The opposite of hidden variable: No hidden variable

The opposite of hidden variable is no hidden variable. It is not non-locality. From the literature, the experiments reject the existence of hidden variable. But the experiments don’t confirm non-locality. There are no direct experimental evidence confirming non-locality with individual pairs of entangled photons or electrons. All results are statistical averages that may be subject to different interpretations.

I asked ChatGPT. It said non-locality as a possible explanation. “the rejection of hidden variables is one piece of evidence that has led to the consideration of non-locality as a possible explanation for certain quantum phenomena.” But the public statements, supported by a Nobel Prize, seem to make non-locality, or entanglement, a settled issue. Please tell me if my understanding is wrong.

I have read 1969 CHSH paper. I don’t understand the mathematical derivations. I couldn’t even understand the first equalities in Page 881.

The following are the question to and answer by ChatGPT.

Question: The opposite of hidden variable is no hidden variable. It is not non-locality. Why rejecting hidden variable becomes confirmation of non-locality in quantum mechanics?

Answer: The relationship between hidden variables and non-locality in quantum mechanics is a complex and debated topic. Let's break it down step by step:

1. **Hidden Variables**: Hidden variables are hypothetical, unobservable properties that, if they existed, would determine the outcomes of quantum measurements. In other words, they would provide a complete description of a quantum system, allowing us to predict its behavior with certainty.

2. **Bell's Theorem**: In the 1960s, physicist John Bell formulated a theorem known as Bell's Theorem, which showed that certain predictions of quantum mechanics cannot be explained by any theory based solely on local hidden variables. In other words, if hidden variables exist, they would have to exhibit non-local behavior to explain the results of certain quantum experiments.

3. **Experimental Violation of Bell Inequalities**: Subsequent experiments, such as those performed by Alain Aspect, tested Bell's inequalities and found that they were violated. This experimental violation suggests that the behavior of entangled quantum particles cannot be explained by any theory based on local hidden variables.

4. **Entanglement and Non-Locality**: Quantum entanglement is a phenomenon where two or more particles become correlated in such a way that the measurement of one particle instantaneously affects the state of another, even if they are separated by large distances. This apparent non-local connection between entangled particles is one of the key reasons why the rejection of local hidden variables is often associated with the concept of non-locality in quantum mechanics.

So, to clarify, it's not that the rejection of hidden variables by itself confirms non-locality in quantum mechanics. Instead, it's the combination of Bell's theorem, experimental violations of Bell inequalities, and the phenomenon of quantum entanglement that suggests a non-local aspect to quantum physics when local hidden variables are ruled out as an explanation. In other words, the rejection of hidden variables is one piece of evidence that has led to the consideration of non-locality as a possible explanation for certain quantum phenomena.