doesn't take 782 posts.

[Reality Check]

awww Reality Check I thought you'd be pleased that the threads "logical proof that invalidates SRT" has been proven incorrect, that this threads topic has been proven false and that SRTstands as valid.:confused::)
I sort of missed that in your post. I guess it is: 'I would assume then that both obserers wil see the same light infomation in their respective HSP's, there for the contention of this thread is false.
and the photonsphere retains simultaneity.'

Thus the end of this thread is that you have presented a not-quite-standard diagram that illustrates the relativity of simultaneity in SRT. It is a pity that it was not in your second post or that you did not bother to look at similar diagrams also illustrating the relativity of simultaneity in SRT.:)

I think you need to add a :blush: or :o to the last post!

[ozziemate]

There is no such thing as a 'global HSP'. There is only the HSP for each observer. Observers can agree to synchronize their clocks but they still have their own HSP.

oops again I forgot...I shall refer to it in future as a GPHS instead ok...:o

[ozziemate]

I sort of missed that in your post. I guess it is: 'I would assume then that both obserers wil see the same light infomation in their respective HSP's, there for the contention of this thread is false.
and the photonsphere retains simultaneity.'

Thus the end of this thread is that you have presented a not-quite-standard diagram that illustrates the relativity of simultaneity in SRT. It is a pity that it was not in your second post or that you did not bother to look at similar diagrams also illustrating the relativity of simultaneity in SRT.:)

I think you need to add a :blush: or :o to the last post!
Something else I just realised is in the use of language:
non-simultaneity and relative simultaneity have entirely different meanings so it seems.

The focus had to be on the HSP's to logically "see" how SRT deals with its relativity of sim. and not just understand it as if out of a text book. Looking at a diagram tells you only a certain amount but actually visualising it logically in a real setting is another.

[ozziemate]

any ways, just for your amusement the nextthread I am constructing is about the inverse sphere and absolute zeo. Should be fun and another ball breaker....ha

[Perpetual Student]

any ways, just for your amusement the nextthread I am constructing is about the inverse sphere and absolute zeo. Should be fun and another ball breaker....ha

What a waste of time!

[Reality Check]

any ways, just for your amusement the nextthread I am constructing is about the inverse sphere and absolute zeo. Should be fun and another ball breaker....ha
Not fun - just silly and trivial.

It might be interesting to see your rigorous mathematical definitions of the inverse sphere and absolute zero. But everyone knows that you do not have any.

[ozziemate]

Not fun - just silly and trivial.

It might be interesting to see your rigorous mathematical definitions of the inverse sphere and absolute zero. But everyone knows that you do not have any.
the funny thing about dealing with absolutes , you don't need much math to do it.

[Reality Check]

the funny thing about dealing with absolutes , you don't need much math to do it.
the funny thing about dealing with reality, you need math to do it.

[Tubbythin]

The focus had to be on the HSP's to logically "see" how SRT deals with its relativity of sim. and not just understand it as if out of a text book. Looking at a diagram tells you only a certain amount but actually visualising it logically in a real setting is another.

Not true. I'd never used an HSP before and I understand relativity of simultaneity (at least reasonably well).

[Reality Check]

Something else I just realised is in the use of language:
non-simultaneity and relative simultaneity have entirely different meanings so it seems.

simultaneity = the observation that 2 events happen at the same time according to an observer.
non-simultaneity = the observation that 2 events do not happen at the same time according to an observer.
relative simultaneity = the SRT conclusion that simultaneity and non-simultaneity in a reference frame moving relative to another reference frame according to the observer in that reference frame depends on the relative velocity.


The focus had to be on the HSP's to logically "see" how SRT deals with its relativity of sim. and not just understand it as if out of a text book. Looking at a diagram tells you only a certain amount but actually visualising it logically in a real setting is another.
The text books do provide the means to 'logically "see" how SRT deals with its relativity of sim.'. Every text book that I have seen on SRT has diagrams that illustrate relativity of simultaneity and the actual mathematics. They even use real settings (at least as real as your illustration).
I suspect that the focus had to be on the HSPs beacuse you were a bit obsessed with this minor part of the light cone diagram.

[Dancing David]

Wow


Originally Posted by ozziemate
the funny thing about dealing with absolutes , you don't need much math to do it.


Platonic foolsihness of the first caliber. Mental space precludes reality. IGNORE has saved me much frustration. there are no absolutes in reality.

[The Man]

Unless I've completely misunderstood what you've just said (certainly not beyond the realms of possibility) then you seem to be making things unecessarily complicated. If A was at the start and knew the distance to the gate at the end then the correction for light travel time from one end to the other is trivial. It might take a long time before A knows how long it took B to get to the end but it doesn't matter. Its a thought experiment, nobody has to actually stand around and wait for a light signal to come back.

Ie:
*A and B start clocks at the time B leaves A and passes through first light gate.
*B passes through second light gate and stops his clock. At this time the gate releases a photon in the direction of A.
*A receives photon from second light gate and stops clock. He measures a time T on his clock.
*A concludes it took B a time of T-d/c to get from the first light clock to the second light clock (where d is the distance in his reference frame between the two gates).


The primary point is ozzimates consideration of the starting and stopping of A’s and B’s clock being simultaneous. Even if we move A’s clock to the first lightgate , where A’s and B’s clock will start simultaneously, but then the travel time of the photon from the second lightgate will mean that A’s clock will stop 1,000,000 years after B’s clock stops. So we can have either the starting or stopping or A’s and B’s clocks as being essentially simultaneous but not both.

Yes this might seem unnecessarily complicated if one is just considering the elapsed time in both frames, but this is not the basis of ozzimates assertions.


Its a thought experiment, nobody has to actually stand around and wait for a light signal to come back.

