B Special relativity and expansion of the Universe, A paradox

[Rafeek AR]

None of this is contradictory. Both A and B's predictions are correct. Both signals are red-shifted due to the expansion of the space between. This is what @Ibix pointed out in #4.

Edit: Note that it is "FLRW metric". Not matrice.

The usual red shift is due to the fact that the light ray have to travel a distance. And if the distance increases that creates a red shift from the earlier light rays. But in relative motion time in a moving body does dilates with respect to an another stationary body. In the body where time is dilated the clock ticks slowly and that very slowing would result in a frequency variation. Yes you are right that expanding makes a red shift in light along with the variation in frequency due to the time dilation in the moving body. Consider a usual moving body ( not under expansion) , there too the variation in frequency can be obtained and both A and B will observe the shift due to the increasing space in between them. But in the ordinary case one of the two body is moving through space and the other is stationary in space there occurs a time dilation in the moving body and the frequency shift thus obtained is explicit to the frequency shift due the increase in distance. The frequency shift due to the increase in distance would be similar in two bodies when checking the incoming light, but in one body the time dilates and the frequency shift varies by that amount from the other body, and we all know that is how the usual twin paradox is solved.
In the case of expansion neither of the bodies are moving through space but according to each of them the other one is moving. Yes the red shift due to the increase in distance between them would be similar, but each of them will calculate an extra shift for the other body due to the time dilation in the other body that both the observers doesn't know if the movement of other body is due to the expansion of universe or ordinary motion. That extra shift necessarily have to contradict since both the observers include it.

 

[jbriggs444]

But in the ordinary case one of the two body is moving through space and the other is stationary in space there occurs a time dilation in the moving body and the frequency shift thus obtained is explicit to the frequency shift due the increase in distance.

There is no such thing as "moving through space". There is no such thing as being "stationary in space". There is no such thing as time dilation due to motion in space.

An observed frequency can be explained in different ways in different coordinate systems. None of these explanations are right and none of these explanations are wrong in any absolute sense.

In the case of expansion neither of the bodies are moving through space but according to each of them the other one is moving.

In co-moving coordinates, neither of the bodies claims that the other is moving. Only that the distance between them is increasing.

 

[Ibix]

But in the ordinary case one of the two body is moving through space and the other is stationary in space there occurs a time dilation in the moving body and the frequency shift thus obtained is explicit to the frequency shift due the increase in distance.

Here you have adopted a frame of reference in which one of the bodies isn't moving and the other is. Fine, but that's an arbitrary choice.And the whole point of special relativity's time dilation is that once you subtract out the effects of the movement of the source on the frequency you receive there is something left over; this is time dilation.

In the case of expansion neither of the bodies are moving through space but according to each of them the other one is moving.

If you start from the position that something is both moving and not moving you will inevitably get contradictions. Noone would claim that the other body is both moving and not moving at the same time. However, in general relativity you can have a phenomenon called metric expansion where an unmoving object is getting further away due to the time dependence of the metric. In other words, we chose a definition of distance that changes with our chosen definition of time. Then we attribute redshift to the changing distance, not to time dilation.

 

[Dale]

in "WHICH BODY TIME DILATES? A OR B". Can we tell A or B? Or can we tell A &B? Or can we tell not A &notB. Those three are the possible answers

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.

 

[Rafeek AR]

There is no such thing as "moving through space". There is no such thing as being "stationary in space". There is no such thing as time dilation due to motion in space..

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".

 

[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.