Twins Paradox: Symmetry & Acceleration

[mysearch]

Question related to post #26/Granpa

This response references post #26 so apologises for being so out-of-sync with the current exchanges. However, an aspect of this thread was raised in another thread entitled `Gravitational Redshift`, which touched on a triplet extension to the twin paradox – outlined below.

I was particular interested in the link given in #26.
http://www.sysmatrix.net/~kavs/kjs/addend4.html

Initially I thought this link was trying to explain how 2 frames of reference could both justify how time was running slower in the other frame. Having now having had a chance to take a closer look at the detail, I don’t believe the example supports such a conclusion. While it may resolve the time difference between the 2 frames, it is clear at the start and end of the journey that only 1 frame was moving with respect to the other and it was this frame that underwent time dilation.

Note: There is no inference of an absolute frame of reference being made in this statement, simply that because there is an unambiguous start/stop point, where the frames recombined, there is no ambiguity of relative velocity or time dilation.

The triplet variant, mentioned above, is just an extension of the twin paradox. However, while 1 triplet stays on Earth, the other 2 take identical journeys at the same relative speed (and acceleration), as each other with respect to the stay-at-home triplet, but always in the opposite direction, i.e.

Triplet-1: A
Triplet-2: A-B-A-C-A
Triplet-3: A-C-A-B-A

Calculations, based on special relativity, seem to suggest that triplet 2 & 3 both measure the same elapsed time, which is less than triplet-1, at the end of the journey. However, there is a point in the journey above, when triplets 2 & 3 pass each other, as well as triplet-1, at point (A), where all have a relativistic velocities with respect to each other. This suggests that triplets 2 and 3 must experience some relativistic time dilation, with respect to each other, while the overall suggestion is that triplets 2 and 3 mark the same time throughout the journey with respect to triplet-1.

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler

The link above outlines both the Doppler Shift and GR explanations of the twin paradox based on a relative velocity of 0.866c giving \gamma=2. As such, it is the ‘stationary’ twin that transmits twice as many light pulses and the ‘moving’ twin. It can be seen that the ‘moving’ twin always receives twice as many pulses than it transmits over the entire journey due to the effects of time dilation. While the change in relative velocity makes the arrival rate complex, it is not impossible to calculate exactly when the pulses will arrive, assuming that the time dilation is a constant ongoing effect.

So finally, applying this same analysis to the triplet example, it seems to suggest that time for triplets 2 and 3 runs at the same rate throughout the journey, which is only time dilated with respect to triplet-1. If so, it suggests that no ‘physical or meaningful’ time dilation takes place as triplets 2 and 3 pass each other at 0.866c+0.866c=0.99c. Therefore, would be interested in any other interpretations.

 

[RandallB]

I'm not disagreeing with you but I thought the discussion was about Special Relativity. In that context I believe I'm correct in my assertion that there is no preferred, or absolute, frame of reference.

I have much less experience with GR although I must say I have never seen a claim that a preferred or absolute frame should exist in GR either. Please correct me if I'm wrong.

Actually I thought this started as NOT about SR, but about the twin paradox and how or if it relates to GR in an effort to understand the Twins at a level somewhere beyond SR alone.

All I added was that the “assertion that there is no preferred, or absolute, frame of reference” only applies to the on paper interpretation of a SR world. And cannot be automatically extended as true for a complete description of reality, as Astrophysicists must observe reality.
Since 1908 or so it has been known that SR was not capable of a complete description of reality; that is why of more advanced relativistic theories continued to develop beyond SR.

At a minimum when you assert “no preferred frame” it should be better stated as “no preferred frame within the limits of SR”. Otherwise you are likely to miss the simple fact (which I think you are missing) that Astrophysics does require the use of a particular form of preferred frame of reference. Do not think that the idea of a preferred frame goes un-used in physics.

 

[paw]

Actually I thought this started as NOT about SR, but about the twin paradox and how or if it relates to GR in an effort to understand the Twins at a level somewhere beyond SR alone.

Well you may be right, although I don't see any explicit reference to GR in the OP. However, all the comments I've made were in reference to an absolute frame in SR. I did try to make that clear a number of times but I guess it wasn't clear enough.

All I added was that the “assertion that there is no preferred, or absolute, frame of reference” only applies to the on paper interpretation of a SR world. And cannot be automatically extended as true for a complete description of reality, as Astrophysicists must observe reality.

Sure, I understand that.

Since 1908 or so it has been known that SR was not capable of a complete description of reality; that is why of more advanced relativistic theories continued to develop beyond SR.

I agree.

At a minimum when you assert “no preferred frame” it should be better stated as “no preferred frame within the limits of SR”.

I tried but I'll keep in mind in the future to be even more explicit.

Otherwise you are likely to miss the simple fact (which I think you are missing) that Astrophysics does require the use of a particular form of preferred frame of reference. Do not think that the idea of a preferred frame goes un-used in physics.

I am aware that astrophysisists use preferred frames to solve certain problems. I believe this is done for convenience in most cases, although sometimes I think it's used to explore new ideas as well. I don't think it's ever been stated that preferred frames in this context actually represent physical reality though. For example, I haven't read anything coming from the astrophysical community claiming there IS some form of absolute motion; at least in the sense that two simultaneous events in the absolute frame would be simutaneous in all other inertial frames. Please correct me if I'm wrong in this?

 

[RandallB]

Preferred Frames not in SR are used in Astrophysics

I am aware that astrophysisists use preferred frames to solve certain problems. I believe this is done for convenience in most cases, although sometimes I think it's used to explore new ideas as well. I don't think it's ever been stated that preferred frames in this context actually represent physical reality though. For example, I haven't read anything coming from the astrophysical community claiming there IS some form of absolute motion; at least in the sense that two simultaneous events in the absolute frame would be simutaneous in all other inertial frames. Please correct me if I'm wrong in this?

So as not to hijack this thread with the issue of preferred reference frames I’ve opened a separate thread to respond. https://www.physicsforums.com/showthread.php?t=237570"

https://www.physicsforums.com/showthread.php?t=237570