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, 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 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.
Brent
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