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
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