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Now they've done it. I have to go back and review all this Sommerfeld stuff...

And didn't Einstein originally just assume the speed of light as a constant?

And didn't Einstein originally just assume the speed of light as a constant?

I think he deduced it as a consequence of Maxwell's equations. That's where he got the symbol "c" from, I'm told. But as always, I'll yield to the experts, who often correct my babblings.

And didn't Einstein originally just assume the speed of light as a constant?

Here's an explanation, take it or leave it as you will.

Two scientists named Michaelson and Morley conducted an experiment to measure the speed of the earth through the 'ether' - a material characteristic to space assumed to exist. After all, 'when light waves, what waves?' In other words, what propogates light through what appears to be a vacuum? The theory said there was something called ether that existed even in a vacuum.

In their experiment, they set up a right-angled apparatus, one leg of which was aligned with the direction of the earth's motion around the sun, and the other perpendicular to it. By measuring the difference in the time it took a light pulse to travel both legs, you could get a measure of the speed of the earth through the ether which is what 'waved' when a light wave went by (since the ether would drag the light along with it).

They didn't find any difference. A host of other similar experiments showed that, regardless of the circumstances, the speed of light (in a vacuum) was always the same to the limits of accuracy of the measurement.

So, Einstein didn't 'assume' the speed of light was constant. That's what the data showed.

Two other guys names Lorentz and Fitsgerald developed a relationship that quantified how much things at very high speed behaved differently than those at normal speeds. This 'Lorentz-Fitgerald contraction' was SQRT(1 - V**2/C**2).

Einstein came along and in his 'Special' theory of relativity showed that the speed of light as measured by an observer is constant regardless of his own velocity if the rate of time passes differently for the observer based on his velocity, using the Lorentz-Fitsgeral contraction to quantify the amount of change in perceived rate of time passage.

Then Einstein extended from the 'Special Theory Relativity' to the 'General Theory of Relativity' by devloping a mathematical expression for the curvature of the universe which related linear dimensions to time, with the units worked out by combining t (time) with c (speed of light). The mathematical expression is called a 'tensor', and it's as good an example of how you can't 'speak' real science without mathematics as I've ever bumped my head up against.

One good thing about the General Theory of Relativity is that it provided an explanation for gravity. It was always a challenge to conventional physics to explain action at at distance without an interaction phenomenon. How does the earth know the sun is over there pulling on us? And how does the sun manage to grab the earth and yank it around without a string between the two? The curvature of space described by solving the Einstein tensor for local conditions offers the prediction that the earth is following an equal-value (in the tensor) line around the sun even as it changes direction. In other words, the earth goes 'straight', but 'straight' is not straight in the Euclidean sense. Instead, the 'straight' travel of a body in motion is actually to follow an equipotential line in the Einstein tensor value for space.

The other good thing about the General Theory (okay, there are lots of them, but this is already a long note) is that it predicts that light itself obeys gravity, despite having no rest mass for the conventional Newtonian model to act upon. This is provable by lots of experimental data, so the General Theory gained a lot of credibility.

Now, to wrap it up, if the speed of light is not a constant, then the Einstein tensor doesn't provide a solution to the motion of bodies in space-time. There's another variable that makes it impossible to solve. There is an awful lot of observable data that would need another explanation. (Obviously, if the speed of light is almost a constant, then the Einstein tensor is almost right, and still very useful for lots of situations.)

I don't know if this data on the natural nuclear reactor proves the speed of light is variable or not, but there are lots of challenges with a totally constant, for all time, speed of light, too (as mentioned in the article), so it'll be interesting to see what happens.