Then how is A’s clock stopped if it is not around when the stop signal arrives at it?

We can think anything we want, but a “thought experiment” requires the relevant elements of an actual experiment otherwise it is just a thought.


Ozzimates thinking appears to be that if all observers on a given HSP will observe the same events as simultaneous and non- simultaneous infers that all observers make those observations simultaneously. From both A’s and B’s perspectives the starting and stopping of B’s clock and the crossing of the lightgates are effectively simultaneous. However A and B can not make both of those observations at the same times (due to the speed of light). So they will observe those events as simultaneous but not make those observations simultaneously.

[The Man]

To put it more succinctly, if we have observers on A (and all references in A’s frame) at both lightgates and a lamp on B that turns on when its clock starts and goes off when it stops. We can also have lights on the lightgates that go on as the gate is crossed. The observer at the first lightgate will observe the light on B turning on (as its clock starts) and the light on the lightgate going on as simultaneous. 1,000,000 years later the observer at the second lightgate will also observe the light on B and the light on the first lightgate as turning on simultaneously but will make that observation at a different time (or non-simultaneous) with the observer at the first gate, even though they are in the same HSP. Another 1,000,000 years later the observer at the second lightgate will see the light going off on B and the light on the second lightgate going on as simultaneous events. The observer at the first light gate will also observe those events as simultaneous but another 1,000,000 years later. So again observers in a given HSP (A) will observer those events as simultaneous but will not make those observations simultaneously.

[Tubbythin]

The primary point is ozzimates consideration of the starting and stopping of A’s and B’s clock being simultaneous. Even if we move A’s clock to the first lightgate , where A’s and B’s clock will start simultaneously, but then the travel time of the photon from the second lightgate will mean that A’s clock will stop 1,000,000 years after B’s clock stops. So we can have either the starting or stopping or A’s and B’s clocks as being essentially simultaneous but not both.

Yes this might seem unnecessarily complicated if one is just considering the elapsed time in both frames, but this is not the basis of ozzimates assertions.

Then you were more aware of precisely what ozziemate was asserting wrt this experiment than I was. The point I was making was that, for the first time, ozzie had constructed an experiment that actually made some semblance of sense in SRT. Your comments seemed to be counter-productive with regard to actually making progress.


Then how is A’s clock stopped if it is not around when the stop signal arrives at it?

We can think anything we want, but a “thought experiment” requires the relevant elements of an actual experiment otherwise it is just a thought.
You missed my point entirely. A thought experiment has to be consistent with the theory under study. What it does not have to be is practical.

[The Man]

Then you were more aware of precisely what ozziemate was asserting wrt this experiment than I was. The point I was making was that, for the first time, ozzie had constructed an experiment that actually made some semblance of sense in SRT. Your comments seemed to be counter-productive with regard to actually making progress.

Well I am certainly glad to see ozzie trying to utilize SRT in his attempt to refute it. Progress has been slow on this thread so I was attempted to get at the primary difficulty ozzie is having with SRT, which seems to me to be his focus on temporal considerations without spatial considerations, as they are linked by the speed of light.



You missed my point entirely. A thought experiment has to be consistent with the theory under study. What it does not have to be is practical.

No, I did not miss your point, but the thought experiment has to be consistent with all the theories under study which in this case is not just SRT but also ozzie’s notion as to why it might have been invalid. Ozzie considered that thought experiment consistent with his notion of universal time, which is not practical under SRT, by excluding the spatial considerations that demonstrates even though all observers in a given HSP consider the same events as simultaneous, all observers (even in a given HSP) do not make those observations simultaneously. So, yes a thought experiment has to be consistent with the theory under study but just making it consistent with ones preferred theory (universal time) does not make it a practical thought experiment. I do not mean practical in the sense that the experiment can actually be preformed (certainly constructing a 1,000,000 light year long test apparatus would be impractical) but practical in the sense that the thought experiment must include all relevant elements (like signal travel time) to make it worth thinking about. Otherwise it is just a construct to support some preferred theory and not an exploration of the implications and perhaps counter indications of that theory. I do not think we are in disagreement but just perhaps misreading each other.

[Tubbythin]

I do not think we are in disagreement but just perhaps misreading each other.

Quite possibly. Or we are just interpreting where ozzie was trying to lead us differently.

[The Man]

Quite possibly. Or we are just interpreting where ozzie was trying to lead us differently.

Agreed.

[ozziemate]

Hi Guys,
Just a thread about what I have been discussing elsewhere as an "Inverse sphere" which may or may not have profound consequences. [ this I leave up to you]
At first this may seem trite and very trivial but if you bear with the description you may see how "absolute zero" or "absolute nothing-ness" can be derived using an "inverse sphere" as a vehicle.

Simply put:
An inverse sphere is an area of volume created by default of substance surrounding it rather than the substance of the inverse sphere it self. IN this case ultimately it is precisely the fact that the inverse sphere contains a volume with absolutely nothing within that volume that proves the no-existence of absolute nothingness or zero space.
Zero space being the term I have coined for the volume with in this inverse sphere.

Firstly a description of the basic premise:

We have an iron ball that is near perfect in it's spherical shape.

At the center of this ball we have a spherical area cut out, and this area is filled with air.

http://bizzymate.com/uploads/images/physics/invsphere01.jpg

So you can imagine a simple ball with a hole at it's center. Simple yes?

How ever the notion of the inverse sphere is basically that the hole at the center is a sphere and not a ball, it is created only by the material or the outer ball and has no real existence by itself.
In other words it's existence as a inner volume is created by the balls substance and the dimensions of the inner cavity.
again no big deal..yes?

