On 27-05-2020 11:07, Alan Grayson wrote:
On Tuesday, May 26, 2020 at 6:24:32 PM UTC-6, Brent wrote:
On 5/26/2020 6:49 AM, Alan Grayson wrote:
On Tuesday, May 26, 2020 at 5:51:50 AM UTC-6, 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 ONE of the 4 labels for spacetime points, can they
be assigned at random? What specific function do they satisfy? AG
How is the time coordinate chosen such that the Lorentz distance
between spacetime points is meaningful? AG
The proper distance/duration is an invariant, it doesn't depend on the
coordinate system.
Brent
I think the invariance of proper distance/duration a direct result of
the Lorentz transformation, and is one of the results of SR. If that's
the case, is it used in GR to derive EFE's? TIA, AG
The Lorentz transform results from demanding that ds^2 for a flat
space-time is an invariant. It's easy to derive this, as you know
rotations and translations leave the ordinary Euclidic metric invariant,
the relative minus sign between time and space means that instead of
cos(theta) and sin(theta), you get cosh(theta) and sinh(theta) in
transforms that mix time and space.
Saibal
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