On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
On 4/15/2019 7:14 PM, [email protected] wrote:
On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
[email protected] wrote:
On Thursday, April 11, 2019 at 10:56:08 PM
UTC-6, Brent wrote:
On 4/11/2019 9:33 PM, [email protected]
wrote:
On Thursday, April 11, 2019 at 7:12:17 PM
UTC-6, Brent wrote:
On 4/11/2019 4:53 PM,
[email protected] wrote:
On Thursday, April 11, 2019 at
4:37:39 PM UTC-6, Brent wrote:
On 4/11/2019 1:58 PM,
[email protected] 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
Another problem is the inconsistency of the
fictitious gravitational force, and how the
other forces function; EM, Strong, and Weak,
which apparently can't be removed by changes in
coordinates systems. AG
It's said that consistency is the hobgoblin of
small minds. I am merely pointing out the
inconsistency of the gravitational force with the
other forces. Maybe gravity is just different. AG
That's one possibility, e.g entropic gravity.
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.
I was referring earlier just to the
transformation to the tangent space; what
specifically does it buy us; why would we want
to execute this particular transformation? AG
For one thing, you know the acceleration due to
non-gravitational forces in this frame.
*IIUC, the tangent space is a vector space which has
elements with constant t. So its elements are linear
combinations of t, x, y, and z. How do you get
accelerations from such sums (even if t is not
constant)? AG*
*
*
So you can transform to it, put in the
accelerations, and transform back.
*I see no way to put the accelerations into the tangent
space at any point in spacetime. AG*