However and this is where I think it gets interesting...
If we apply an infinite reduction to the entire ball, we are left with not a inner cavity that disappears into zero volume as this is required by science. The distinction is that substance can not reduce to zero but must always be >0 when applying infinity.

So we end up with an inner volume of the hole at the center that is created by the inner surface of the outer ball that is infinitesimal in "concave" area.

Again this image but imagine now it is reduced infinitely.
http://bizzymate.com/uploads/images/physics/invsphere01.jpg
The inner circle as shown now has a circumference of infinitesimal [ which is >0]

So the question remains:

How much volume does the inner sphere actually have if:
1] there is nothing inside it "remembering that everything of substance must be >0 in volume.
2] There is a inverse surface area of the "inverse sphere" that must be >0 and infinitesimal.

I ask:
Do we have a volume of space that must be zero in dimension yet retain a substance surface area of infinitesimal dimension?

we seem to be left with a conundrum?

The volume must be >0 yet there must also be "absolutely nothing" in it.
I believe using this method we can determine the reality of absolute zero.

care to discuss?:)

[ozziemate]

simultaneity = the observation that 2 events happen at the same time according to an observer.
non-simultaneity = the observation that 2 events do not happen at the same time according to an observer.
relative simultaneity = the SRT conclusion that simultaneity and non-simultaneity in a reference frame moving relative to another reference frame according to the observer in that reference frame depends on the relative velocity.


The text books do provide the means to 'logically "see" how SRT deals with its relativity of sim.'. Every text book that I have seen on SRT has diagrams that illustrate relativity of simultaneity and the actual mathematics. They even use real settings (at least as real as your illustration).
I suspect that the focus had to be on the HSPs because you were a bit obsessed with this minor part of the light cone diagram.
The focus on the HSP's and then on the global PHS [ my term GPHS] has been for a number of reasons:

It is all that exists, the cones themselves are merely temporal.
That if the hsp's are zero in duration than all events must be simultaneous by virtue of the fact that the must all occur in the same zero duration HSP [ global]

By then looking at the diagram provided by the link you gave you can see how SRT fudges the issue by claiming relative simultaneity when in fact it appears that it is merely light info delays.

If we apply a Global PHS [GPHS[ which SRT must do to derive it's notion of relative simultaneity we can see that SRT claims non-simultaneity on a hyper surface that has zero duration.
Of course this poses a contradiction in the use of HSP's unless one simply realizes we are talking about light info delays and mere geometry of perspectives.
This is not non-simultaneity as non-simultaneity must require at least two HSP's of zero duration existing non-simultaneously [ one in the future of the other] thus the light cones would not line up.
But as the light cones for all HSP's involved according to SRT do line up then all events must be existent in that single constantly changing zero duration moment.
So the issue of relative simultaneity may still hold but not because of time but more because of location and perspective.
Where as the issue of non-simultaneity can not be logically concluded. IMO.

So concentrating on the "minor" aspects of HSP's has it's benefits.
the end result is a GPHS that has this general time function:
http://zeropointtheory.com/images/stories/images/time/10.gif
[please replace the word "NOW" with Global PHS or Global HSP]


IMO

[ozziemate]

Quite possibly. Or we are just interpreting where ozzie was trying to lead us differently.
The thing is that just because the observers record different elapsed time does not necessarilly imply a loss of simultaniety.
e.g.
______________A_____________B
event 1 --------12.00----------12.00
event 2---------12.30----------12.35
event 3---------13.00----------13.10

All events in this example are simultaneous but are recorded at different time due to dilation of the clocks by either RF depending on gedanken perspectives.

In the light gate experiment it is certain that both observers will not agree on elapsed time but that does not necessarilly imply a loss of simultaneity of events.

IMO
As previously stated: If all events occur in a single constantly changing zero duration HSP then the above conclusion is the only logical outcome is one extends to a global perspective [GPHS or GHSP]which SRT requires to determine whether non-simultaneity exists or not.

[ozziemate]

Here is that light Gate animation again.
http://bizzymate.com/uploads/images/physics/lightgate01.gif
Notes:

the distance of between oberver B and observer A is perpendicular to vector and set at very small distances [ insignicant light info delays]
Both clocks will record the light gate interruption event simultaneousy all along the journey whether we swap perspectives or not.

Whilst length contraction onlong vector and time diation may be present this does not imply a loss of simultaneity in fact to show non-simultaniety would be a real challenge using this gedanken IMO.

[Tubbythin]

The focus on the HSP's and then on the global PHS [ my term GPHS] has been for a number of reasons:

It is all that exists, the cones themselves are merely temporal.
That if the hsp's are zero in duration than all events must be simultaneous by virtue of the fact that the must all occur in the same zero duration HSP [ global]

By then looking at the diagram provided by the link you gave you can see how SRT fudges the issue by claiming relative simultaneity when in fact it appears that it is merely light info delays.
Nope, the "breaking" of simultaneity has nothing to do with light transit time.


If we apply a Global PHS [GPHS[ which SRT must do to derive it's notion of relative simultaneity we can see that SRT claims non-simultaneity on a hyper surface that has zero duration.
Of course this poses a contradiction in the use of HSP's unless one simply realizes we are talking about light info delays and mere geometry of perspectives.
Huh? There are no "global" reference frames or surfaces in SRT.
Once again the effects of SRT in different reference frames is not caused by light transit time.


This is not non-simultaneity as non-simultaneity must require at least two HSP's of zero duration existing non-simultaneously [ one in the future of the other] thus the light cones would not line up.
I have no idea what you mean. The issue of (non-)simultaneity is whether or not two events occur at the same time in a given reference frame. If two events occur at the same time in one inertial reference frame but not in another then there can be no absolute simultaneity.


