On Tuesday, May 26, 2020 at 5:51:50 AM UTC-6, Alan Grayson wrote: > > > > On Sunday, May 24, 2020 at 4:49:48 PM UTC-6, Brent wrote: >> >> >> >> On 5/24/2020 11:21 AM, Alan Grayson wrote: >> >> >> >> On Sunday, May 24, 2020 at 8:51:35 AM UTC-6, Alan Grayson wrote: >>> >>> >>> >>> On Saturday, May 23, 2020 at 12:06:33 PM UTC-6, Brent wrote: >>>> >>>> >>>> >>>> On 5/22/2020 11:25 PM, Alan Grayson wrote: >>>> >>>> >>>> >>>> On Friday, May 22, 2020 at 11:03:40 PM UTC-6, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 5/22/2020 9:48 PM, Alan Grayson wrote: >>>>> >>>>> >>>>> >>>>> On Friday, May 22, 2020 at 9:05:23 PM UTC-6, Brent wrote: >>>>>> >>>>>> >>>>>> >>>>>> On 5/22/2020 6:26 PM, Alan Grayson wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Monday, May 18, 2020 at 3:28:40 PM UTC-6, Alan Grayson wrote: >>>>>>> >>>>>>> Suppose the universe is a hyper-sphere, not expanding, and an >>>>>>> observer travels on a closed loop and returns to his spatial starting >>>>>>> point. His elapsed or proper time will be finite, but what is his >>>>>>> coordinate time at the end of the journey? TIA, AG >>>>>>> >>>>>> >>>>>> It's not a dumb question IMO. If you circumnavigate a spherical >>>>>> non-expanding universe, what happens to coordinate time at the end of >>>>>> the >>>>>> journey? Does something update the time coordinate? Or does it somehow >>>>>> miraculously(?) remain fixed? TIA, AG >>>>>> >>>>>> >>>>>> Are you supposing the universe is a 3-sphere? In that case It's just >>>>>> like going around a circle. The degree marks on the circle are >>>>>> coordinates, they have no physical meaning except to label points. So >>>>>> if >>>>>> you walk around the circle you measure a certain distance (proper time) >>>>>> but >>>>>> come back to the same point. >>>>>> >>>>>> Or are you supposing it's a 4-sphere so that all geodesics are closed >>>>>> time-like curves? I don't know how that would work. I don't think >>>>>> there's >>>>>> any solution of that form to Einstein's equations. >>>>>> >>>>>> Brent >>>>>> >>>>> >>>>> I'm supposing a 4-sphere and (I think) closed time-like curves. The >>>>> traveler returns presumably to his starting position, but is the time >>>>> coordinate unchanged? AG >>>>> >>>>> >>>>> I don't think there's any very sensible answer in that case. Goedel >>>>> showed there can be solutions with closed time-like curves if the >>>>> universe >>>>> is rotating. But solutions of GR don't have any dynamic connection to >>>>> matter and the entropy of matter. In the same spirit there could be a >>>>> solution to quantum field theory that was close around the time like >>>>> curve...in which case you'd experience "Groundhog Day"...including your >>>>> thoughts. >>>>> >>>>> Brent >>>>> >>>> >>>> What does entropy have to do with this problem? AG >>>> >>>> >>>> Increasing entropy points the direction of time. >>>> >>>> Brent >>>> >>> >>> Let me pose the question another way: Is coordinate time ever updated? >>> AG >>> >> >> Or say, in the Twin Paradox, the elapsed or proper time for the traveling >> twin is less than for the Earth-bound twin, but when they meet, do they >> share the same coordinate time? AG >> >> >> Yes. Coordinates are labels for points, so if you're together with your >> twin, you both are at the same point in spacetime and that point only has >> one label in any given coordinate system. >> >> Brent >> > > Since time is just ONE of the 4 labels for spacetime points, can they be > assigned at random? What specific function do they satisfy? AG >
How is the time coordinate chosen such that the Lorentz distance between spacetime points is meaningful? 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/9932d47e-58c0-47a6-9ce9-24f786f8c168%40googlegroups.com.
