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I understand that in general relativity all observers agree on what it is they see (looking at the same object or event) when they account for the effects on their observations of the gravitational field they sit in, on their distance and motion relative to the observed.

Does this mean that in general relativity there is a universe-wide present all objects and observers everywhere live in (so they are contemporaries, living at the same moment in cosmic time, X years after the big bang) but that it only for practical reasons -time dilation and the (finite) speed of light which makes that we see a distant galaxy as it was in a distant past- cannot actually be observed?

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  • $\begingroup$ Science doesn't define the present. Your consciousness does. Forget about all observers, you can't even agree with yourself. On Monday you think the present is Monday, but on Tuesday you already think the present is Tuesday. $\endgroup$ – safesphere May 6 '18 at 5:20
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Your first paragraph contains some physics misunderstandings. Gravitational time dilation depends on the gravitational potential, not the gravitational field, and in any case we can't define a gravitational potential for a cosmological spacetime. Also, we can't define the motion of one object relative to another object if they are separated by cosmological distances.

Does this mean that in general relativity there is a universe-wide present all objects and observers everywhere live in (so they are contemporaries, living at the same moment in cosmic time, X years after the big bang) but that it only for practical reasons -time dilation and the (finite) speed of light which makes that we see a distant galaxy as it was in a distant past- cannot actually be observed?

This is not a very well-defined physics question, since physics doesn't make philosophical claims like "there is a universe-wide present." We can define a preferred cosmological time coordinate which is the time reading on a clock that has been at rest relative to the Hubble flow since the big bang. If you want to say that this implies a "universe-wide present," you can, but it's not a meaningful scientific statement.

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  • $\begingroup$ Big bang cosmology states that the universe has a beginning, a definite age -which can be inferred by extrapolating the expansion of the universe backwards in time, say. Is this age the age as measured with ‘a clock that has been at rest relative to the Hubble flow since the big bang’? If “we can’t define a gravitational potential for a cosmological spacetime,’ then does this mean that the amount of energy (the source of the potential) in some area isn’t defined in the sense that it is a relative, observer dependent quantity? $\endgroup$ – Anton May 7 '18 at 2:34
  • $\begingroup$ The problem with the idea that the universe has a beginning, a definite age is that if it can create itself, it always must have been able to. Though time is said to only have started at the big bang, a beginning implies a previous state in which it didn’t yet exist, meaning that it has a beginning in time: that time already existed, passed even before the bang -even though nothing much may have happed until then In that case big bang cosmology, despite trying to describe it from the inside, in its assumption that the universe is homogeneous, conceives of the universe ... $\endgroup$ – Anton May 7 '18 at 2:38
  • $\begingroup$ … as an object which lives in a time realm not of its own making, which at any time is in some particular evolutionary phase as a whole, which evolves at about the same pace everywhere -which to me seems to come down to saying that it is the same time everywhere inside of it, that there is a universe-wide present, that time is something absolute (which, if I’m correct, general relativity says it isn’t). If when the universe at any moment in cosmic time is in some particular state as a whole as seen from within (which it only can be if we assume that we see distant galaxies as they were in .. $\endgroup$ – Anton May 7 '18 at 2:41
  • $\begingroup$ … a distant past, if we assume that light moves at a finite velocity), then it also is in that same particular state as ‘seen’ from the outside -never mind that there is nothing outside of it, that it cannot be observed from without. My point is that if by definition there’s nothing outside the universe, nothing relative to which it can be said to exist, nothing it can interact with to express any property -a net electric charge or have some particular temperature, say- then it also cannot have any particular property, be in any particular state … $\endgroup$ – Anton May 7 '18 at 2:42
  • $\begingroup$ ... -have a nonzero electric charge or energy content, have some particular temperature as a whole as seen from within -contradicting big bang cosmology. $\endgroup$ – Anton May 7 '18 at 2:42

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