But as the light cones for all HSP's involved according to SRT do line up then all events must be existent in that single constantly changing zero duration moment.
So the issue of relative simultaneity may still hold but not because of time but more because of location and perspective.
Where as the issue of non-simultaneity can not be logically concluded. IMO.
Yes it can. Try this:
Go back to the issue of the light source. Now enclose the source in a hollow sphere of radius R. Now imagine the origin of your co-ordinate system ((x,y,z)=(0,0,0)) is at the source, x is the axis going left to right and y the axis bottom to top. Now imagine two people standing on the sphere, one at (-R,0,0) and one at (0,R,0). Now at t=0 light is emitted isotropically by the light source. The wavefront will thus be spherical and will reach the person at (-R,0,0) and at (0,R,0) at the same time (t=R/c). Now suppose the arriving wave fronts set off devices that jettison these two poor luckless people into space. Because the wavefront is spherical, the people are jettisoned at the same time ACCORDING TO AN OBSERVER AT REST WITH RESPECT TO THE LIGHT SOURCE.
Now, imagine you are in a spacecraft on a flyby and moving along the x axis at a substantial fraction of c. To you the sphere on which the people stand will not be spherical at all, it will be ellipsoidal due to length contraction. But the wavefronts must, due to the constancy of c be spherical (yes, I got this completely wrong earlier). So the wavefronts will reach the two people on the sphere/ellipsoid at two different times. And thus be jettisoned at two different times.
And bang: absolute simultaneity has gone.

[Tubbythin]

The thing is that just because the observers record different elapsed time does not necessarilly imply a loss of simultaniety.
This is true.


e.g.
______________A_____________B
event 1 --------12.00----------12.00
event 2---------12.30----------12.35
event 3---------13.00----------13.10

All events in this example are simultaneous but are recorded at different time due to dilation of the clocks by either RF depending on gedanken perspectives.
And I'd thought we'd been making progress. But apparently not...
For two events to be simultaneous to a specific inertial observer they must occur at the same time. Hence NONE of the above events are simultaneous in either reference frame.

[ozziemate]

Tubbythin,

...snip... The issue of (non-)simultaneity is whether or not two events occur at the same time in a given reference frame. If two events occur at the same time in one inertial reference frame but not in another then there can be no absolute simultaneity.
Where I am at a loss is that for the events to occur at all they must all do so in a zero duration moment.
And if they are not simultaneous then they must occur in at least two time separated single zero duration moments.
And as been proved all events occur according to SRT in the same single duration moment.
Thus non-simultaneity is actually a non-issue.
non simultaneity in this context is not that one event occurs at 10 am and another occurs at 10.15 am...in this contect we are discussing the HSP's
which by neccessity of SRT must share the same single zero duration moment which automatically implies simultaneity.

The space time diagram:
http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png
shows quite clearly how regardless of perspective the same zero duration moment is involved regarding all observers observations.

just swappin observers doesn't change this fact.
If this is not a fact then the light cones will not line up when you draw this composite diagram as shown above.

[Fredrik]

Huh? There are no "global" reference frames or surfaces in SRT.

I don't know what Ozzie had in mind when he used that word, but knowing him I'm sure that whatever he was thinking is so far beyond wrong that there are no words for it. There are however things that I would call "global coordinate systems" in SR. They are just coordinate systems that have the entire spacetime manifold as their domains of definition.

[Tubbythin]

Where I am at a loss is that for the events to occur at all they must all do so in a zero duration moment.
And if they are not simultaneous then they must occur in at least two time separated single zero duration moments.
And as been proved all events occur according to SRT in the same single duration moment.
What on Earth are you talking about?


Thus non-simultaneity is actually a non-issue.
non simultaneity in this context is not that one event occurs at 10 am and another occurs at 10.15 am...in this contect we are discussing the HSP's
which by neccessity of SRT must share the same single zero duration moment which automatically implies simultaneity.
To discuss relativity of simultaneity there is no requirement whatsoever to ever mention HSPs.


The space time diagram:
http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png
shows quite clearly how regardless of perspective the same zero duration moment is involved regarding all observers observations.
You what?


just swappin observers doesn't change this fact.
If this is not a fact then the light cones will not line up when you draw this composite diagram as shown above.
And huh?

[Tubbythin]

I don't know what Ozzie had in mind when he used that word, but knowing him I'm sure that whatever he was thinking is so far beyond wrong that there are no words for it. There are however things that I would call "global coordinate systems" in SR. They are just coordinate systems that have the entire spacetime manifold as their domains of definition.

Fair point.
I think... but I could be completely wrong... he was trying to define an HSP that was somehow the same for all observers. Just like he previously tried to have a unique reference frame.
But who knows? I'm not completely sure he does.

[Fredrik]

Where I am at a loss is that for the events to occur at all they must all do so in a zero duration moment.

Events are just points in spacetime. E.g. any point in the diagram you just posted (the black one, with different colored lines) is an event.

A "moment" would by definition be of zero duration, so it's unnecessary and confusing to call it a "zero duration moment". I assume you're referring to horizontal lines in the diagram. Every one of those consists of events that one inertial observer would assign the same time coordinate. The observer represented by the almost vertical red line would not assign the same time coordinate to any two events in a horizontal line. To him two events are simultaneous if they are both on a line that's parallel to the almost horizontal red line.

I explained this in #770. My advice is that you read that again.


And if they are not simultaneous then they must occur in at least two time separated single zero duration moments.

Translated: If two events are not in the same horizontal line, they must be in two different horizontal lines.

This is true but as trivial as anything can get. It's like saying that if Alice and Bob aren't in the same country, they must be in different countries.


And as been proved all events occur according to SRT in the same single duration moment.

