Self-explanatory. Einstein builds his 1905 paper on electrodynamics in part on the postulate that the speed of light is constant regardless of the velocity of the emitter. I know that, obviously, Einstein’s theories hold up pretty well.
But…okay, why? Do we know? If not, do we think we can figure it out? Does it have something to do with Minkowski’s ‘time and space are basically the same thing’ theory?
(I’m pretty sure that the more quantum mechanics I study, the less I know about it. Good god the universe is weird.)
That’s certainly relevant. Basically, it’s the same as the reason that a meterstick has the same length if it’s vertical or horizontal. A change of velocity is a rotation in spacetime, and there are lots of things which stay the same when you rotate them. The speed of light is one of those things.
Actually, Einstein probably didn’t even know about the Michelson-Morley experiment. The first clue that it’s invariant (which isn’t technically the same thing as constant) is Maxwell’s equations for electromagnetism.
Not that any of the above answers are wrong, but I can see where you might want a bit more explanation. You can’t really answer why using special relativity, because the constancy of the speed of light is a built in assumption. To properly answer why, you must be able to derive relativity from a more fundamental theory, and we’re not quite there, yet. (Quantum field theory springs from incorporating relativity into quantum mechanics. I took a while, but I believe string theory is now beyond its start of building in relativity. Whether allowing 10 to the 100 different sets of fundamental constants constitutes an explanation is hardly clear.) However, you can go backwards, and see it from a less fundamental theory: Maxwell’s Electromagnetics.
One of the reasons Maxwell was very excited as developed his eponymous equations is that he was able to derive the speed of light from them. (FYI, He mostly consolidated, or unified, other equations, adding only the displacement current, IRRC. He used a mechanical model to do so, but fully realized it was just a contrivance.) I believe the phrase he used was “great guns”.
At any rate, Maxwell’s equations predict that the speed of light to be the inverse square root of the product of two constants. Nowhere in the derivation of the speed of light does a velocity relative to the medium known as the ether appear. But, human beings being what we are, physicists assumed the speed of light was similar to the speed of other waves and depended on the speed of motion through the ether. I presume they must have thought that one or the other, or both, of the constants depended on one’s through the ether. That is, since the constants are properties of the vacuum, their values must depend on one’s speed through the vacuum. Special relativity says, no they aren’t. And from thence you proceed to derive all that is cool in relativity.
I was interrupted while making my post and you and Chronos both posted whilst I did so. I believe Physics Today had an article on this very topic, perhaps in 2006. It is possible I’m conflating the Einstein bio “Subtle is the Lord” with another article on what Einstein knew as worked out Special Relativity. The author opined that Einstein forgot in his later years what he knew when, but that Einstein very likely did know of the MM result.
An article in a recent New Scientist based on work by Mitchell Feigenbaum suggests that the speed of light is a mathematical result of the curvature of space/time and classical relativity - ie, that Einsteins 2nd postulate (invariant speed of light) is not necessary.
Einstein’s first postulate was that frame of reference does not matter - the laws of physics stay the same. Maxwells equations required the speed of light, but had no place for a frame of reference, so Einstein added the second - the speed of light was invariant in any frame of reference. Using these two postulates, he derived the complex maths of Special Relativity.
But the first postulate was an established principle, originally expounded by Galileo. But Galileo did not have the maths to extend this principle into a non-euclidean universe. If you introduce curvature of the universe, the maths resolves to giving a definite maximum velocity based on that curvature. And light happens to travel at that maximum velocity, and so it is the one thing we see doing so.
Apparently, this places Relativity on a purely mathematical basis without changing any of Einstein’s conclusions, and gives new theoretical tools to further explore how the universe really is.
My summary is brief and reflects my understanding of it, it is a New Scientist article, physicists and mathematicians can feel free to comment, but it isn’t my fault if you disagree ;).
>And light happens to travel at that maximum velocity, and so it is the one thing we see doing so.
Better that we should refer to the constant c than calling it the “speed of light”. I think there is something very important about information, the third sign of a coin it shares with mass and energy, and the limiting rate at which it can propagate, c. There is a border between things that exhibit causal relationships and things that can’t, which in cosmology we would call the “world lines” of those things. The opposite of information, uncertainty, is all kinds of woven into the universe too, in quantum mechanics and the second law of thermodynamics and entropy.
So, c is the velocity that defines a border around causality. And light and radio and xrays and radiant heat etc etc all travel at c.
