Hidden variables & partial correlations

[gabeeisenstei]

I recently understood Bell’s theorem (the inequality and the QM calculation), with the help of you guys. But something still bothers me: assuming for the moment that Bell’s inequalities were NOT violated by experiment, how we would we understand the dependence of the varying correlations on the angular separation between axes of measurement? How would the hidden variables produce non-correlation at 90 degrees and 50% correlation at 45 degrees?

In the QM framework, we just say that the operators for orthogonal measurements don’t commute, and we accept the cosine formula. But what do we say about the hidden variable model? Doesn’t the noncorrelation at 90 degrees already demand something like the “noncommuting operators” explanation?

 

[eljose79]

First of all, congratulations on understanding Bell's theorem and the QM calculation! It can be a complex and challenging concept, so it's great that you were able to grasp it with the help of others.

To address your question, if Bell's inequalities were not violated by experiment, then we would have to consider alternative explanations for the varying correlations at different angular separations. One possibility is that there are hidden variables at play, as you mentioned. These hidden variables could potentially explain the non-correlation at 90 degrees and the 50% correlation at 45 degrees.

However, it's important to note that there is no agreed-upon hidden variable theory that can fully account for all the results and predictions of quantum mechanics. In fact, Bell's theorem was specifically designed to rule out certain types of hidden variable theories. So while the noncorrelation at 90 degrees may suggest the need for something like the "noncommuting operators" explanation, it's not as simple as that. The noncommuting operators in quantum mechanics are a fundamental aspect of the theory, while in hidden variable theories they are a result of underlying, unknown mechanisms.

In the end, the varying correlations at different angles of measurement are still not fully understood, and this is one of the reasons why Bell's theorem and the experiments that violate it are so significant. They show that there is something fundamentally different about the way the world works at the quantum level, and it cannot be explained by classical physics or hidden variables alone. Ultimately, further research and experimentation will continue to shed light on this fascinating and complex topic.