On 4/11/2019 9:33 PM, agrayson2...@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 <javascript:> 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. What is gets you is it
enforces and explains the equivalence principle. And of course
Einstein's theory also correctly predicted the bending of light,
gravitational waves, time dilation and the precession of the perhelion
of Mercury.
Brent
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