On 4/16/2019 7:56 AM, agrayson2...@gmail.com wrote:
On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
On 4/15/2019 7:14 PM, agrays...@gmail.com <javascript:> wrote:
On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:
On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent
wrote:
On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
On Thursday, April 11, 2019 at 4:37:39 PM UTC-6,
Brent wrote:
On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
He might have been referring to a
transformation to a tangent space where
the metric tensor is diagonalized and its
derivative at that point in spacetime is
zero. Does this make any sense?
Sort of.
Yeah, that's what he's doing. He's assuming a
given coordinate system and some arbitrary
point in a non-empty spacetime. So spacetime
has a non zero curvature and the derivative of
the metric tensor is generally non-zero at
that arbitrary point, however small we assume
the region around that point. But applying the
EEP, we can transform to the tangent space at
that point to diagonalize the metric tensor
and have its derivative as zero at that point.
Does THIS make sense? AG
Yep. That's pretty much the defining
characteristic of a Riemannian space.
Brent
But isn't it weird that changing labels on
spacetime points by transforming coordinates has
the result of putting the test particle in local
free fall, when it wasn't prior to the
transformation? AG
It doesn't put it in free-fall. If the particle has
EM forces on it, it will deviate from the geodesic
in the tangent space coordinates. The
transformation is just adapting the coordinates to
the local free-fall which removes gravity as a
force...but not other forces.
Brent
In both cases, with and without non-gravitational forces
acting on test particle, I assume the trajectory appears
identical to an external observer, before and after
coordinate transformation to the tangent plane at some
point; all that's changed are the labels of spacetime
points. If this is true, it's still hard to see why
changing labels can remove the gravitational forces. And
what does this buy us? AG
You're looking at it the wrong way around. There never
were any gravitational forces, just your choice of
coordinate system made fictitious forces appear; just
like when you use a merry-go-round as your reference
frame you get coriolis forces.
If gravity is a fictitious force produced by the choice of
coordinate system, in its absence (due to a change in
coordinate system) how does GR explain motion? Test particles
move on geodesics in the absence of non-gravitational forces,
but why do they move at all? AG
Maybe GR assumes motion but doesn't explain it. AG
The sciences do not try to explain, they hardly even try to
interpret, they mainly make models. By a model is meant a
mathematical construct which, with the addition of certain verbal
interpretations, describes observed phenomena. The justification
of such a mathematical construct is solely and precisely that it
is expected to work.
--—John von Neumann
*This is straight out of the "shut up and calculate" school, and I
don't completely buy it. E.g., the Principle of Relativity and Least
Action Principle give strong indications of not only how the universe
works, but why. That is, they're somewhat explanatory in nature. AG*
Fine, then take them as explanations. But to ask that they be explained
is to misunderstand their status. It's possible that they could be
explained; but only by finding a more fundamental theory that includes
them as consequences or special cases. Whatever theory is fundamental
cannot have an explanation in the sense you want because then it would
not be fundamental.
Brent
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