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Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does?

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Possible duplicate: physics.stackexchange.com/q/3158/2451 and links therein. –  Qmechanic Apr 14 '13 at 23:40
    
Related: physics.stackexchange.com/q/37861/4552 –  Ben Crowell Apr 15 '13 at 0:25
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To answer this kind of question properly, it's important to clarify the foundational issues of why SR forbids superluminal speeds and what kind of superluminal speeds it forbids. There are several independent arguments of this kind that tell us several different things.

  1. Superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the time-ordering of such events is different according to different observers. Since we never observe causality to be violated, we suspect that superluminal transmission of information is impossible. This leads us to interpret the metric in relativity as being fundamentally a statement of possible cause and effect relationships between events.

  2. We observe the invariant mass defined by $m^2=E^2-p^2$ to be a fixed property of all objects. Therefore we suspect that it is not possible for an object to change from having $|E|>|p|$ to having $|E|<|p|$.

  3. Composing a series of Lorentz boosts produces a velocity that approaches $c$ only as a limit. Therefore no continuous process of acceleration can bring an observer from $v<c$ to $v>c$. Since it's possible to build an observer out of material objects, it seems that it's impossible to get a material object past $c$ by a continuous process of acceleration.

  4. If we could boost a material object past the speed of light, even by some discontinuous process, then we could do so for an observer. However, there is a no-go theorem, Gorini 1971, proving that this is impossible in 3+1 dimensions.

Entanglement doesn't violate any of these arguments. It doesn't violate #1, since it doesn't transmit information. It doesn't violate #2, #3, or #4, since it doesn't involve boosting any object past the speed of light.

V. Gorini, "Linear Kinematical Groups," Commun Math Phys 21 (1971) 150, open access at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103857292

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I have never understood why entanglement doesn't transmit information faster than the speed of light. I alway imagine two entangled, polarized photons, one going right and the other going left. Then you'd measure one to force the other to the same state. It seems like you could transmit information faster than the speed of light this way (or some variation on it). Why can't you? Do you have a layman's explanation or a link to one? –  Brandon Enright Apr 14 '13 at 23:56
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@BrandonEnright Because the outcome of a quantum measurement is random and uncontrollable, and there is no way for the receiver to know whether the state has changed or not without doing a measurement themselves. –  Michael Brown Apr 15 '13 at 0:03
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@BrandonEnright: That's more of a separate question. At the simplest level, I like this analogy: physics.stackexchange.com/a/3162/4552 –  Ben Crowell Apr 15 '13 at 0:15
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@BenCrowell, be careful, because that analogy with gloves is not correct: it is exactly the kind of local hidden variable model that is provably inconsistent with the predictions of quantum mechanics via Bell's theorem. –  Mark Mitchison Apr 15 '13 at 0:27
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@BenCrowell Yeah I'm sure you understand the problem, and I don't want to get drawn into this but I'll just say that the top answers and comments on the page you linked are only really sensible from an anti-realist point of view. Any readers that believe in a reality existing independently of observers (what is an observer, exactly?) should treat the comments and answers given on the linked page with caution. –  Mark Mitchison Apr 15 '13 at 0:41
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Spooky action at a distance is faster than light Chinese boffins put the clock on information transfer between entangled particles By Richard Chirgwin Posted in Science, 8th April 2013 05:09 GMT

As Einstein put it, it's impossible for anything – even information – to move faster than the speed of light. Yet the lower bound of that impossibility, the minimum speed at which entanglement can't possibly be transmitting information between two particles, appears to be around four orders of magnitude higher than $c$, the speed of light in a vacuum.

http://www.theregister.co.uk/2013/04/08/chinese_entanglement_transfer_experiment/

http://arxiv.org/abs/1303.0614

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Here's an example I like of why entanglement doesn't let you violate relativity. Say you have two spaceships moving in opposite directions along a line, with constant velocity. At $t = 0$, they synchronize clocks and entangle two particles. They also decide, at some predetermined time $T$, to measure the spins of the particles (actually, ship 1 will measure at time $T$, and ship 2 will measure at $T + \epsilon$). They will interpret these measurements as ship 1 picking out a definite value for the spin of their particle (and thus of its entangled partner) and ship 2 measuring this value by comparing their own measured spin with the initial entangled state. If this worked, it would seem the spin information was transmitted from ship 1 to ship 2 faster than light, for sufficiently small $\epsilon$.