No, nothing like that has been proved. We have only concluded that if an inertial observer assigns the same time coordinate to two events, they are simultaneous to him. This is also trivial. He assigns the same time coordinate to them because they are simultaneous according to the definition of simultaneity I posted earlier. That definition isn't trivial however.


Thus non-simultaneity is actually a non-issue.

Translation: We don't have to worry that two of the events we're considering aren't simultaneous in the inertial frame we're using, if we are only considering simultaneous events.

This is also trivial. All of your statements seem to be either false or true by definition. You haven't actually said anything in this entire thread that contains any real information.


non simultaneity in this context is not that one event occurs at 10 am and another occurs at 10.15 am...in this contect we are discussing the HSP's
which by neccessity of SRT must share the same single zero duration moment which automatically implies simultaneity.

No, "simultaneous" means "occuring at the same time" which means "has the same time coordinate". If one thing happens at 10:00 in the inertial frame we're using and another at 10:15 in the same frame, then they are not simultaneous in that frame.


The space time diagram:
http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png
shows quite clearly how regardless of perspective the same zero duration moment is involved regarding all observers observations.

just swappin observers doesn't change this fact.
If this is not a fact then the light cones will not line up when you draw this composite diagram as shown above.
No, it shows exactly the opposite of what you're saying. I explained it in #770. You should read that post.

[Fredrik]

The focus on the HSP's and then on the global PHS [ my term GPHS] has been for a number of reasons:

You agreed not to attempt to replace the well-defined "HSP" with some undefined magical fantasy object called the "PHS", and now you're doing it anyway?!

[Reality Check]

The focus on the HSP's and then on the global PHS [ my term GPHS] has been for a number of reasons:
It is all that exists, the cones themselves are merely temporal.
That if the hsp's are zero in duration than all events must be simultaneous by virtue of the fact that the must all occur in the same zero duration HSP [ global]
By then looking at the diagram provided by the link you gave you can see how SRT fudges the issue by claiming relative simultaneity when in fact it appears that it is merely light info delays.

If we apply a Global PHS [GPHS[ which SRT must do to derive it's notion of relative simultaneity we can see that SRT claims non-simultaneity on a hyper surface that has zero duration.
Of course this poses a contradiction in the use of HSP's unless one simply realizes we are talking about light info delays and mere geometry of perspectives.
This is not non-simultaneity as non-simultaneity must require at least two HSP's of zero duration existing non-simultaneously [ one in the future of the other] thus the light cones would not line up.
But as the light cones for all HSP's involved according to SRT do line up then all events must be existent in that single constantly changing zero duration moment.
So the issue of relative simultaneity may still hold but not because of time but more because of location and perspective.
Where as the issue of non-simultaneity can not be logically concluded. IMO.

So concentrating on the "minor" aspects of HSP's has it's benefits.
the end result is a GPHS that has this general time function:
http://zeropointtheory.com/images/stories/images/time/10.gif
[please replace the word "NOW" with Global PHS or Global HSP]


IMO
One more time: There is no such thing as a global hypersphere of the present (HSP). There is a HSP for each observer.

[Gord_in_Toronto]

Hi Guys,
Just a thread about what I have been discussing elsewhere as an "Inverse sphere" which may or may not have profound consequences. [ this I leave up to you]
At first this may seem trite and very trivial but if you bear with the description you may see how "absolute zero" or "absolute nothing-ness" can be derived using an "inverse sphere" as a vehicle.

Simply put:
An inverse sphere is an area of volume created by default of substance surrounding it rather than the substance of the inverse sphere it self. IN this case ultimately it is precisely the fact that the inverse sphere contains a volume with absolutely nothing within that volume that proves the no-existence of absolute nothingness or zero space.
Zero space being the term I have coined for the volume with in this inverse sphere.

Firstly a description of the basic premise:

We have an iron ball that is near perfect in it's spherical shape.

At the center of this ball we have a spherical area cut out, and this area is filled with air.

http://bizzymate.com/uploads/images/physics/invsphere01.jpg

So you can imagine a simple ball with a hole at it's center. Simple yes?

How ever the notion of the inverse sphere is basically that the hole at the center is a sphere and not a ball, it is created only by the material or the outer ball and has no real existence by itself.
In other words it's existence as a inner volume is created by the balls substance and the dimensions of the inner cavity.
again no big deal..yes?

However and this is where I think it gets interesting...
If we apply an infinite reduction to the entire ball, we are left with not a inner cavity that disappears into zero volume as this is required by science. The distinction is that substance can not reduce to zero but must always be >0 when applying infinity.

So we end up with an inner volume of the hole at the center that is created by the inner surface of the outer ball that is infinitesimal in "concave" area.

Again this image but imagine now it is reduced infinitely.
http://bizzymate.com/uploads/images/physics/invsphere01.jpg
The inner circle as shown now has a circumference of infinitesimal [ which is >0]

So the question remains:

How much volume does the inner sphere actually have if:
1] there is nothing inside it "remembering that everything of substance must be >0 in volume.
2] There is a inverse surface area of the "inverse sphere" that must be >0 and infinitesimal.

I ask:
Do we have a volume of space that must be zero in dimension yet retain a substance surface area of infinitesimal dimension?

we seem to be left with a conundrum?

The volume must be >0 yet there must also be "absolutely nothing" in it.
I believe using this method we can determine the reality of absolute zero.

care to discuss?:)

"The volume must be >0 yet there must also be "absolutely nothing" in it." Why? and Why?

:boggled: and :confused:

[Fredrik]

...and it's a hypersurface, not a hypersphere.

[Reality Check]

So you have a hollow sphere with an outer radius of R and an inner radius of r.
What you get when you "apply an infinite reduction to the entire ball" depends on what you mean by 'infinite reduction' and is described by mathematics (not science).

