The impossibility of FTL information

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I want to make an index over all things against FTL transmission of classical information. All theories, hypotheses, theorems, axioms and rules... you name it.

I'm not looking for explanations or references, only the headlines such as Eberhard's theorem, Special Relativity, and Shanon's information theory.

Of course you can say that it is sufficient to know that to extract the encoded information in entanglement, you need a classical channel to access the correlation between Alice's and Bob's measurements. That's one broken link in the chain, but I want to know all the other links.

I'm not a physicist, but I want to increase my knowledge of quantum mechanics to test the "hidden" hypothesis in my signature.
 
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Relativity is the only reason we believe information can propagate no faster than light. Anything else is just a statement that this or that theory is consistent with relativity. For instance, you can't derive an upper bound to information's speed of propagation in quantum mechanics. However, you can show, as you noted, that entanglement doesn't allow the transmission of quantum information without exchanging signals (which, as we know from SR, can only propagate at or slower than the speed of light) and so quantum mechanics is consistent with relativity. If relativity were falsified, there would be no other independent reasons to believe the speed of light is the maximum speed of information. Of course, relativity theory is the foundation for all of modern physics and one of the most well-established experimental facts in scientific history—so when I say it's the "only" reason for disbelieving FTL communication, that is rather understating the situation a little.
 
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It should be noted that Maxwell's laws of electromagnetism predict a VERY specific velocity for electromagnetic radiation (light). More specifically the "speed of light" is really the "speed of massless particles". To my knowledge (and please correct me if I am wrong - anyone), ALL massless particles travel at 'c'.