On Saturday, January 5, 2019 at 8:36:34 PM UTC, Brent wrote: > > > > On 1/5/2019 12:50 AM, agrays...@gmail.com <javascript:> wrote: > > > > On Saturday, January 5, 2019 at 6:49:43 AM UTC, Brent wrote: >> >> >> >> On 1/4/2019 9:20 PM, agrays...@gmail.com 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
