On 3/8/2018 4:36 PM, agrayson2...@gmail.com wrote:
On Thursday, March 8, 2018 at 2:52:11 PM UTC-5, Lawrence Crowell wrote:
Modern physics tends to operate on the idea of geodesics and
geometric determined flows.
*Do you agree that the fact that the flow is geodesic is ultimately a
postulate, and the existence of the flow is rooted in the monotonic
increase of time? AG
*
There is no "flow". Time is just another dimension and there are
different configurations at different times just as there are different
configurations at different places. It's a block universe picture.
Brent
A geodesic is "determined" from an initial point, which can just
be a point where data is specified instead of some point of
origin, where the position on a manifold and the tangent vector
are specified. From there the dynamics is completely determined.
For a quantum system things are more nuanced with there being a
bundle of paths with some congruent condition given by
diffeomorphism and Weyl transformations "modded out."
In spacetime and general relativity these geodesic flows obey the
geodesic deviation equation dU/ds = R(UV)V, and are determined by
the curvature of spacetime. Here U = dx/ds is the relative
velocity between two test masses. Now we might imagine a tether
between these two test masses. Now their relative separation
distance is constant and the two masses are not on a geodesic
path. However, the center of mass of the two are on a geodesic.
The individual masses are then on nongeodesic paths due to the
material forces of the tether.
LC
On Thursday, March 8, 2018 at 6:24:59 AM UTC-6,
agrays...@gmail.com wrote:
On Wednesday, March 7, 2018 at 11:04:09 PM UTC-5, Brent wrote:
On 3/7/2018 5:39 AM, agrays...@gmail.com wrote:
*Thanks for your time and effort, but I don't think you
understand my*
*question. Suppose a test particle is restrained
spatially, say in *
*the Sun's gravitational field. When released, it starts
to move (toward *
*the Sun). How does GR explain this motion? By the
advance of time? AG*
Time was advancing all along. Your restraint was a force
causing the particle to follow a non-geodesic path through
space-time. When you released it, it then followed the
"straightest path possible", i.e. a geodesic.
Brent
So time is the "culprit". What has this resumption of spatial
motion (along a geodesic in spacetime) have to do with
conservation of momentum, if at all ? TIA, AG
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