Quantum Entanglement

[IM Egdall]

Am reading How to Teach Physics to your Dog by Chad Orzel. Good book on quantum mechanics in layman's terms. It discusses a subtle point on Quantum Entanglement and Bell's Theorum.

 

Orzel says that Bohm's version of quantum mechanics uses nonlocal hidden variables, and reproduces all the predictions of quantum theory using particles with definite positions and velocities. Then Orzel says that Bell's theorum experiments have conclusively shown that quantum mechanics is nonlocal. So far so good. Both standard QM and Bohm's QM are nonlocal.

 

So Bell's theorum experiments show that the universe is nonlocal. But do they say anything about hidden variables? As I understand it, if hidden variables are allowed, then the attributes of a particle (e.g. postion, polarization) are there before we do a measurement. But per standard QM, these attributes are undefined until they are measured. The photon, for example, is in both polarization states until it is measured.

 

I have seen this issue argued about in physics journals. So is there a definitive answer; what exactly does Bell's theorum tests say or not say about hidden variables?

[swansont]

AFAIK, local hidden variables are excluded. Bohm's hidden variables are nonlocal. But I don't know a lot of detail beyond that.

[IM Egdall]

AFAIK, local hidden variables are excluded. Bohm's hidden variables are nonlocal. But I don't know a lot of detail beyond that.

 

Yes. As I understand it, any local theory is excluded by the results of Bell's theorum tests. But the question remains; how about nonlocal hidden variable? Do the Bell test results tell us whether particles have attributes before they are measured or not?

[swansont]

Yes. As I understand it, any local theory is excluded by the results of Bell's theorum tests. But the question remains; how about nonlocal hidden variable? Do the Bell test results tell us whether particles have attributes before they are measured or not?

 

Locally, yes. I don't think the Bell tests rule out nonlocal effects.

[webplodder]

 

I have seen this issue argued about in physics journals. So is there a definitive answer; what exactly does Bell's theorum tests say or not say about hidden variables?

 

 

Bell's Theorem shows that entangled particles (i.e. particles that have come originally from just one particle and still in some mysterious way represent one system) are in 'touch' with one another, no matter how far apart, even on opposite sides of the universe. So that if a measurement is made on one 'twin' the other twin is instantaneously aware of the measurement made on the other and, depending on what exactly is measured on the first twin, 'becomes' measured itself but in a complimentary way. What do I mean by that? Well in basic terms if you, say, measure a property of one of a pair of entangled particles, for instance, its 'spin', then whatever direction that spin is measured to be in, you know without having to look that its 'twin', millions or even billions of miles away, will automatically be measured at the same instance but its spin will be in the opposite direction. This is because the two particles are still acting as one system and, therefore, the two spins have to cancel one another out to maintain a balance or symmetry.

 

Bell's Theorem proved that, mathematically, the statistical probabilities of local variables behaving in the same way as entangled particles spatially separated by large distances was violated in the sense that if you measure a local variable and another local variable they did not conform to the same statistical pattern of entangled particles, thus something else is going on at a distance and discounts local reality.

 

Of course, you have to remember that until an actual measurement is made on one of the entangled particles they are both in a superposition of states, in other words, they both are in all possible spin states at the same time until one is measured, thereupon only one state become 'real.'

 

This is not the transfer of information in the normal sense because you can never predict exactly what you are going to find before measurement as it's all down to probabilities, not certainties, so you could not send Morse code using quantum entanglement, for example.

[IM Egdall]

Bell's Theorem shows that entangled particles (i.e. particles that have come originally from just one particle and still in some mysterious way represent one system) are in 'touch' with one another, no matter how far apart, even on opposite sides of the universe. So that if a measurement is made on one 'twin' the other twin is instantaneously aware of the measurement made on the other and, depending on what exactly is measured on the first twin, 'becomes' measured itself but in a complimentary way. What do I mean by that? Well in basic terms if you, say, measure a property of one of a pair of entangled particles, for instance, its 'spin', then whatever direction that spin is measured to be in, you know without having to look that its 'twin', millions or even billions of miles away, will automatically be measured at the same instance but its spin will be in the opposite direction. This is because the two particles are still acting as one system and, therefore, the two spins have to cancel one another out to maintain a balance or symmetry.

 

Bell's Theorem proved that, mathematically, the statistical probabilities of local variables behaving in the same way as entangled particles spatially separated by large distances was violated in the sense that if you measure a local variable and another local variable they did not conform to the same statistical pattern of entangled particles, thus something else is going on at a distance and discounts local reality.

 

Of course, you have to remember that until an actual measurement is made on one of the entangled particles they are both in a superposition of states, in other words, they both are in all possible spin states at the same time until one is measured, thereupon only one state become 'real.'

 

This is not the transfer of information in the normal sense because you can never predict exactly what you are going to find before measurement as it's all down to probabilities, not certainties, so you could not send Morse code using quantum entanglement, for example.

 

Thanks for the detailed write-up. But I still have a question. Maybe I need to ask it more clearly. Doesn't hidden variables mean that a particle is in a definite state before it is measured?

 

I know this goes against standard QM which say that the particle is in a superposition of states before measurement. And I know that Bell's theorum testing shows that the universe is nonlocal. I get that. But what does it say or not say about nonlocal hidden variables? In other words, based on Bell testing, do particles have a definite state or not prior to measurement?

 

I hope I have made my question more clear.

[webplodder]

 

I know this goes against standard QM which say that the particle is in a superposition of states before measurement. And I know that Bell's theorum testing shows that the universe is nonlocal. I get that. But what does it say or not say about nonlocal hidden variables? In other words, based on Bell testing, do particles have a definite state or not prior to measurement?

 

I hope I have made my question more clear.

 

 

No they don't. The hidden variables idea suggests that underlying the strange effects of quantum entanglement are a set of hidden variables which might 'explain' 'spooky action at a distance' and that essentially preserve the idea of locality. It's kind of like saying that both entangled particles have some kind of pre-programmed variables within them (local) and that it can be predicted in principle what is going to happen beforehand. But I noticed you said 'non-local hidden variables rather than local ones, so is this what you meant by that? The idea of hidden variables, whether local or non-local been tested many times and found to be false. The fact is, quantum mechanics is just strange and although people have tried to find rational mechanisms with which to explain it goes against all our intuitions. One can only assume there must be some deeper level of reality other than spacetime that operates as part of the overall fabric of the universe. Some people have suggested that because quantum objects have no definite properties until measured it is somehow consciousness than is involved in the 'concrete' universe by 'measuring' it. Not sure about that.

 

In a way, we should not be too surprised about strange phenomena such as we have been discussing because it is probably the case that we only see our little bit of reality which might be but a small sub-set of a much larger one. The multiverse is today a legitimate idea among cosmologists, so here we are in our one universe of universes and think we know it all. We don't!

Edited February 22, 2011 by webplodder