If you mean divide R and r by infinity then that cannot be done because infinity is not a number.
If you mean set R and r to zero then you get a point.
If you mean the limit as R/n and r/n as n goes to infinity then I think you get a sphere with an infinitesimal R and an infinitesimal r. The inner sphere has a non-zero area and volume.
This is fairly trivial.

[Dancing David]

MMMMM, tacos.

[TjW]

No.

[Zep]

The "Riddle" of the inverse sphere!




Ha ha ha!




Oh? That's not the funny part?

[Fredrik]

The volume and surface area of a sphere of radius R is 4*pi*R3/3 and 4*pi*R2 respectively. Both of these clearly go to 0 as R goes to 0. If your "sphere" is defined by a void inside a realistic material (i.e. one composed of atoms), it's not really a sphere at all. It's not going to have a well-defined shape, so neither the volume nor the surface area is going to be well-defined.

And please don't use words like "infinitesimal" when you don't know what they mean.

[Reality Check]

Another point inspired by Fredik:
ozziemate: Maybe your question is what happens when we apply "an infinite reduction to the entire ball" where the ball is a physical sphere (radius R) with a spherical void at the center (radius r)?
In that case at some point the thickness of the balls surface, R-r, becomes less than 1 atom. The ball then ceases to be a ball. It becomes a collection of atoms distributed on the surface of a really small sphere.

[ozziemate]

Another point inspired by Fredik:
ozziemate: Maybe your question is what happens when we apply "an infinite reduction to the entire ball" where the ball is a physical sphere (radius R) with a spherical void at the center (radius r)?
In that case at some point the thickness of the balls surface, R-r, becomes less than 1 atom. The ball then ceases to be a ball. It becomes a collection of atoms distributed on the surface of a really small sphere.
if the inner void has an outer infinitesimal surface area [ sorry Fredrik ] and there can be no dimension any smaller we still have a spherical void of an undefinable volume. As the volume cannot be smaller than the infinitesimal surface area of the sphere unless it is zero volume.

So I ask you the question:

What do you get if you mathematically apply infinite reduction to any ball of substance?
What is the surface area?
and what is the volume of the infinitely reduced ball?

ok then make this ball hollow and apply the same reduction what do you end up with?
From what I can tell you end up with a sphere that has a surface area that is infinitesimal and this begs the question about the inner volume of the sphere?
how big is it?
and what is it?

my bet is it is absolute zero or nothing-ness.

The spheres surface area must be the smallest you can go yet > 0 therefore the volume within the sphere must be zero.
any ways thats the reasoning.

in discussions in the past much reference was made to zenos paradoxes especialy the tortice and the hare and how infinitesimals are used instead of zero. [ we were trying to conclude the duration in time of the HSP's in SRT[ the poitn beteween the light cones. I was arguing the case for zero duration and the other gent was arguing that it must be infinitesimal in duration - as it turned out we may be both correct - but that's another thread]

BTW if Fredrik would like to discuss infinitesimals I am all ears...:)

[Reality Check]

Define "mathematical reduction."
If you have a valid definition then you end up with 2 spheres of infinitesimal radius, area and volume. One just started out and remains inside the other (r < R).

You are treating infinitesimals as numbers. This is wrong.
An infinitesimal sphere can contain another infinitesimal sphere just as an infinite sphere can contain another infinite sphere.

[nathan]

hm, an infinitesimal void with infinitesimal surface and volume. If that's causing you problems, then you sure don't want to look at Gabriel's Horn

[Reality Check]

ozziemate: Something you seem not to understand - the hypersurface of the present consists of 2 sets of spacetime points:

The position of the observer at their present time.
Everywhere that the observer is not at their present time.
The second set of points are uninteresting. SRT is interested in the observer - not where they are not. That is why Special Relativity goes on about observers at the positions that they are. Observers cannot observe from where they are not and so those positions are ignored in SRT.

However HSPs are talked about. For example:

arXiv has a grand total of 18 preprints with the phrase "hypersurface of the present".
Google has 512 results for "hypersurface of the present".
Google Scoholar has 1 result for "hypersurface of the present".

[Reality Check]

...snip...
how big is it?
and what is it?

my bet is it is absolute zero or nothing-ness.

The spheres surface area must be the smallest you can go yet > 0 therefore the volume within the sphere must be zero.
any ways thats the reasoning.
...snip...
Its size is infinitesimal in radius, area and volume according to my simple knowledge of infinitesimals. That assumes that your "mathematical reduction" results in infinitesimals. It may result in very small but finite numbers.
It is a mathematical object. It is not "absolute zero or nothing-ness" because it is definitely something.
"the smallest you can go yet > 0" is not the definition of infinitesimal (http://en.wikipedia.org/wiki/Infintesimal) and so your reasoning is wrong.
The easiest way to see that your reasoning is wrong is to turn it around: If the volume of the inner sphere is zero then its radius must be zero. If its radius is zero then its surface area must be zero. This contradicts your assumption that "The spheres surface area must be the smallest you can go yet > 0".

[NobbyNobbs]

An inverse sphere is an area of volume created by default of substance surrounding it rather than the substance of the inverse sphere it self.

What you have described already has a mathematical definition. It is called a "sphere". There is no need to make up new terms for it simply because it is defined by what artists call "negative space".

How ever the notion of the inverse sphere is basically that the hole at the center is a sphere and not a ball, it is created only by the material or the outer ball and has no real existence by itself.

At first this confused me, but it seems to me now that you are distinguishing a "sphere" to be a mathematical construct and a "ball" to be that object with the properties of the mathematical construct known as "sphere"? Fair enough.

However and this is where I think it gets interesting...
If we apply an infinite reduction to the entire ball,

Stop. Please define "infinite reduction". If possible, please do it mathematically, so that there is no quibbling over semantics.

