Gravitational time dilation, proper time and spacetime interval

[Dale]

A recent thread derail has been deleted, and the thread is reopened

 

[sweet springs]

Hi.

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.

 

[Orodruin]

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.