Special relativity and expansion of the Universe, A paradox

[Ibix]

All that I mean by moving through " space" is - in a usual time- distance graph ( one directional i,e through x axis) the time dilates in a body which have an actual projection on x- axis. The other body will not have a projection in x axis, that have I point by saying " stationary in space". Finding out which body does have more projection in the spatial dimension is the task involved in solving the " earlier twin paradox" which I understood that that body breaks the symmetry. symmetry breakage is the essential tool through which the twin paradox is solved. My question is " can we break the symmetry of motion due to expansion, such that time dilation can be attributed to any of the bodies or to both of the bodies or to none of the bodies".

The key point of the twin paradox is that the twins meet up again. That means getting into a rocket. So far you haven't talked about rockets at all. If you add one then the twin paradox works more or less the same way as in flat spacetime. It's just that the return leg is longer than the outbound leg due to metric expansion so the maths is more complex.

 

[Rafeek AR]

There is always another possible answer: "mu", meaning that the question itself is flawed and needs to be un-asked. Here the question is flawed because it assumes that time dilation is defined in this scenario, which is not the case.

The answer " mu" implies there is no logical problem exists. Well search in google the " the twin paradox in an expanding universe" and you can see peer reviewed papers even in 2009 ( The last one I noted and I don't know if something exist after that. The results of that paper doesn't seems so digestible that it argues either one spatial dimension have to be " compacted" in order to solve the issue. The conclusion of that paper even suggest a deviation in the force law. Too much overloaded assumptions and conclusions.). Yes you might say such papers might be published in under rated journals, which is even better than the answer " mu". There are more than one paper you can identify in google. So un asking the question doesn't solve the problem.

 

[Ibix]

The answer " mu" implies there is no logical problem exists. Well search in google the " the twin paradox in an expanding universe" and you can see peer reviewed papers even in 2009 ( The last one I noted and I don't know if something exist after that. The results of that paper doesn't seems so digestible that it argues either one spatial dimension have to be " compacted" in order to solve the issue. The conclusion of that paper even suggest a deviation in the force law. Too much overloaded assumptions and conclusions.). Yes you might say such papers might be published in under rated journals, which is even better than the answer " mu". There are more than one paper you can identify in google. So un asking the question doesn't solve the problem.

Reference, please. Preferably a link to the paper.

 

[Rafeek AR]

Reference, please. Preferably a link to the paper.

https://arxiv.org/pdf/gr-qc/0503070.pdf.. Try it out

 

[Ibix]

That is not about an FLRW universe. From a skim of the abstract it is discussing a "cylindrical" universe, which is fun and interesting but not relevant to this thread. An FLRW spacetime is not like that one.

 

[EdgarLOwen]

First of all It should be noted that there is no twin "paradox". That's a misnomer. The twin example has a simple straightforward explanation in relativity that makes perfect sense. Paradoxes don't (yet) have simple straightforward explanations that make sense.

Edgar L. Owen

 

[Dale]

Well search in google the " the twin paradox in an expanding universe"

What is the relevance to your question? Your question is not a "twin paradox" since A and B are not co-located at the beginning and the end.

The answer to YOUR question remains "mu", despite the fact that OTHER questions are answerable.

 

[Rafeek AR]

That is not about an FLRW universe. From a skim of the abstract it is discussing a "cylindrical" universe, which is fun and interesting but not relevant to this thread. An FLRW spacetime is not like that one.

That is exactly my question. In an FLRW universe does such a question arise? If not why?. If it does. What is the solution?.

 

[Rafeek AR]

That is not about an FLRW universe. From a skim of the abstract it is discussing a "cylindrical" universe,.

He made the cylindrical abstraction by compacting one dimension in order to " make up" a universal frame of reference. Neither am I interested in "twin paradox". The question I am asking is simple. " in two bodies moving away due to expansion of the space in between them, in which body the time dilates?." It is claimed that in an FLRW universe there arise no problem of time dilation. I would like to know why?.

 

[Ibix]

That is exactly my question. In an FLRW universe does such a question arise? If not why?

No. Because an FLRW spacetime doesn't have any traversable closed inertial paths. In short, it's not the right "shape".

 

[jbriggs444]

The question I am asking is simple. " in two bodies moving away due to expansion of the space in between them, in which body the time dilates?."

mu

 

[PeterDonis]

The question I am asking is simple. " in two bodies moving away due to expansion of the space in between them, in which body the time dilates?."

This question has already been answered in this thread, repeatedly. Asking it again and again will not change the answer. The best quick summary of the answer was in post #16 by @Dale :

In GR, the usual solution describing a homogenous and isotopic universe, the one consistent with the data, is called the FLRW metric. It is not a static metric, so there is no global gravitational time dilation. However, there is still local kinematic time dilation. Any non-comoving observer is time dilated relative to a local comoving observer, but two non-local comoving observers cannot be unambiguously compared.

 

[PeterDonis]

The OP question has been answered. Thread closed.