Scientists 'break speed of light'

Quantum Mechanics yields all sorts of supposedly superluminal effects. None of them are causing me to lose much sleep. For instance:

(i) Tunneling. Thats the subject of this article, and is well known and studied (including by Aephraim who is quoted above, but many other folks as well).

(ii) Violation of Bell inequalities. Ok, so I lied - I do lose some sleep over this one, because it really does seem nuts.

(iii) http://en.wikipedia.org/wiki/Scharnhorst_effect

(iv) Drummond-Hathrell effect (see e.g. http://arxiv.org/abs/0708.2189 for a paper that is intelligible to a non-expert, and also discusses the Scharnhorst effect, though I'm not certain of his conclusions on this one).

(v) Take a (square integrable wavefunction) defined on compact support (that is, say [latex]\psi(x)[/latex] is non-zero only between between x=0 and x=1) then evolve it for a infinitesmal time dt under the Schroedinger eqn. You'll find there is a finite amplitude for finding the particle arbitrarily far away (e.g. [latex]\psi(x=100)>0[/latex] for any time dt>0).

(vi) When you detect a particle at one point, then the wavefunction vanishes to 0 instantly at every other point in space.

And so on.

One point to note is that when you analyze these things carefully, they never allow for transmission of information faster than light.

ETA: Damn that latex is ugly. Why is the default font size so large??
 
Also Hawking radiation wouldn't be possible unless tiny particles could travel faster than light due to quantum mechanics.
 
Tez said:
(v) Take a (square integrable wavefunction) defined on compact support (that is, say [latex]\psi(x)[/latex] is non-zero only between between x=0 and x=1) then evolve it for a infinitesmal time dt under the Schroedinger eqn. You'll find there is a finite amplitude for finding the particle arbitrarily far away (e.g. [latex]\psi(x=100)>0[/latex] for any time dt>0).
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I know this is true for non-relativistic quantum mechanics, but is it true for relativistic QM as well? In the former case, there really isn't a problem, since the theory doesn't prohibit superluminal wave packets to begin with, so we know the theory is wrong. But I confess I don't have much experience dealing with relativistic QM, and if the problem persists in that case, it is a little more disconcerting. But I think all that really indicates is that such wave functions are nonphysical, because in order to construct a superposition which is compact, you either need infinite potential wells (which you can also turn off) or you need to add components whose energy is unbounded.
 
Ziggurat said:
I know this is true for non-relativistic quantum mechanics, but is it true for relativistic QM as well? In the former case, there really isn't a problem, since the theory doesn't prohibit superluminal wave packets to begin with, so we know the theory is wrong. But I confess I don't have much experience dealing with relativistic QM, and if the problem persists in that case, it is a little more disconcerting. But I think all that really indicates is that such wave functions are nonphysical, because in order to construct a superposition which is compact, you either need infinite potential wells (which you can also turn off) or you need to add components whose energy is unbounded.
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Your intuition as to the unphysicality of the "infinite potentials" is correct - any wavefunction constructed from analytic potentials etc will itself be analytic, and automatically have tails at infinity. However I believe it can be shown in complete generality that there are no measurements I can do which can detect the "size of the increase" in the analytic tails when I (non-analytically) vary some time dependent potential far away (as I might do to try and communicate say). That is, it seems that non-relativistic QM does obey the "no superluminal signalling" for this example (as it does with tunneling) even though there is no real reason that it should!! (It also obeys it for Bell inequalities, though thats now a two-particle effect and quite different).

And yeah the same thing is in QFT as well - there you normally first encounter it as the fact that the Feynman propagator (the jiggers - you use when you construct the amplitudes for some Feynman diagrams, which are just equivalent to the Greens functions of the solution to the Schroedinger eqn for the non-rel example) become nonzero over arbitrary spacelike separated points. However in QFT the argument that you cant measure the superluminal propagation is somewhat vacuous - commutation of field operators at spacelike separated points is an axiom. A big problem is that there is no decent "theory of measurement" for QFT - we can calculate certain correlation functions (primarily only of the ground state of the theory!) and relate those to scattering experiments. But there is no good theory on how to update your field configurations after a measurement, or theory for how to represent arbitrary measurements (such as phase, which has no hermitian observable) by positive operator valued measures (as there is in non-relativistic QM). So maybe its kind of premature to be tackling some of the QFT paradoxes related to casimir vacua etc. I dunno - I'm no expert in those things.

Oh - but you can use the non-vanishing nature of those propogators to distill EPR pairs from the vacuum: http://arxiv.org/abs/quant-ph/0008006 which is kind of neat.
 
Tez said:
Man alive,
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I love that phrase. I especially liked the Simpson's use of it, when a fully suited HazMat team bursts into Moe's Tavern after it fills with toxic fumes, sees Homer, Moe and Barney, and says, "Man alive! There are men alive!"
 
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