The volume must be >0 yet there must also be "absolutely nothing" in it.


This sentence describes a vacuum. Big deal?



What do you get if you mathematically apply infinite reduction to any ball of substance?

I think this is where you are losing some folks. Please describe, mathematically if possible, what you mean by this. Thanks.

[NobbyNobbs]

hm, an infinitesimal void with infinitesimal surface and volume. If that's causing you problems, then you sure don't want to look at Gabriel's Horn

I remember my 11th grade math teacher showing us Gabriel's Horn. It blew my mind! I walked around in a daze for days trying to reconcile it in my mind.


I don't think I ever did.

[Fredrik]

if the inner void has an outer infinitesimal surface area [ sorry Fredrik ] and there can be no dimension any smaller we still have a spherical void of an undefinable volume. As the volume cannot be smaller than the infinitesimal surface area of the sphere unless it is zero volume.

It's not spherical. The smallest void you can create is one with only one atom removed from the solid. That void isn't going to be spherical. It's not even going to have a well-defined shape.

It's also not going to be of infinitesimal size. It's going to be about the size of an atom.


What do you get if you mathematically apply infinite reduction to any ball of substance?
What is the surface area?
and what is the volume of the infinitely reduced ball?

You can't apply a mathematical operation to a physical object!

What you can do is to define a sphere with radius r as the set of all (x,y,z) that satisfy x2+y2+z2=r2, and then take the limit r ---> 0. As I said before, both the volume and the surface area are 0 in that limit.


BTW if Fredrik would like to discuss infinitesimals I am all ears...:)
That's a very difficult subject. Almost no physicists know the definition of infinitesimals, and I'm sure a lot of mathematicians don't either. The word is used a lot in physics books without a definition, and it really bugged me at first. It took me while to figure out what they mean when they use it. They're not talking about infinitesimals at all. When they say that a variable is an infinitesimal, it isn't. It's just a number, but they say that it's an infinitesimal if the equations they're about to present are approximations to nth order in that variable, usually with n=1. I'm not sure why I'm explaining that to you though. You obviously don't know enough math to know what "first order" means.

[Fredrik]

It seems that the two threads were merged, without any comments from a moderator. The posts are in a pretty confusing order now, but I guess we can live with it. (For example, #815 is supposed be immediately after #813).

[sol invictus]

That's a very difficult subject. Almost no physicists know the definition of infinitesimals, and I'm sure a lot of mathematicians don't either.

By "the definition", you have in mind surreal numbers? Or something else?

The word is used a lot in physics books without a definition, and it really bugged me at first. It took me while to figure out what they mean when they use it. They're not talking about infinitesimals at all. When they say that a variable is an infinitesimal, it isn't. It's just a number, but they say that it's an infinitesimal if the equations they're about to present are approximations to nth order in that variable, usually with n=1.

Yeah, I suppose that's right. It makes sense to physicists because in physics more or less everything is an approximation, and more or less all approximations can be thought of as expansions carried out to some order in a small parameter. So the fact that (for example) there exists a mathematically precise definition of velocity is more or less uninteresting to a physicist, since dx/dt (where dx and dt are finite but sufficiently small) is good enough.

[Fredrik]

By "the definition", you have in mind surreal numbers? Or something else?

I meant any mathematically rigorous definition of "numbers" that are smaller than all the positive real numbers, but still >0. I checked the Wikipedia article before I wrote the previous post, and it said that there are two ways:

1. Use the ZFC axioms of set theory to construct a larger set of "numbers" that includes the real numbers, the infinitesimals, and more.
2. Modify the axioms of ZFC set theory instead, so that the standard definition of real numbers includes infinitesimals.

The first successful attempt to follow the first approach defined the hyperreal numbers. I had heard about that before, but I knew almost nothing about it. I had also heard that the second approach was a possible way to go, but I didn't know if the construction of the hyperreals was made that way or not.

I looked up surreal numbers after reading your post. I had heard the word, but had no idea what they were. Apparently they include the hyperreals.

[Vorpal]

I meant any mathematically rigorous definition of "numbers" that are smaller than all the positive real numbers, but still >0.
Oh, that much is trivial. Say, over R2, define (a,b)·(c,d) = (ac,ad+cb), identify 1 = (1,0) and d = (0,1), and we have f(x+yε) = f(x) + yεf'(x) for any smooth function f, with the obvious domain extension. But I gather from your subsequent comments that you had a much some other notion of "number", which makes it more difficult. This is a local ring, not a field, but many things that are routinely called "numbers" are constructed in much the same way and also fail to form a field.

1. Use the ZFC axioms of set theory to construct a larger set of "numbers" that includes the real numbers, the infinitesimals, and more.
2. Modify the axioms of ZFC set theory instead, so that the standard definition of real numbers includes infinitesimals.
Which definition is "standard"? (Or do you just mean that other axioms on top of ZFC imply the existence of similarly "hyperreal" model of the reals? That's true.)

The first successful attempt to follow the first approach defined the hyperreal numbers.
To be precise: the hyperreals are the first proper ordered field extension to the reals that realizes every consistent formula of up to countably many constant that's provable in ZFC.

[Fredrik]

This is the definition of real numbers I had in mind: "An ordered field with the property that every subset that's bounded from above has a least upper bound". I know that there are several different ways to construct a field with those properties from the rational numbers, but I think of those as "constructions", not as definitions. I'm not sure what mathematicians prefer to call them.

I assumed that the hyperreals would be an ordered field too. That's what I had in mind when I used the word "numbers".

It's interesting that it's that easy to get f(x+yε) = f(x) + yεf'(x) to hold. I didn't know that. But is it possible to define an ordering relation on this set? Is 0 < ε < x for all positive real numbers x? And did you mean ε=(0,1)?

