The discussion centers on the interpretation of Schwarzschild's gravitational time dilation and the relationship between proper time and spacetime intervals. Participants clarify that the spacetime interval can be defined for non-inertial observers, and that the equality between proper time and the spacetime interval holds under specific conditions, particularly when the metric components are stationary. The confusion arises from the distinction between infinitesimal and finite differences in spacetime, leading to a deeper understanding of how proper time is calculated along different paths in curved spacetime.
PREREQUISITESStudents and researchers in theoretical physics, particularly those focusing on General Relativity, spacetime geometry, and gravitational effects on time measurement.
P.247 of the text https://archive.org/stream/TheClassicalTheoryOfFields/LandauLifshitz-TheClassicalTheoryOfFields#page/n257/mode/2up/search/world+timehaushofer said:I agree that the coordinate time is a bookkeeping device, but you can stick an observer to it. I'd say the coordinate t is measured as the time difference between the two events by an observer very far away from the black hole where spacetime can be considered to be flat.
So what? This should be true for any coordinate system and there is nothing special about Schwarzschild coordinates apart from what I mentioned in #58. If you pick a different foliation of space-time, any observer will still be able to identify what the corresponding time coordinate is.sweet springs said:Hi.
P.247 of the text https://archive.org/stream/TheClassicalTheoryOfFields/LandauLifshitz-TheClassicalTheoryOfFields#page/n257/mode/2up/search/world+time
calls this coordinate time under stationary gravitation the world time. I am not sure whether the naming is popular but common and universal nature of the coordinate time in the sense that everybody in everywhere can translate it to his or anybody's real time is well expressed in this naming. Best.