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Was wondering if you guys would mind critiquing, correcting, or adding any good insights to the following which was posted elsewhere by me, thanks!

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.... remember a ways back there was a finding that went viral about the speed of light not being constant? I forget the details now, but it had everybody up in arms that it would be the downfall of Special Relativity.

But, I don't think it really would have been (as most physicists were saying at the time), but it shows the subtleties involved. In Special Relativity, you have the all-important metric at the heart of the theory:

d_tau^2 = -c^2*dt^2 + dx^2

This equation outlines the geometric structure of space-time as it measures distances in space-time, in a similar fashion to how Pythagorean Theorem measures distances in Euclidean Space (ds^2 = dx^2 + dy^2). What's special about c, is not any role as a Universal "speed limit", but that it actually helps define this unified geometric structure of space-time and converts between time and space in such a way as to keep the interval (distances in space-time) invariant. Again, this is the same thing as distances staying invariant under a Euclidean Space, or regular space, as we normally think about it

But, if themagnitudeof the speed of light, or c, changes, theformof the Lorentz Transformation equations donotnecessarily have to change. The underlying symmetry which preserves the invariance of the interval under Lorentz Transformations, and theformof all the equations would stay the same. The form of the equation above for the metric stays the same. But, it seems to meabout the geometric structure of space-time would change as the speed of light changes. If the speed of light in the equation above changed slowly over time, the geometric structure of space-time would slowly change with time. Indeed, I think equivalent experiments done at different times might give different answers, since the measured space-time distance between events would change. Perhaps, it would be somewhat analogous to an n-sided polygon slowly growing/shrinking, the symmetries wouldn't change in that under certain rotations (of 2*pi/n) the appearance of the n-sided polygon would still not change at any given instant of time, but length magnitudes are indeed changing over time. Then again, if you're stuck on the side of the polygon (or in space-time), perhaps from your vantage point nothing does change, as you (and your experimental apparatus) would be changing along with the environment!?!?something

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# I If c changes w/ time, what happens with laws of SR?

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