[Vorpal]

This is the definition of real numbers I had in mind: "An ordered field with the property that every subset that's bounded from above has a least upper bound".
Hmm... alright. (I'll add to get rid of some pathological cases: a uniform, Archimedan, complete, and ordered field.)

I know that there are several different ways to construct a field with those properties from the rational numbers, but I think of those as "constructions", not as definitions.
The way I usually think about it is there is a definition, but "is" is understood to be up to a context-dependent isomorphism. Hence the need for a well-defined starting point.

I assumed that the hyperreals would be an ordered field too. That's what I had in mind when I used the word "numbers".
The hyperreals are, but the dual numbers described above aren't.

It's interesting that it's that easy to get f(x+yε) = f(x) + yεf'(x) to hold. I didn't know that. But is it possible to define an ordering relation on this set? Is 0 < ε < x for all positive real numbers x? And did you mean ε=(0,1)?
Yes, I meant ε instead of d (I switched from d to ε while typing, and didn't replace every instance). The order relation is very easy in lexicographic order: (a,b)<(c,d) iff (a<c or (a=c and b<d)). Then 0 < ε < x for all positive reals x, where x is naturally identified with (x,0).

This is actually a straightforward case of the Cayley-Dickson trick, except for the involution. Over a ring R with an involution *, define on R²
[1] (a,b)+(c,d) = (a+c,b+d), (a,b)* = (a*,-b),
[2] (a,b)·(c,d) = (ac+χdb*,a*d+cb)
[3] (a,b)/(c,0) = (a/c,b/c), (a,b)-1 = (a,b)*/[(a,b)*(a,b)]
For example, repeatedly taking χ = -1 starting from the reals gives the chain reals→complex→quaternions→octonions. Taking χ = +1 also gives interesting number systems. The integers can be built up from the naturals through χ = +1, except that involution and division will not be defined in the above manner because the naturals do not form a ring (Edit: correction on this point).

[NobbyNobbs]

in physics more or less everything is an approximation, and more or less all approximations can be thought of as expansions carried out to some order in a small parameter.

You've made an approximation about approximations.

For some reason, I find that hysterically funny.

[ozziemate]

Regarding the Inverse sphere thread

The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal and because it only exists by what creates it [ everything else outside it.] you have an inverse sphere.

By default.

The inverse sphere must have zero at it's center because everthing on the inside must be on the outside.
thus the resultant spherical volume created is zero [ absolute zero] due to the fact that everything outside is absolutely everything else...

So in this sense absolute zero is proven to exist only by default of everything else.

[Reality Check]

Regarding the Inverse sphere thread

The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal and because it only exists by what creates it [ everything else outside it.] you have an inverse sphere.

By default.

The inverse sphere must have zero at it's center because everthing on the inside must be on the outside.
thus the resultant spherical volume created is zero [ absolute zero] due to the fact that everything outside is absolutely everything else...

So in this sense absolute zero is proven to exist only by default of everything else.
The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal (very small) then its volume and radius is infinitesimal (very small). You then have a very small spherical void in a bigger sphere. The inner sphere is still a sphere. Nothing has been inverted so there is no inverse sphere.

The inner sphere des not have zero at its center. We are free to put its center anywhere. But if you want then we can put it at the point (0,0,0). Thus the resultant spherical volume created is not zero.

[Acleron]

Regarding the Inverse sphere thread

The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal and because it only exists by what creates it [ everything else outside it.] you have an inverse sphere.

By default.

The inverse sphere must have zero at it's center because everthing on the inside must be on the outside.
thus the resultant spherical volume created is zero [ absolute zero] due to the fact that everything outside is absolutely everything else...

So in this sense absolute zero is proven to exist only by default of everything else.

Oh dear. It's not so much that you don't understand what anybody else tells you, you don't understand what you say yourself.

[Reality Check]

Regarding the Inverse sphere thread

The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal and because it only exists by what creates it [ everything else outside it.] you have an inverse sphere.

By default.

The inverse sphere must have zero at it's center because everthing on the inside must be on the outside.
thus the resultant spherical volume created is zero [ absolute zero] due to the fact that everything outside is absolutely everything else...

So in this sense absolute zero is proven to exist only by default of everything else.
Just notcied the bit in bold.

ozzimate: If the volume of the inner sphere is zero then what you have is a solid sphere. The inner sphere does not exist when its volume is zero or to put another way: when the volume of the inner sphere is zero, the outer sphere contains everything.

A solid sphere is a standard mathematical object.

[Fredrik]

Regarding the Inverse sphere thread

Everything you need to know is in #820 and #829.


The point being that if you reduce the inner spherical volume so that it's surface area is infinitesimal and because it only exists by what creates it [ everything else outside it.] you have an inverse sphere.

No, you don't. And if "everything else outside it" is something physical rather than mathematical, you don't have a sphere at all. And the size of whatever it is you have isn't infinitesimal.


The inverse sphere must have zero at it's center because everthing on the inside must be on the outside.

No, whatever's on the inside is definitely not on the outside. I have no idea why you think a claim like that makes any sense at all. :rolleyes:


thus the resultant spherical volume created is zero [ absolute zero] due to the fact that everything outside is absolutely everything else...

Hm, are you considering a mathematical sphere inside a physical object? Then it makes some sense to say that by choosing its location to be between matter particles and choosing its radius to be smaller than half the distance between particles, then there's no matter inside it. But there's nothing "inverse" or "infinitesimal" about this. You just have a small sphere. (And you could easily put a much smaller sphere inside it).


So in this sense absolute zero is proven to exist only by default of everything else.
No. I don't know what you mean by "absolute zero", but none of this proves anything.