Why Is Time Dilation Considered a Real Phenomenon?

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Sunil said:
The next step would be to accept that given that differential aging we have no chance to measure absolute time with clocks, even if it would exist.
I would say that the problem with absolute time has more to do with definition than with measurement.

The fact that the path length between two points on the Earth's surface depends on the path does not prevent us from measuring the distance between those two points with rulers. We just need to figure out a definition for a "straight path". [think "geodesic" or "shortest path on the surface"]

Nor does the ambiguity in path length to the equator or the prime meridian prevent us from measuring longitude and latitude with rulers once we have an agreement on placement for the equator and the prime meridian.

To bring this back around to General Relativity and the universe within which we live, I believe that it is possible, to define an "absolute time" for essentially every event in the universe based on the interval from the [imagined if necessary] initial singularity to the event in question. In principle, this "absolute time" would be measurable with clocks: the lowest clock reading on any clock that takes a geodesic path that starts in [some small region near] the initial singularity and ends at the target event. Sadly, I do not think this particular definition works. One could have a high speed trajectory to a black hole, a tight trajectory around the black hole and a high speed continuation to the target event, thus yielding an arbitrarily low "absolute time".
 
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