Universal Constants (Umbran, Pbartender)

[Umbran]

So you're saying that in, say, 1870 if someone had asked Maxwell what the coefficient for the time coordinate in the invariant quadratic form was, he would have said "of course, that's the same thing as the speed of light!"

Here's the thing - one can postulate that there's a constant relating time and space coordinates, but that doesn't get you anywhere in and of itself. You can crank up a bunch of math based uipon that postulate, and it's just a toy because it doesn't anchor to anything in the real world on it's own.

If, however, you postulate that the speed of light in a vacuum was a constant for all observers (whcih Maxwell didn't - the results of that postulation didn't come along until Einstein in 1905), then if you're a decent mathematician, the fact that c is the above coefficient falls into your lap - so Einstein revealed. The math there actually isn't all that difficult. Many of Einstein's contemporaries could do it. I can do it. What made Einstein great with SR was the realization of the constant, not in coordinate transformation stuff.

So, the depth of the matter is in figuring out that the speed of light is the same for everyone. And that gets you as deep as you can go - the rest are really fiddly-bit results from the basic fact.