Bell's theorem is a fundamental result in quantum physics that addresses the concept of locality and the nature of quantum mechanical systems. It shows that if certain predictions of quantum mechanics are correct, then no local hidden variable theory can reproduce all the predictions of quantum mechanics.
In simpler terms, Bell's theorem suggests that the predictions of quantum mechanics cannot be explained by assuming the existence of hidden variables—unknown quantities that would determine the outcome of measurements and make the theory local. This means that quantum mechanics, as described by the standard interpretation, is non-local in the sense that the outcomes of measurements on entangled particles appear to be instantaneously correlated regardless of the distance between them.
However, it's important to note that non-locality in the context of Bell's theorem does not imply faster-than-light communication or violate causality. The correlations observed in entangled systems are non-local in the sense that they cannot be explained by classical concepts of locality, but they do not allow for the transmission of information.
Regarding quantum randomness, Bell's theorem does not directly address the issue of randomness in quantum mechanics. Quantum randomness is a fundamental aspect of the theory, as it asserts that certain measurements can only be predicted probabilistically. This randomness is not a result of our lack of knowledge but is inherent to the nature of quantum systems. Bell's theorem, in conjunction with experimental results, supports the idea that these quantum probabilities are not simply due to our ignorance of underlying deterministic processes but are truly random.
In summary, Bell's theorem demonstrates that quantum mechanics is non-local, meaning that the correlations observed in entangled systems cannot be explained by local hidden variables. However, it does not provide a direct explanation for the randomness inherent in quantum mechanics, which is an inherent aspect of the theory itself.