I keep hearing about faster than light communication with quantum entanglement. It seems to be a very persistent misconception. The same "communication" as with quantum entanglement can be done in the classical universe. You can easily create two entangled envelopes. People's minds are blown just because we put the word "quantum" in there.
Take two indistinguishable envelopes. Put a green card in one and a red card in the other. Shuffle the envelopes so that you do not know which card is in which envelope. Have a friend take one of the envelopes many kilometers away. Your envelopes are now entangled.
If you now open your envelope, and it contains the red card, you instantly know your friend's envelope contains the green card. Did information travel faster than light? No, it did not, since in order to communicate by this method you still need to tell your friend what it means to have the green card.
You still need to send slower than light information that Red is 1 and Green is 0 which you can only do once you've measured your own envelope, after which you've destroyed the entanglement of your envelopes.
Quantum entanglement is a phenomenon where you can tell something about the other part of the entangled pair by measuring one part. Just like with the entangled envelopes, you cannot communicate anything by this since you don't know in advance what you're going to measure.
But isn't the essential difference (and what makes the QM effect seem like spooky action-at-a-distance) that it's been proven that it isn't like the envelope example? Namely, there's no definite "redness" or "greenness" to the entangled particle before you examine it (unlike the envelope, which contains a red or green card the whole time). Whether you have a "red" or a "green" quantum part isn't decided until you look, at which point the wave function collapses in both parts simultaneously, no matter how far apart they are.
No, quantum entanglement does not allow Information to travel faster than light. Classic channel is needed to know what if any unitary transformations are needed. Otherwise requiring roll of massively many sided dice. Check out No Communication Theorem.
I can't provide a coherent explanation of Relativity in one little HN box, but what I can say is that Special Relativity is pretty easy to learn and understand if you're willing to put in a bit of effort and deal with some high-school level algebra.
General Relativity is much much more difficult, but once you understand Special Relativity, a lay-person's understanding of GR gets the job done for most purposes.
Re quantum entanglement, no it doesn't imply that data travels faster than light. The versions of QM where the probability waves collapse might, but in the Many Worlds interpretation, which is probably the most popular interpretation now among physicists and philosophers of science, the probability waves never collapse, and so there is nothing to transmit.
In the Copenhagen interpretation, one might argue that the probability wave collapsing transmits information all along that wave instantaneously, but if so, this happens under the covers of the universe. There's no way for anyone to use this feature of QM to transmit usable information from one place to another at faster than the speed of light.
Under SR, for two events (an event is a point in 4D space, i.e. a space and a time) with spacelike separation (i.e. outside each other's light-cones), neither comes objectively before or after the other. Different observers travelling at different speeds have different "surfaces of simultaneity", which say which events happen simultaneously. It's a theorem (or intuitively obvious) that for any two events with spacelike separation, there is a frame (i.e. a velocity at which you could be travelling) for which those two events are simultaneous.
So consider the events A=point 1, time 0; B=point 2, time 0; C= point 1, time 1 hour. As long as points 1 and 2 are more than 1 light-hour apart, it is legitimate to say that A is simultaneous with B, or that C is simultaneous with B. And so if you have a device that lets you travel from point 2 to point 1 in less than an hour (i.e. faster than light), you leave at B and arrive after A but before C. Then from the perspective of some observers (and the point of relativity is that all observers are equally legitimate), you arrived before you left.
The collapse of quantum entanglement can be confusing, which is part of why I prefer to follow many-worlds (i.e. no collapse postulate). You can construct quantum wavefunctions such that they're consistent with SR; for two entangled but spatially separated particles, you simply have a wavefunction that's a superposition of two states. When you as an observer observe one of those particles, you entangle yourself and your own state becomes part of the superposition. Of course "from the inside" it feels like you measured the particle and got one result or the other, but the actual wavefunction is just an ordinary superposition. From this perspective it's obvious no data was transmitted - you just became entangled with this distant particle without communicating with it, which is kind of odd, but no danger of violating causality.
But is it really important that it looks like you arrived after you left? Can't we just know that the light from one thing took longer to reach us than the other so what we are seeing is just an artifact of FTL.
Can that prevent causality? Or does it prevent relativity?
All observers are equally valid under SR; it would be very arbitrary to say that some of them are seeing "artifacts". Physics is based on observation, and the natural way to interpret our observations is to say that what we saw really happened. (Obviously this isn't true if some observable effect is distorting our perception, but that's not what's happening here - the observer who sees the person arrive before they left is a perfectly normal observer using perfectly normal equipment). Now if you want to say physics works differently for observers in different frames, that's fine, but it goes against relativity and all known physics.
Now assuming we accept that FTL-traveller really did arrive before they left, if that's all they do it's a matter of language as to whether they have violated causality by so doing. But it would take some very perverse physics (again, basically discarding relativity) to say they couldn't simply jump back, again going backwards in time, and arrive back at their starting point before they left it, at which you definitely have causality violation.
I don't know the specifics about quantum entanglement, but any means of making information travel faster than light that can work reliably in two different inertial frames (thus communicating four different points, two not moving relative to each other in space in each) can be used to break causality
or relativity. This is achieved by constructing a loop in which if the second pair of devices is used to disable the first you have a time paradox.
Also, doesn't quantom entanglement imply that data travels faster than light?