Isn't the local no-hidden-variable theory inconsistent with standard QM?

  • #1

Summary:

When the entangled particles are measured (for their spin) in the same direction by two different spatially separated detectors, won't the predictions of a local theory without hidden variables contradict standard QM?
Consider a pair of entangled particles described by a local theory without hidden variables. Because there are no hidden variables, the results of an experiment on one particle of the entangled pair must be perfectly random. Due to locality, the particles also have no way of coordinating the results of the experiment.

When the entangled particles are measured (for their spin) in the same direction by two different spatially separated detectors, won't the predictions of a local theory without hidden variables contradict standard QM? If one of the particles is measured up, there's no reason for the other particle to be measured down if there are no hidden variables, if there is no way for the two particles to communicate and if the results of each experiment is perfectly random.

Prediction of local theory without hidden variables: the measurement results of the two particles are independent and are anti-correlated 50% of the time.

Prediction of standard quantum mechanics: the measurement results of the two particles are perfectly anti-correlated 100% of the time.

So, my question is: Aren't local theories without hidden variables inconsistent with experimental results? Aren't local no-hidden-variable theories just as false as local hidden variable theories (as proven by Bell)? Why do people stay away from hidden variable theories if no-hidden-variable theories are also just as bad at predicting QM? If local no-hidden-variable theories and local hidden variable theories are both wrong, doesn't the issue then lie with locality? Why does everyone keep saying that local hidden variables have been disproved, but no one seems to assert that local no-hidden-variable theories are also wrong? Is there something wrong with my analysis?
 

Answers and Replies

  • #2
DarMM
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Summary: When the entangled particles are measured (for their spin) in the same direction by two different spatially separated detectors, won't the predictions of a local theory without hidden variables contradict standard QM?

Due to locality, the particles also have no way of coordinating the results of the experiment
Quantum Theory is a generalization of probability theory mathematically. The lack of hidden variables does not imply everything must be uncorrelated.
 
  • #3
The lack of hidden variables does not imply everything must be uncorrelated.
If there are no hidden variables and if there are no communications between the particles, how can the random outcomes of the two measurement devices be perfectly correlated? Like I said, I agree that there could be some correlation (1/2 * 1/2 + 1/2 * 1/2 = 50% anti-correlation). However, there's no way that we could have 100% correlation with standard probability theory.
 
  • #4
DarMM
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If there are no hidden variables and if there are no communications between the particles, how can the random outcomes of the two measurement devices be perfectly correlated? Like I said, I agree that there could be some correlation (1/2 * 1/2 + 1/2 * 1/2 = 50% anti-correlation). However, there's no way that we could have 100% correlation with standard probability theory.
What's "standard probability theory" and why does it imply no correlation?
 
  • #5
What's "standard probability theory" and why does it imply no correlation?
It doesn't imply no correlation. It implies 50% correlation. If particle 1 outcome was up, the probability that particle 2 outcome is down is 1/2. Thus the probability that particle 1 is up and particle 2 is down is 1/2 * 1/2 = 1/4. Accounting the case for when particle 1 is down, the total probability that they both have opposite spins is 1/4 + 1/4 = 0.5, which is obviously different from 1, which is what is predicted by QM.
 
  • #6
DrChinese
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Consider a pair of entangled particles described by a local theory without hidden variables. Because there are no hidden variables, the results of an experiment on one particle of the entangled pair must be perfectly random. Due to locality, the particles also have no way of coordinating the results of the experiment.

When the entangled particles are measured (for their spin) in the same direction by two different spatially separated detectors, won't the predictions of a local theory without hidden variables contradict standard QM? If one of the particles is measured up, there's no reason for the other particle to be measured down if there are no hidden variables, if there is no way for the two particles to communicate and if the results of each experiment is perfectly random.

Prediction of local theory without hidden variables: the measurement results of the two particles are independent and are anti-correlated 50% of the time.

Prediction of standard quantum mechanics: the measurement results of the two particles are perfectly anti-correlated 100% of the time.

So, my question is: Aren't local theories without hidden variables inconsistent with experimental results? Aren't local no-hidden-variable theories just as false as local hidden variable theories (as proven by Bell)?
You are basically assuming that hidden variables are needed to explain QM's predictions. They aren't. There are a number of interpretations of QM that are local but lack hidden variables. Look those up (quantum interpretations). Orthodox QM itself is silent on the issue.
 
  • #7
atyy
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Why does everyone keep saying that local hidden variables have been disproved, but no one seems to assert that local no-hidden-variable theories are also wrong? Is there something wrong with my analysis?
There isn't such a thing as a no hidden variable theory that explains the correlations. QM itself does have hidden variables if the wave function is taken to be real. If the wave function is not interpreted as being real, then the quantum mechanics predicts the correlations, but does not explain it, and the question of being local or non-local does not arise.
 
  • #8
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You can have a no hidden variable (or even hidden variable)interpretation that denies realism, for instance. Contextual interpretations....if one takes measurement results to be subjective. Also, Many Worlds Interpretation is local.
 

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