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Before I ask this question, I just want to clarify that I am by no means an expert and that this question most likely came about due to my ignorance on the subject. If this is the case, please let me know where the understanding is in an intuitive way rather than explaining with calculations because although I can respect that equations can describe the universe I have a much better time understanding it when an example is used.

On to the question:

Let's say we can measure the time dilation between two frames of reference, and we pick out the frame where time runs faster due to time dilation thus choosing the frame that is moving slower compared to the other frame. If we then compare that frame of reference to another frame of reference where time runs faster due to time dilation again, and keep repeating this process over and over, can a frame of reference in which time runs the fastest (there is the least amount of dilation) be found in which to compare to the rest of the universe?

Axis Omega
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I'm afraid your idea won't work. Time dilation is symmetrical. Suppose your frame of reference and mine are moving inertially relativity to each other. A clock in your frame will seem dilated relative to the clocks in my frame, while a clock in my frame will seem equally dilated relative to the clocks in yours, so there is no way to say whether one of our frames is moving faster than the other.

If you are confused about how the effect can be symmetrical, you should not imagine that clocks in one frame run more slowly than clocks in the other, as that would lead to a conundrum. Instead, assume all the clocks still tick at the same rate, but the clocks in one frame are systematically out of synch with the clocks in the other. Next, remember that you cannot directly compare two individual clocks as they are wizzing past each other at great speed- instead you have to compare the time on a moving clock with the time on two stationary ones some distance apart. That is how the effect arises, because if the second stationary clock is out of synch with the first stationary clock-- suppose it is running a minute ahead- then the moving clock will seem to have lost a minute (ie to have experienced time dilation) when moving between the two stationary ones.

Marco Ocram
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    Your answer is special relativity, but the question is about general relativity, escpecially the FLRW metric – Yukterez Jun 05 '22 at 07:21
  • The issue raised in this answer exists in GR and the FLRW metric, so I think it is a good answer – Dale Jun 06 '22 at 00:16
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Axis Omega asked: "can a frame of reference in which time runs the fastest (there is the least amount of dilation) be found in which to compare to the rest of the universe?"

That is the frame of comoving observers for whom the CMB looks isotrope in each directions since they move along with the Hubble flow, in their frames the maximum time of 13.82 billion years has passed since the big bang. Observers who have a peculiar velocity relative to comoving observers see a dipole in the CMB and have a proper time of less than 13.82 billion years since the big bang. If we could catch a neutrino flying around since the big bang with almost c and read off its internal clock its proper time would be much lower than ours.

Yukterez
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  • I don't think the last sentence is correct. The CNB has been severely redshifted; it now has a (predicted) temperature of ~1.95 K, so those neutrinos are now (mostly) sub-relativistic. At least, their thermal energy is much smaller than their rest mass. (And of course, neutrinos don't have an internal clock, but some readers may not know that). – PM 2Ring Jun 05 '22 at 22:00
  • I don't know about subrelativistic neutrinos, last time I checked their precise velocity was unknown but since my older formulation "close to 0" might be ambiguous I changed it to "much lower than ours" – Yukterez Jun 05 '22 at 22:15
  • That's better. :) Sure, we don't really know what energy they have, and we may never be able to detect them. Some info on slow CNB neutrinos: https://physics.stackexchange.com/q/267035/123208 & https://neutrinos.fnal.gov/wp-content/uploads/2018/04/neutrino-energy-scale-web.jpg – PM 2Ring Jun 05 '22 at 22:41