On 1/4/2019 9:20 PM, [email protected] wrote:
*Still a little murky. Does coordinate time ever differ from proper time? TIA, AG *Of course. That's like asking does change in longitude ever differ from distance sailed. Brent*Suppose I imagine a path in spacetime, say with loops, returning to the same spatial location. *
Ok. Like the traveling twin.
*Some amount of proper time will have elapsed*
Along that path.
*, invariant for all observers, but the elapsed coordinate time will in general be different, with proper time and coordinate time initialized to identical but arbitrary values as the path in spacetime is traversed. *
You can set proper time and coordinate time to the same value at one event (the initial event). But I don't know what you mean by "intialized...as the path is traversed".
*The other imagined coordinate clocks can't be synchronized since they relate to different events in spacetime, *
I don't know what this means. In generic spacetimes there are no "coordinate clocks". Coordinates are just smooth functions that provide labels to each point in 4-space. Since they don't have any physical significance, in general there isn't any physical clock that keeps "coordinate time". I don't know what you mean by "relate to different events in spacetime". Clocks just mark intervals along their paths.
*so something is wrong with this model, specifically if the imagined path in spacetime does not return to its initial spatial position. TIA, AG*
But you hypothesized that it did. Now you're worrying that it didn't?? Remember that clocks measure intervals between EVENTS (things that have four coordinate values), not between PLACES (things that have three coordinate values).
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