On Monday, April 15, 2019 at 9:26:59 PM UTC-6,
Brent wrote:
On 4/15/2019 7:14 PM, agrays...@gmail.com 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
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*
