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

In summary: Consider a pair of 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
  • #1
OldBeginnings
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TL;DR 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?
 
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  • #2
OldBeginnings said:
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
DarMM said:
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
OldBeginnings said:
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
DarMM said:
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
OldBeginnings said:
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
OldBeginnings said:
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
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.
 

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

1. What is a local no-hidden-variable theory?

A local no-hidden-variable theory is a type of theory in quantum mechanics that proposes the existence of hidden variables to explain the probabilistic nature of quantum mechanics. It states that there are hidden variables that determine the outcome of measurements in a deterministic way, rather than relying on probabilities.

2. How is a local no-hidden-variable theory inconsistent with standard QM?

A local no-hidden-variable theory is inconsistent with standard quantum mechanics because it violates the principle of non-locality. In standard QM, particles can be entangled and exhibit instantaneous correlations, even when they are separated by large distances. This is not possible in a local no-hidden-variable theory, which assumes that particles have predetermined properties that determine their behavior.

3. Can a local no-hidden-variable theory be tested?

Yes, a local no-hidden-variable theory can be tested through experiments that measure the correlations between entangled particles. If the results of these experiments violate the predictions of a local no-hidden-variable theory, then it can be considered inconsistent with standard QM.

4. Are there any alternative theories to a local no-hidden-variable theory?

Yes, there are several alternative theories to a local no-hidden-variable theory, such as the pilot-wave theory and the many-worlds interpretation. These theories attempt to explain the probabilistic nature of quantum mechanics without relying on hidden variables.

5. Why is the debate between local no-hidden-variable theories and standard QM important?

The debate between local no-hidden-variable theories and standard QM is important because it challenges our understanding of the fundamental principles of quantum mechanics. It also has implications for how we interpret the nature of reality and the role of determinism in the universe.

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