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

Click For Summary
SUMMARY

The discussion centers on the inconsistency of local no-hidden-variable theories with standard quantum mechanics (QM). It highlights that when measuring entangled particles, local theories predict a 50% anti-correlation, while standard QM predicts a 100% anti-correlation. Participants argue that local no-hidden-variable theories fail to explain the observed correlations in experiments, similar to local hidden variable theories, which have been disproven by Bell's theorem. The conversation emphasizes the need to explore interpretations of QM that do not rely on hidden variables yet still account for the observed phenomena.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly entanglement and measurement.
  • Familiarity with Bell's theorem and its implications for hidden variable theories.
  • Knowledge of different interpretations of quantum mechanics, such as Many Worlds and contextual interpretations.
  • Basic grasp of probability theory and its application in quantum contexts.
NEXT STEPS
  • Research the implications of Bell's theorem on local hidden variable theories.
  • Explore various interpretations of quantum mechanics that do not involve hidden variables.
  • Study the Many Worlds Interpretation and its stance on locality and realism.
  • Investigate contextual interpretations of quantum mechanics and their explanations for measurement outcomes.
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in the foundations of quantum theory and the implications of locality and hidden variables in quantum experiments.

OldBeginnings
Messages
3
Reaction score
0
TL;DR
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?
 
Physics news on Phys.org
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.
 
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.
 
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?
 
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.
 
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.
 
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.
 
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.
 

Similar threads

High School Quantum entanglement and hidden variables
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Looking For Help Understanding Bell's Theorem, Hidden Variables & QM
  • · Replies 80 ·
3
Replies
80
Views
8K
High School Entanglement - lack of "symmetry" in no-hidden variables explanation
  • · Replies 44 ·
2
Replies
44
Views
5K
Graduate No hidden variables in QM - a paradigm shift?
  • · Replies 5 ·
Replies
5
Views
1K
High School Is there another workable interpretation of the Bell Inequality?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Concrete contrast between local and nonlocal hidden variable
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad Could Hidden Variables Explain Quantum Mechanics without Locality?
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Hidden variables and Bell's inequality
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Local hidden variable theories
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Is the fork in the Einstein Podolsky Rosen argument correct?
  • · Replies 45 ·
2
Replies
45
Views
2K