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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/77c54369-3090-4511-ada5-cd600de1a521n%40googlegroups.com.
