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*
