I Gravitational time dilation, proper time and spacetime interval

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The discussion revolves around the confusion regarding the derivation of gravitational time dilation in Schwarzschild spacetime, specifically the relationship between proper time and spacetime intervals. The main point of contention is whether the equality between the spacetime interval and proper time holds for non-inertial observers, as the standard derivation seems to imply. Participants clarify that while proper time can equal the spacetime interval for stationary observers in a stationary gravitational field, this relationship is more complex for non-inertial observers and finite separations. The conversation highlights the distinction between infinitesimal and finite differences in spacetime intervals, emphasizing that the definition of spacetime intervals in general relativity is not as straightforward as in special relativity. Ultimately, the discussion underscores the need for careful consideration of the definitions and conditions under which these relationships hold.
  • #61
A recent thread derail has been deleted, and the thread is reopened
 
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  • #62
Hi.
haushofer 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.
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.
 
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  • #63
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.
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.
 

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