I like this example because you could (hypothetically) try it in real life, so there must be some concrete reason it wouldn't work. In fact, the relativity of simultaneity makes the interpretation of the measurements as information-transfer invalid. Ship 2 will make its measurement at time $T + \epsilon$, but it can't interpret the result as information sent from ship 1, because (as ship 2 can tell from its own clock plus a simple calculation) ship 1 hasn't made a measurement yet in ship 2's reference frame. The same reasoning applies in reverse; neither ship receives information about the other's measurement unless $\epsilon$ is large enough to make the simultaneity absolute.

So while there's undoubtedly more to be said about what's going on in general, this example reassures me that there's no immediate contradiction here.

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Quantum mechanics in its original form has no lightspeed restriction so allows experiments to be interpreted without that restriction, thus FTL allowed same as in Newtonian physics. Special relativity (SR) starting with its assumption of lightspeed constancy (in vacuum, free of influence from fields) asks what is the consequences of that assumption and answers time dilation and other effects, so that clocks are set to go at different rates etc. Not going by that assumption and having clocks set to go at same rate then we get variable lightspeed. Its just in the maths: c' ^2 t' ^2 = (c^2-v^2)t^2 , if set c' =c then time dilation, if set t=t' then variable light speed as per quantum mechanics. So to the question of does quantum entanglement violate SR, the answer is many people have misunderstood SR. What we have is that setting lightspeed as constant is only a convention. Not going by that convention and we have FTL as per quantum mechanics. Einstein himself abandoned SR in order to create GR (general relativity). And so as people go higher up in the study of relativity they find that FTL is allowed in some frames of reference, from such as Wheeler school of relativity, where Wheeler is supposed to be the succesor to Einstein. There are those at a lower level of understanding of Einstein's relativity, and start making false claims about SR. For instance something like saying: “Superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the time-ordering of such events is different according to different observers.” - well what needs to be emphasised in such a claim is that it is in the context of SR, and that's when the convention of lightspeed is being set constant, so of course in that setting it would be causality violation, but in the setting of how Newtonian physics treats spacetime and which quantum mechanics adopts, the way FTL is treated there is no causality violation. So the point that needs raising is there is no causality violation in the way that quantum mechanics is treating FTL, and talk of is there information or not being transferred is just a red herring, because of course information is being transferred - an object whether classical or quantum when it moves at a certain speed moving from one position to another is transmitting information by so doing, its how the maths has it in those theories. Its when SR wants to save itself in the way that it treats things that it tries to throw up red herrings. The maths at the foundational level when it is setup to deal with SR clearly shows what is happening, there is the Pythagorean triangle with its hypotenuse as ct with horizontal as vt then for the vertical it equates to ct' this then gives us time dilation equation. However the things to note here is that it is switching between an unprimed frame of reference (with its t) to a primed frame (with its t'), such a switch is not happening in the set up of quantum mechanics, if keep things all set in the same frame with frame switching then the maths of that setup is allowing FTL to be treated in the Newtonian way. (If you were doing the frame switching between t and t' in the way that SR wants then you would be dealing with a different type of FTL.) So in the unprimed frame with its velocity Pythagorean triangle its hypotenuse as c and vertical as v there is velocity in vertical of sqrt(c^2-v^2) in other words its being treated in same way as any other vector in Newtonian physics, and hence Newton's equations of motion still applies. So overall its needs to summarised that – the way quantum mechanics is treating velocity (its the same way as Newtonian physics) information is transferred in velocities FTL, its not the same way that SR is treating velocities. SR would like quantum mechanics adjusted to deal with lightspeed and velocities in the same way that it deals with things by frame switching (between unprimed and primed frames) etc., but quantum mechanics has no need to deal with it that way, and so has it from the way it treats FTL that is information transfer. Its why Einstein referred to it as “spooky” because he knew it disposed of SR. But for him he abandoned SR and went to general relativity anyway, with the idea that theories have a range of applicability, and the “spooky” quantum mechanics had just moved out of the range of applicability of SR. He didn't like it so started saying things about God not playing dice or doing this or that.

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