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If we are in empty space far from a black hole, at rest relative to the hole, we would look at a clock and a light source inside the gravitational field of the hole, then we would, according to the gravitational time dilation of relativity, see the clock run at a slower pace (relative to our own clock) and the light to be shifted farther to red as they are deeper inside the field of the hole and they are at rest relative to its event horizon. If when we look deeper into the hole’s field, we look farther into the past, then wouldn’t that mean that time would have passed at a slower pace in the past than it does today?

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  • $\begingroup$ "If when we look deeper into the hole’s field, we look farther into the past", whose past? Certainly not ours, and there is no global "past" in relativity. Time passes at a slower pace closer to the black hole, the same is true of Earth, by the way, although the effect is many orders smaller, but what does that have to do with the "past"? $\endgroup$ – Conifold May 17 '17 at 0:56
  • $\begingroup$ To me the concept of cosmic time -the idea that the universe has a beginning, a definite age- only makes sense if it is the same time everywhere inside of it, if time passes at the same pace everywhere -in which case we can(not but) speak about “the” past -a global or universe-wide past- and there should exist no gravitational time dilation. $\endgroup$ – Anton May 17 '17 at 1:42
  • $\begingroup$ Since the gravitational time dilation does exist, it was measured, something must be off in the reasoning. Cosmic time is indeed well-defined in FLRW solutions, but it corresponds to a specific choice of frame, comoving with the universe. If you measure time in the same frame, FLRW one or some other, it will indeed be the "same" everywhere, no different paces. But the gravitational time dilation is due to acceleration (by equivalence principle equivalent to gravity), so you are comparing paces in different frames, not global paces. $\endgroup$ – Conifold May 17 '17 at 2:12
  • $\begingroup$ Either something is off with my reasoning -which is what I want to know- or, as the gravitational time dilation actually is observed, we don’t live in a big bang universe. In fact, to say that the universe has a beginning, that it has a definite age -no matter what frame of reference one cares to choose- comes down to saying that the universe lives in a time continuum not of its own making, that time and its unit, the second, is defined even outside of it -which is nonsense. $\endgroup$ – Anton May 17 '17 at 2:34
  • $\begingroup$ The problem with your reasoning is absolutization of the comoving frame into something metaphysical. FLRW ("big bang") universes simply admit a preferred frame in which it is convenient to register cosmic dates. But physical effects you are experiencing still depend on your personal state of motion, not that of the comoving frame (ours on Earth just happens to be a good approximation to it). The universe does have a "beginning" in most frames, because the singularity is preserved by nice enough transformations, but no frameless "definite age", cosmic time is just the comoving proper time. $\endgroup$ – Conifold May 17 '17 at 2:55

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