On 5/26/2020 4:51 AM, 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, AGAre 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? AGI 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? AGIncreasing 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? AGYes. 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. BrentSince time is just of the 4 labels for spacetime points, can they be assigned at random? What specific function do they satisfy? AG
They're not assigned at random because they need to form a locally smooth flat tangent space so that Einstein's equations will apply. And that's their function...they label in the points so that the equations apply and when you solve the equations you will know what value goes with what point.
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