On Saturday, January 5, 2019 at 8:36:34 PM UTC, Brent wrote: > > > > On 1/5/2019 12:50 AM, [email protected] <javascript:> wrote: > > > > On Saturday, January 5, 2019 at 6:49:43 AM UTC, Brent wrote: >> >> >> >> 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". > > * That's all I meant, as in your first sentence above. AG* > > *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". > > *OK, no coordinate clocks. The coordinate t is just the time label for an > event. AG* > > 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). > > * This is my problem; maybe a non problem; for any path between two > events, the proper time interval is invariant, meaning the same for all > observers, but it will be different depending on the paths. But the elapsed > coordinate time intervals are the same, since the endpoints represent the > same pair of events. So there doesn't seem to be any relationship between > elapsed proper time and elapsed coordinate time. AG* > > > The relation is provided by the metric. If you choose different > coordinate systems (e.g. cylindrical or spherical or whatever) then there > is different metric tensor. So the integral along the path of g_ab dx^a > dx^b is the same. > > Brent >
*I assume you're showing why the proper time along a given path is the same for all observers, and this has nothing to do with coordinate time being unrelated to proper time. AG * -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
