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
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