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
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