Sending information faster than light

If I could ever send my friend any information faster than light it would violate causality. If he just guesses the information and acts on it before he could ever recieve it, everything is fine. What is different here?

I can understand that nothing can ever move faster than light but I can't understand why causality would be violated if something did. Or does it really have to? Since wormholes are mathematically sound, is it only a question of traversing faster than light? Is it ok if I find a way of transferring information faster than light as long as I don't move anything faster than light?

• If you could consistently transfer information faster than light (as opposed to just occasionally making a lucky guess), then this would allow you to consistently transfer information backwards in time to your own past (as opposed to just luckily guessing what information you would decide to send in the future), assuming relativity is correct about the laws of physics working the same in all inertial frames--see my answer here. Jan 23 '15 at 0:33
• @user71361 And if he doesn't guess? If your friend has the property that he guesses the information, why do you have to send it? Relativity has no connection with guesses. Jan 23 '15 at 0:42
• If your friend can guess with a 100% accuracy rate, then you're not sending any information he doesn't already have. Jan 23 '15 at 10:44

What is different here?

In some reference frames, your friend guesses the information and acts before you send it and in others, he guesses and acts after you send it.

But there is no causality problem since his action is caused by his guess rather than the received information.

In all reference frames, the guess precedes the action.

Now consider the actual effect of receiving the information. Perhaps a tone is sounded or a light is activated.

If the information propagates faster than $c$ from the transmitter to the receiver in some frames of reference, there are other frames of reference in which the event that the tone is sounded occurs before the event the information is transmitted, i.e., the cause and effect are reversed.

This is clear if you draw a spacetime diagram of two events, E1 and E2, with spacelike interval and note that, in some reference frames, t(E1) < t(E2) and, in others, t'(E2) < t'(E1).

There is actually a strong relationship between information and guessing.

For every message, we can talk about the data it contains and the information it contains. Both are measured in bits, but they're not quite the same thing.

The data in a message is just its size (eg. how many times we flashed our light, or switched our electricity, or whatever we did to transmit the message).

The information in a message is how much new knowledge it gives us, or how much it improves our guesses about the world.

Information and data aren't the same thing. If your friend can reliably guess the message you'll send, then you're not actually sending him any information! You could send him an informationless message faster than light without breaking causality, since it won't change anything that happens (he already knew what it says).

Information is precisely how unpredictable your message is.

In terms of causality, transmitting information is essential. If your friend can guess what to do, even without receiving your message, then you've not caused his actions at all! They were pre-determined, perhaps by some prior meeting you both had before zooming away from each other in space ships.

In order to cause his actions, you must be able to affect them; to alter the probability that he does one thing or another. That change in probability is directly related to information: if you're equally-likely to have him do one of two actions, then telling him which one to do takes 1 bit of information. When there are many actions to choose from, with varying probabilities of being chosen, then more information is required. It's possible to have "fractions of a bit", eg. a choice between 3 equally-likely actions takes 1.5 bits, but only whole numbers of bits can be transmitted, so we must round up.

The better your friend can guess what you're going to ask for, the less information he obtains when you tell him. If your two examples (sending a message vs. him guessing) were actually the same, then your message would contain no information, and hence couldn't violate causality.

The equations of special relativity imply that a hypothetical superluminal signal would arrive at the receiver before it was transmitted from the source. Since the effect precedes the cause, the "law of causality" would be violated. Therefore superluminal signals are not considered possible -- if the special theory is correct.

If you could send a superluminal signal, special relativity would be falsified. Any attempts to use the equations of special relativity would give absurd/impossible results, such as the violation of causality, and particles with imaginary masses.

Recently, superluminal neutrinos were thought to have been detected at the large hadron collider. The implication was not that the neutrinos had violated causality, or had been sent backwards in time, the implication was simply that special relativity had been falsified.

Note that quantum nonlocality implies that superluminal causal connections do exist, and that entangled particles "influence" one another superluminally. However this does not violate special relativity because the quantum state information transmitted between entangled particles cannot be used to send a superluminal signal.