On 3/5/2019 10:02 PM, [email protected] wrote:
On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, [email protected]
wrote:
On Friday, March 1, 2019 at 10:14:02 PM UTC-7, [email protected]
wrote:
On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote:
On 2/28/2019 4:07 AM, [email protected] wrote:
On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7,
Brent wrote:
On 2/27/2019 4:58 PM, [email protected] wrote:
*Are you assuming uniqueness to tensors; that only
tensors can produce covariance in 4-space? Is that
established or a mathematical speculation? TIA, AG *
That's looking at it the wrong way around. Anything
that transforms as an object in space, must be
representable by tensors. The informal definition of
a tensor is something that transforms like an object,
i.e. in three space it's something that has a
location and an orientation and three extensions.
Something that doesn't transform as a tensor under
coordinate system changes is something that depends
on the arbitrary choice of coordinate system and so
cannot be a fundamental physical object.
Brent
1) Is it correct to say that tensors in E's field
equations can be represented as 4x4 matrices which have
different representations depending on the coordinate
system being used, but represent the same object?
That's right as far as it goes. Tensors can be of any
order. The curvature tensor is 4x4x4x4.
2) In SR we use the LT to transform from
one*non-accelerating* frame to another. In GR, what is
the transformation for going from one *accelerating*
frame to another?
The Lorentz transform, but only in a local patch.
*That's what I thought you would say. But how does this
advance Einstein's presumed project of finding how the laws of
physics are invariant for accelerating frames? How did it
morph into a theory of gravity? TIA, AG *
*Or suppose, using GR, that two frames are NOT within the same
local patch. If we can't use the LT, how can we transform from
one frame to the other? TIA, AG *
*
*
*Or suppose we have two arbitrary accelerating frames, again NOT
within the same local patch, is it true that Maxwell's Equations
are covariant under some transformation, and what is that
transformation? TIA, AG*
*I think I can simplify my issue here, if indeed there is an issue:
did Einstein, or anyone, ever prove what I will call the General
Principle of Relativity, namely that the laws of physics are invariant
for accelerating frames? If the answer is affirmative, is there a
transformation equation for Maxwell's Equations which leaves them
unchanged for arbitrary accelerating frames? TIA, AG
*
Your question isn't clear. If you're simply asking about the equations
describing physics/*as expressed*/ in an accelerating (e.g. rotating)
reference frame, that's pretty trivial. You write the equations in
whatever reference frame is convenient (usually an inertial one) and
then transform the coordinates to the accelerated frame coordinates.
But if you're asking about what equations describe some physical system
while it is being accelerated as compared to it not being accelerated,
that's more complicated. Maxwell's equations apply to the description
of the EM field of an accelerating charged particle and show that the
particle loses energy to an EM wave, but how the particle interacts with
it's own field when accelerated produces unrealistic results which were
superceded by quantum field theory. Bill Unruh showed that the
accelerated system interacts with the vacuum as though the vacuum is hot.
Brent
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