I have regularly heard that the Michelson-Morley experiment demonstrates that the speed of light is constant in all reference frames.
By doing some research I have found that it actually demonstrated that the luminiferous aether probably didn't exist and that the speed of light didn't vary depending on which direction the planet was travelling in. I don't see how it demonstrated that motion towards a light source for instance doesn't affect the observer's speed relative to the light, as there were no moving parts in the experiment.
The other sources I've looked at which say that the Michelson Morley experiment proved nothing like this one: Is the second postulate of Einstein's special relativity an axiom? and this one: How can we show that the speed of light is really constant in all reference frames? tend to say that Maxwell's equations were actually more significant to Einstein as they predict that light moves at a constant velocity, and this velocity has to be relative to something (or in relativity's case, everything). That something was thought to be the aether, but in the absence of that why could it not be relative to whatever emitted it? It seems like a more obvious immediate conclusion to come to than the idea that it's the same relative to everyone and all the counterintuitive results that ensue.
Another idea is that the speed of light is the universal speed limit and therefore must have a fixed value just to work under galilean relativity.
But then that argument goes in circles:
"Why can't you go faster than the speed of light?"
"Because otherwise your mass becomes infinite."
"Why does your mass become infinite?"
"Because of Einstein's special relativity."
But this is based on the original fact that you can't go faster than the speed of light, so there's no argument I can find which completely answers why the speed of light has to be constant, other than that it has been regularly tested since.
So my questions are:
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Is there something I'm missing about the Michelson-Morley experiment or Maxwell's equations which explains my objections and definitively shows that the speed of light is constant and it is impossible to go faster than it?
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If not, is there any other specific example, ideally which would have been there for Einstein, which I can use to explain to people with no knowledge of relativity why it is the case?
Best Answer
For a basic treatment of the Michelson-Morley experiment please see 1. It's not important to know the technical details of the experiment to answer your questions though. The only relevant thing is the result, let me put it in basic terms since you seem to struggle with the "physics slang":
While the total velocity of a ball thrown from a truck is the sum of the velocity of the ball relative to the truck and the velocity of the truck relative to the observer, the velocity of a light beam emitted from the truck is not. Much more the velocity of the light beam seems completely independent of the velocity of the truck.
Michelson and Morely didn't have a truck, they had the earth orbiting the sun.
Please make it clear to yourself that this experimental fact can be explained by stating that the speed of light is constant. If I say to you the speed of light is constant in every frame of reference, then the above result isn't surprising at all to you.
But you want more. You want me to prove to you that the speed of light is universally constant. I cannot. There will never be an experiment that shows that this axiom is universally true. How should one ever construct such an experiment, how should one, for example, test the theory in the Andromeda galaxy? It's impossible, but it doesn't matter: Why not just stick with the axiom, as long as we can explain everything we see around us with it?
As you already said there's an interesting connection between the invariance of the speed of light and Maxwell's equations. One can indeed prove that the speed of light has to be constant, otherwise, Maxwell's theory can't be true for all inertial frames. But this is no proof that can convince you either, since accepting Maxwells equations is no different to accepting the invariance of the speed of light. Furthermore, the basis of Einstein's theory is not the invariance of the speed of light, but the invariance of the speed of action. Which cannot be concluded from Maxwell's theory, even though it's a reasonable guess.
Physical theories are not provable. But as long as they comply with reality, we accept them as truths.
Addendum: I recommend this short lecture for layman by R. Feynman on the topic. Feynman and I present a very similar line of reasoning.