# Information, what counts as it, why isn't phase velocity etc. information?

When someone asks the question why can some stuff go faster than c, they get the answer that "it's not a transfer of information- special relativity says that no INFORMATION can travel faster than light."

Why don't processes such as phase velocity and entangelment transmit information? What does physical information really mean, and what distinguishes physical processes that transmit information from those which don't?

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Good question, I don't really have an answer.

I can answer why entanglement can't be used to transmit information though, that's quite easy. If you have an entangled pair of spin-1/2 particles, and you send one of the particles to your friend, then if your friend measures the spin of his particle, he instantly knows which spin your particle has.
Now suppose you decided on the following: if he measures his particle to be spin up, that means your particle is spin down, and that is decided to mean 0. If your particle is spin up (and so, his particle spin down) then that's a 1.
This way, by simply measuring a large number of entangled particles, he could send you a string of 0's and 1's, which could be interpreted as a message.

But, he cannot use this to send you a message, simply because he cannot decide which spin he measures! His measurement is completely random, yielding 'spin up' with 50% chance and 'spin down' with 50% chance. Sure, after measuring, he knows with 100% chance which spin your particle is, but he cannot decide if he sends you a 0 or a 1, which makes it impossible to send a message.

The only way to convey information is by conveying energy. You might think of energy as 'containing' information. So conservation of energy and conservation of information go hand in hand. The concept of phase velocity doesn't represent any movement of energy, so no information is transferred in phase velocity. Entangled particles can certainly be used to convey information, but not faster than light because no energy is moved faster than light.

Why don't processes such as phase velocity and entangelment transmit information?
Both of these processes (I presume you mean the superluminal phase velocity of de Broglie waves) may at first appear to send signals faster than light until we deal with the fact that in order to communicate any information the superluminal signal must be measured, and at that point we see that the measurement process does not allow any information or message to pass through. Nick already explained why entanglement cannot be used, and the idea of using matter waves to communicate superluminaly fails for a similar reason i.e. you cannot determine or prescribe in advance the outcome of a quantum measurement.

What does physical information really mean, and what distinguishes physical processes that transmit information from those which don't?
Physical information is just a message, encoded in any alphabet you want. Transmitting information means sending a message to a receiver. If you try to find a scheme to send messages faster than light using quantum mechanics, then if you do the math right you will see that the scheme can't work. For example, how would you propose to send a message using entanglement correlations, or using a phase velocity?

So conservation of energy and conservation of information go hand in hand.
There is no conservation of information. If we are using thermodynamic analogies, than information is most analogous to entropy.