Is c the invariant speed?

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Thank you everyone so much for all the explanations. However, I have another question here. I was reading Mr Tompkins and I understand that relativity of time exists because we have a certain absolute speed, beyond which nothing can travel. For our universe it is c. Are there any other proofs confirming that light has the ultimate speed in all reference frames in our universe except the solutions to Maxwell's equations in vacuum?

[Mentors' note: this thread was forked off from another thread]
 
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"Proof" is not a good word to use in physics, since there is no "proof" of anything here the way it is in maths. Anyway, the best "proof" that you can get in physics is the outcomes of experiments. And the experimental confirmation of special relativity is enormous.
 
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  • #3
Nugatory
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The starting point is the assumption that the speed of light is the same for all observers. Everything else, including not being able to move faster than light, follows from that assumption.

Maxwell's equations suggest that we shouldn't be surprised to find that the world works that way, but the real proof is in the many many many experiments that have been done over the past century to confirm this. The "experimental proof" sticky thread at the top of this forum is a good starting point.
 
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Mister T
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Are there any other proofs confirming that light has the ultimate speed in all reference frames in our universe except the solutions to Maxwell's equations in vacuum?
Maxwell's Equations are part of his theory. They do not constitute proof of anything.

You must appeal to experiment to get evidence to support or refute a theory.

There is an overwhelming amount of evidence that light travels at the invariant speed, and if there's an invariant speed it must be the fastest speed.
 
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The famous starting point is the Michelson-Morley experiment (see https://en.wikipedia.org/wiki/Michelson–Morley_experiment). They expected to measure the effect of aether on the speed of light, but never found any. Other experiments followed. The results are very convincing evidence of the constant speed of light.
 
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haushofer
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The starting point is the assumption that the speed of light is the same for all observers.
Inertial observers.

To be nitpicking :P
 
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phinds
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... we have a certain absolute speed, beyond which nothing can travel. For our universe it is c.
There's a slight subtlety of terminology here. First, I would call it the "ultimate" speed, not "absolute" since that carries some connotations which are unfortunate in this context, but yes, we have "a certain absolute speed, beyond which nothing can travel" and we call it "c", BUT ... "c" also means "the speed of light" and while there is not even the slightest experimental evidence that light travels at anything but the ultimate speed, nor is there any belief that any such evidence will ever be found, it cannot be ruled out. SO ... it is conceivable (WAY unlikely) that light might be found to have a tiny mass and thus travel at something other than the ultimate speed. If that were found to be the case, we'd have to come up with differentiating symbols, one for the speed of light and one for the ultimate speed.
 
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  • #8
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Inertial observers.

To be nitpicking :P
A necessary and important nitpick though....
 
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Matterwave
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"Proof" is not a good word to use in physics, since there is no "proof" of anything here the way it is in maths. Anyway, the best "proof" that you can get in physics is the outcomes of experiments. And the experimental confirmation of special relativity is enormous.
I might modify this to be a little more precise. There are of course "proofs" in physics the same as in math - one starts off with a few assumptions (e.g. constancy of the speed of light, principle of relativity, etc.) and prove properties of that theory given the mathematical framework in which the theory is produced (e.g. all of the consequences of special relativity). Statements can be proven or disproven within the framework of a theory - given the assumptions of that theory - and we get theorems out of that (another example: Birkhoff's theorem in General Relativity). What "can't be proved" in physics are the assumptions of the theory - those can only be experimentally tested. This is the same as in math. Mathematical axioms are not proven. The difference in physics though is that physical postulates should reflect our view of the physical world and can be experimentally tested - mathematical axioms have no such restriction and are basically evaluated based on usefulness.

In the case of this thread, OP asked to prove the assumptions of constancy of the speed of light in the context of special relativity. Since constancy of the speed of light is an assumption of special relativity one says that it can not be proven within that context - only experimentally verified. Special relativity is a foundational block upon which all of modern physics is built (GR and the SM both respect it!) so one tends to avoid speaking of the speed of light as any sort of "provable" statement. It is not inconceivable though that there is some higher level theory out there (quantum gravity maybe?) from which constancy of the speed of light can be deduced (i.e. proven) from some as yet unknown more fundamental set of assumptions.

Perhaps I would say to the OP: in the context of modern physics (i.e. modern physical theories) as we know it, the constancy of the speed of light is an experimentally verified assumption and therefore can not be proven.
 
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