I see! You indeed need to transform both the 4-vector and the coordinate
system for the GR formalism to apply here.
Saibal
On 02-10-2024 00:45, Alan Grayson wrote:
On Tuesday, October 1, 2024 at 6:44:04 AM UTC-6 smitra wrote:
On 26-09-2024 12:22, Alan Grayson wrote:
Maxwell's Equations are written in vector form, and vectors are
tensors, and tensors are invariant under change of coordinates. It
is
known that ME are invariant under the Lorentz transformation, and
predict that EM waves travel at the velocity of light regardless
of
the coordinate system. So, applying instead the Galilean
transformation to ME, shouldn't they also predict the same
velocity of
light as the Lorentz transformation? TY AG
Yes see:
https://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime
So, the speed of light in a global coordinate system scales with the
square root of the determinant of the metric tensor. If you define
distances and time intervals locally using the metric tensor at each
point, the locally defined speed of light will be the same constant
everywhere.
Saibal
Note that the LT and the GT are FRAME transformations, NOT coordinate
transformations (they're not the same) so even if ME are written in
tensor
form (vectors are rank 1 tensors), there's no reason to expect ME to
be
invariant under either transformation. But they are, only under the
LT, but
not under the GT. Do you know why? I don't see how your answer relates
to my question. Please clarify. TY, AG
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