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This question already has an answer here:

In Wikipedia, the age of the universe is defined as the "time elapsed since the Big Bang" while "time" links to "the cosmological time parameter of comoving coordinates" which itself links to "the elapsed time since the Big Bang according to a clock of a comoving observer", the latter being defined as "the only observer that will perceive the universe, including the cosmic microwave background radiation, to be isotropic".

Meanwhile, we also find in Wikipedia: "The theory of relativity does not allow the existence of absolute time because of the nonexistence of absolute simultaneity. Absolute simultaneity refers to the experimental establishment of coincidence of two or more events in time at different locations in space in a manner agreed upon by all observers in the universe."

While both makes sense to me, I feel like a contradiction between them in the sense that the age of the universe for the comoving observer located where and when an event occurs could be considered as the absolute time at which this event occurs. Indeed, such a definition of time would probably be impossible to implement in practice due to measurement uncertainties. However, it could be used in principle to define in which order two events actually occur in a way on which all possible observers should agree.

So, what did I miss and how can we reconcile these two points of view?

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marked as duplicate by John Rennie general-relativity Jan 29 '16 at 12:41

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Among other things: The comoving observer who sees the universe as isotropic exists only in models which have abstracted away the detailed structure of the Universe, such as the (apparently non-isotropic) distribution of individual galaxies, individual stars, individual planets, and individual particles of dust. These models can be very useful approximations for some things, and much less useful for others. $\endgroup$ – WillO Jan 28 '16 at 14:26
  • $\begingroup$ Simultaneity is not restored by cosmological time, neither is absolute time. That the universe is homogeneous and isotropic is an assumption for an average over volume elements that contain many galaxies, and it's not even that great an assumption when we look at the detailed distribution. We are even using the counterexample to the homogeneity assumption (the CMB) to lear very important information about the early universe. $\endgroup$ – CuriousOne Jan 28 '16 at 16:28
  • $\begingroup$ @CuriousOne: Do you mean that comoving time is an ill-defined concept? $\endgroup$ – Georges Jan 28 '16 at 16:42
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    $\begingroup$ Is temperature an ill-defined concept because different parts of the system will experience different Brownian motion? $\endgroup$ – CuriousOne Jan 28 '16 at 16:43
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A comoving observer and an observer that has been moving at $0.866c$ since Big Bang will disagree on their measured age of the Universe by a factor of 2. While both measurements are correct, we can say that the comoving observer measures a more "natural" age of the Universe. For instance, the comoving observer is the only observer who will measure the Universe to be isotropic. But a time being more natural, or making more sense in terms of calculations, does not make it "absolute".

It's true that we can use comoving coordinates to define which event happened first, $A$ or $B$. And I agree that these coordinates make sense to define as "natural" coordinates. But you're free to use any other set of coordinates, and no-one is allowed you call your coordinates, or your measurements, "wrong". If you travel at $v=.866c$ toward Betelgeuze, and you observe $A$ and $B$ to happen simultaneously, this is reality$^\mathrm{\tiny{TM}}$ in your reference frame; it's not an optical illusion.

See also this similar question on the diameter of the Universe.

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    $\begingroup$ My question is related to the fact that the "comoving time" at which an event occurs could in principle be used to experimentally establish the coincidence (or the order) of two or more events in time at different locations in space in a manner agreed upon by all observers in the universe. This is precisely the (Wikipedia-cited) definition of an absolute time. $\endgroup$ – Georges Jan 28 '16 at 14:49
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    $\begingroup$ But the comoving frame is not more "correct" that other frames, it just makes more sense for many practical purposes. $\endgroup$ – pela Jan 28 '16 at 14:53
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    $\begingroup$ It can still be used (in principle) to decide of the coincidence (or of the order) in time of events at different locations in space in a manner agreed upon by all observers in the universe, what relativity denies to be possible. $\endgroup$ – Georges Jan 28 '16 at 15:01
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    $\begingroup$ @WillO: I am sorry, I don't see how this would follow from what I wrote. I am not sure either to understand what you mean. My "problem" is that "comoving time" is a mean to define a coincidence (or an order) in time for events at different locations in space in a manner agreed upon by all observers in the universe while relativity says this is not possible. $\endgroup$ – Georges Jan 28 '16 at 15:30
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    $\begingroup$ @WillO: The problem is not that such a foliation exist, it is that all observers will independently discover the same one, making it somehow special compared to all possible other ones. $\endgroup$ – Georges Jan 28 '16 at 16:53
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Suppose two observers, Alice and Bob, are moving relative to each other since the beginning of the universe. While they do it, they construct the chronologies of all the events of the universe, as they record them in their frame of reference. They will construct different chronologies.

