# Hidden variables, Bell's theorem, etc

Hello all,

I'm having a couple of problems with interpretations of Quantum mechanics and just want to summarise my understanding so that it can be verified and/or corrected.

Schroedinger's cat leads to the idea of entanglement, namely the observation of one event indicates that other events have occurred. (seeing a dead cat means that the poison was released. Likewise, measuring the spin of one photon may give a measurement of the spin of another (entangled) photon.

Bell's theorem states that there cannot be a theory (which predicts the correct result of experiments) using local hidden-variables. Is that the same as saying that the spins have no value before they are measured? Or if they do, then there is a mechanism for changing the spin of another particle after the first is measured, a mechanism which communicates the change of spin faster than the speed of light?

Bohm's interpretation says that the whole universe is entangled and that the universal wavefunction is modified by the whole universe (and effects can travel faster than the speed of light)? but this doesn't break causality nor the rules of special relativity.

The Copenhagen interpretation says that "observing" the spin of the first photon breaks the entanglement and the second photon must collapse into a given state? It gets around the "observation" problem, by saying that every time a wavefunction collapses, other universes are set up in which every possible outcome has its own universe?

Have I understood this problem correctly? I know that the philosophy of quantum mechanics is a big topic and that's why I prefer to avoid it completely (shut up and calculate has gotten me through exams). However, several popular science articles confuse the hell out of me. This one for example: http://www.popsci.com/science/article/2010-03/computer-processes-faster-speed-light

This entanglement thing looks, to me, like simple interference effects of two particles (young's slit or whatever). The article states that putting the "computer" in a medium rich in electrons will increase the speed of light. This sounds like anomalous dispersion in a metal/plasma (leading to superluminal phase velocity), but I can't be sure that that's all it is without a better understanding. Following links gets you to the original paper (it's free access): http://arxiv.org/abs/1003.1238

Cheers all!

Demystifier
Gold Member
Bell's theorem states that there cannot be a theory (which predicts the correct result of experiments) using local hidden-variables.
Correct.

Is that the same as saying that the spins have no value before they are measured?
No.

Or if they do, then there is a mechanism for changing the spin of another particle after the first is measured, a mechanism which communicates the change of spin faster than the speed of light?
Yes.

Bohm's interpretation says that the whole universe is entangled and that the universal wavefunction is modified by the whole universe
It's true that everything is more or less entangled, but that's true even without the Bohm's interpretation. In the Bohm interpretation the wave function is not modified by the whole universe. Instead, Bohmian particle trajectories are those which are modified by the whole universe.

(and effects can travel faster than the speed of light)? but this doesn't break causality nor the rules of special relativity.
It's more subtle, i.e., it depends on what exactly do you mean by "effects", "causality" and "special relativity". See e.g. Sec. 2 of
http://xxx.lanl.gov/abs/1002.3226
for a more careful discussion.

zonde
Gold Member
Bell's theorem states that there cannot be a theory (which predicts the correct result of experiments) using local hidden-variables.
Wrong
Bell's theorem states that there cannot be a theory using local hidden-variables which predicts the same result of experiments as QM.

Is that the same as saying that the spins have no value before they are measured? Or if they do, then there is a mechanism for changing the spin of another particle after the first is measured, a mechanism which communicates the change of spin faster than the speed of light?
Depends from interpretation.

The Copenhagen interpretation says that "observing" the spin of the first photon breaks the entanglement and the second photon must collapse into a given state?
Right

It gets around the "observation" problem, by saying that every time a wavefunction collapses, other universes are set up in which every possible outcome has its own universe?
This is not Copenhagen interpretation. It's Many-worlds interpretation.

Wrong. In Many-worlds interpretation, wavefunction never collapses. You are describing some naive pre-decoherence version of MWI.

DrChinese
Gold Member
Hello all,

I'm having a couple of problems with interpretations of Quantum mechanics and just want to summarise my understanding so that it can be verified and/or corrected.

Schroedinger's cat leads to the idea of entanglement, namely the observation of one event indicates that other events have occurred. (seeing a dead cat means that the poison was released. Likewise, measuring the spin of one photon may give a measurement of the spin of another (entangled) photon.

Bell's theorem states that there cannot be a theory (which predicts the correct result of experiments) using local hidden-variables. Is that the same as saying that the spins have no value before they are measured? Or if they do, then there is a mechanism for changing the spin of another particle after the first is measured, a mechanism which communicates the change of spin faster than the speed of light?

Bohm's interpretation says that the whole universe is entangled and that the universal wavefunction is modified by the whole universe (and effects can travel faster than the speed of light)? but this doesn't break causality nor the rules of special relativity.

The Copenhagen interpretation says that "observing" the spin of the first photon breaks the entanglement and the second photon must collapse into a given state? It gets around the "observation" problem, by saying that every time a wavefunction collapses, other universes are set up in which every possible outcome has its own universe?

Have I understood this problem correctly? I know that the philosophy of quantum mechanics is a big topic and that's why I prefer to avoid it completely (shut up and calculate has gotten me through exams). However, several popular science articles confuse the hell out of me. This one for example: http://www.popsci.com/science/article/2010-03/computer-processes-faster-speed-light

This entanglement thing looks, to me, like simple interference effects of two particles (young's slit or whatever). The article states that putting the "computer" in a medium rich in electrons will increase the speed of light. This sounds like anomalous dispersion in a metal/plasma (leading to superluminal phase velocity), but I can't be sure that that's all it is without a better understanding. Following links gets you to the original paper (it's free access): http://arxiv.org/abs/1003.1238

Cheers all!

You are correct that some of your questions come down to "interpretations". Some of the answers above are in fact a result of their interpretation views (Bohmian, etc.) and are correct within that view.

The speed of light in a vacuum is always c as you know. The articles where they report "speed of light exceeded" is always something like you describe. I don't know of any currently known process where a signal can exceed c.

I think it means the speed of light in that (electron rich) medium. Kinda like the physics behind kirchhoff radiation.