The discussion revolves around gravitational time dilation as described in the context of Schwarzschild geometry. Participants explore the relationship between proper time and the spacetime interval, particularly focusing on the implications of non-inertial observers and the conditions under which the spacetime interval equals proper time. The scope includes theoretical considerations and mathematical reasoning.
Participants do not reach a consensus on the implications of the relationship between proper time and the spacetime interval for non-inertial observers. There are competing views regarding the interpretation of these relationships and the conditions under which they hold.
Participants note that the discussion involves complexities related to the definitions of proper time and spacetime intervals, particularly in the context of non-inertial frames. The distinction between infinitesimal and finite differences is highlighted as a source of confusion.
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.