"Triplets" -- Twin Paradox

  • #26
jbriggs444
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Does this mean that in GR we can talk about the "real time dilation independent of observations"; contrary to SR where the real time dilation has no physical sense and we can only reason in terms of what we can actually observe?
Let us not involve event horizons here. They muddy the waters. Under general relativity, there are situations where gravitational time dilation can be considered as "real" time dilation.

Under special relativity (and inertial frames), time dilation is always due to relative velocity. Both observers consider their peer's clock to have slowed down.

Under general relativity, there can be time dilation due to gravitational potential. An observer higher looking down at his peer will consider the peer's clock to be running slow. The lower observer looking upward will consider his peer's clock to be running fast. If you wait long enough, an unambiguous difference builds up between the respective clock readings. This could be thought of as real time dilation. It is physically measurable and does not arise due to differing choices of simultaneity conventions.
 
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  • #27
Ibix
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The problem with time dilation in special relativity is that it only happens between clocks in relative motion. What you actually see is the relativistic Doppler effect, and there is no unique way to divide that into "rate change due to time dilation" and "rate change due to changing distance".

The same is true with bells on in general relativity, except under certain circumstances. For example, if we are both hovering in an unchanging gravitational field, we can keep bouncing radar pulses off each other and confirm that the round-trip time isn't changing (edit: or we could just stand on different floors of a building on a planet). In this case, therefore, there is a sensible way to split Doppler into "rate change due to time dilation" and "rate change due to changing distance", which is that there is none of the latter.

I think it's still arbitrary to some extent, but it's a more physically motivated choice.
 
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