On 4/9/2019 12:47 PM, agrayson2...@gmail.com wrote:
On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:
On 4/9/2019 11:55 AM, agrays...@gmail.com <javascript:> wrote:
On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:
On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
On Monday, April 8, 2019 at 11:16:25 PM UTC-6,
agrays...@gmail.com wrote:
In GR, is there a distinction between coordinate systems
and frames of reference? AG??
Here's the problem; there's a GR expert known to some
members of this list, who claims GR does NOT distinguish
coordinate systems from frames of reference. He also claims
that given an arbitrary coordinate system on a manifold, and
any given point in space-time, it's possible to find a
transformation from the given coordinate system (and using
Einstein's Equivalence Principle), to another coordinate
system which is locally flat at the arbitrarily given point
in space-time. This implies that a test particle is in free
fall at that point in space-time. But how can changing
labels on space-time points, change the physical properties
of a test particle at some arbitrarily chosen point in
space-time? I believe that such a transformation implies a
DIFFERENT frame of reference, in motion, possibly
accelerated, from the original frame or coordinate system.
Am I correct? TIA, AG
You're right that a coordinate system is just a function for
labeling points and, while is may make the equations messy or
simple, it doesn't change the physics.?? If you have two
different coordinate systems the transformation between them
may be arbitrarily complicated.?? But your last sentence
referring to motion as distinguishing a coordinate transform
from a reference frame seems to have slipped into a 3D
picture.?? In a 4D spacetime, block universe there's no
difference between an accelerated reference frame and one
defined by coordinates that are not geodesic.
Brent
Suppose the test particle is on a geodesic path in one coordinate
system, but in another it's on an approximately flat 4D surface
at some point in the transformed coordinate system.
A geodesic is a physically defined path, one of extremal length.
It's independent of coordinate systems and reference frames. If a
geodesic is not a geodesic in your transformed coordinate system,
then you've done something wrong in transforming the metric.
Brent
It would clarify the situation if you would state the acceptable
before and after states of a coordinate transformation that puts the
test particle in a locally flat region for some chosen point in the
transformed coordinate system. AG
Like "geodesic" being "locally flat" is a physical characteristic of the
spacetime. It's just part of being a Riemannian space that there is a
sufficiently small region around any point that is "flat". This is the
mathematical correlate of Einstein's equivalence principle. So it is
not the coordinate system or any transformation that "puts the particle
in a flat region". It's just a property of the space being smooth and
differentiable so that even a curved spacetime at every point has a flat
tangent space.
Brent
Doesn't this represent a change in the physics via a change in
labeling the space-time points? How is this possible without a
change in the frame of reference, and if so, how would that be
described if not by acceleration? AG
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