On 4/9/2019 11:55 AM, agrayson2...@gmail.com 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 <javascript:> 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
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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