Proper time is only defined along a timelike world line, e.g. the timeline of a specific reference point / object. It’s “objective” in the sense that is true for the reference point, but other reference points may (for example) perceive distant events in a different order
Out of my depth here, but it seems that objective timespace coordinates can be determined while still meshing with relativity.
I’ll just leave this here so someone else can explain why I’m wrong:
https://en.m.wikipedia.org/wiki/Proper_time
I know 4D spacetime can be non-euclidean, but I believe those are localized to areas experiencing relativistic extrema.
Proper time is only defined along a timelike world line, e.g. the timeline of a specific reference point / object. It’s “objective” in the sense that is true for the reference point, but other reference points may (for example) perceive distant events in a different order