However, and this is key, each can reconstruct the other's chronology. This is also the content of special relativity. If Alice takes all her data of spacetime events, and knows Bob's velocity, she can reconstruct Bob's chronology. Alice will always agree with Bob that event $x$ happens simultaneously with event $y$ in Bob's frame. A third party, Charlie, will also be able to agree with Alice about the order of events, as recorded by Bob.

By this, I am illustrating that, even in special relativity, all observers can agree on the order of events, as they happen in a particular frame of reference. Being able to agree about the order of events in a particular frame does not mean that you have found an absolute time, it just means that relativity is consistent!

The same is true for the comoving frame.

In our standard model of the universe, there happens to be one frame of reference which is at rest with respect to the CMB. In principle, no matter where you are in the universe, you can determine if you are at rest with respect to the CMB and thus with this particular frame (if you are, you are called a comoving observer). It is to simplify calculations that we use the comoving time as the measure of the age of the universe. It is also useful because the Earth is approximately comoving.

Being able to agree in what order events happen in the comoving frame does not mean that the comoving frame define an absolute time, it just means that you know how fast you have been moving with respect to the comoving frame, and that you know how to calculate.

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  • $\begingroup$ This answers only partly my question. The "comoving time" allows different observers to agree upon the order of events without knowing anything regarding each other’s velocities and even without knowing each other’s existence, which I think is quite different from what you mentioned and closer to an absolute agreement. Maybe too there is something wrong or misleading in the Wikipedia-cited definition of absolute simultaneity. $\endgroup$ – Georges Jan 28 '16 at 16:27
  • $\begingroup$ Thanks for the comment. In the second paragraph, you will see that Charlie can agree with Alice on the order of events as seen by Bob, without knowing Alice's velocity with respect to Charlie or Bob. Does it mean that Bob is the centre of the universe, the master of time? $\endgroup$ – Andrea Jan 28 '16 at 17:33
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Pulling together what's been said in various comments:

1) General relativity admits models where spacetime is foliated by spacelike leaves, all of which are indexed by a global time coordinate. The simplest of these models is Minkowski space. All of your observations about models with comoving observers apply equally well to Minkowski space, so if you want to clarify the source of your confusion, that's the example you should focus on.

2) In Minkowski Space, it's easy to define a single global time coordinate. That doesn't contradict relativity, becauses it doesn't deny that there are also other ways to define coordinates.

3) Models with comoving observers assume isotropy, which is clearly a considerable abstraction from reality. Such models are useful for some purposes and less useful for others. The existence of such models does not deny the existence of other models without global time coordinates.

4) So the existence of a global time coordinate does not contradict relativity for two reasons: First, as in Minkowski space, the existence of this coordinate does not deny the existence of alternative coordinates within the model. Second, it does not deny the existence of other, more precise models.

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  • $\begingroup$ The question finally seems to reduce to whether the comoving time can be defined in a rigorous enough way to be used for establishing the simultaneity of events in a "canonical" way. Does this really require a strong isotropy assumption or is that enough that the comoving observer speed can be accurately defined? Can the CMB dipole speed be used for this? $\endgroup$ – Georges Jan 28 '16 at 17:44
  • $\begingroup$ @Georges: Apparently you're just not interested in reading the answers you've been given. The comoving time can be defined in some models and not others. (I don't understand the difference between "defined" and "defined rigorously" --- it's either defined or it's not.) The existence of models in which it can be defined is not a problem for relativity, for the reasons you've already been given. $\endgroup$ – WillO Jan 28 '16 at 17:47
  • $\begingroup$ I do read answers but I might not understand them. I don't understand in which models a comoving observer could not be defined as long as the CMB is there. $\endgroup$ – Georges Jan 28 '16 at 17:53
  • $\begingroup$ If I understand you, you're now asking for the conditions under which a GR model admits a global time coordinate. That's a great question, but it deserves to be asked separately. $\endgroup$ – WillO Jan 28 '16 at 19:22
  • $\begingroup$ I would say that this is the same question that I possibly formulated poorly though I am not sure of what you mean by a "global time coordinate". It seems to me that the CMB somehow breaks the symmetry postulated by GR (and SR). $\endgroup$ – Georges Jan 28 '16 at 20:15

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