On 5/24/2020 7:51 AM, 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
In general relativity points are labelled by coordinates which locally smooth functions that define a Reimannian space. You can change them to whatever you want whenever you want. They are just labels. I'm not sure what "update" means in this context. Physical time is measured by clocks, and they measure proper time along their world lines.
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