The local hidden variable theory is an interpretation of quantum mechanics that suggests the existence of additional, unknown variables ("hidden variables") that determine the outcomes of measurements and events in a way that is consistent with both the principles of quantum mechanics and locality.
In the context of quantum mechanics, locality refers to the idea that distant events should not have instantaneous influences on each other. It implies that any influence or information transfer between two spatially separated objects should occur at or below the speed of light.
The local hidden variable theory posits that the observed probabilistic nature of quantum mechanics arises due to our ignorance of these hidden variables. According to this theory, the properties of particles are predetermined by these hidden variables, and the apparent randomness and non-determinism of quantum mechanics is merely a result of our lack of knowledge about these hidden variables.
The concept of local hidden variables was famously challenged by the work of physicist John Bell in the 1960s. Bell's theorem and subsequent experiments, such as the Bell test experiments, have shown that certain predictions of quantum mechanics are incompatible with any local hidden variable theory that satisfies a set of reasonable assumptions.
Bell's theorem suggests that the correlations observed in certain entangled quantum systems cannot be explained by any local hidden variables theory. These experiments have provided strong evidence in support of the non-local nature of quantum entanglement and have ruled out the possibility of a certain class of local hidden variable theories.
However, it is important to note that there are alternative interpretations of quantum mechanics that do not rely on local hidden variables, such as the Copenhagen interpretation, the many-worlds interpretation, and the pilot-wave theory (also known as the de Broglie-Bohm interpretation). These interpretations provide different perspectives on the fundamental nature of quantum mechanics and the role of hidden variables, but they do not invoke local hidden variables to explain the probabilistic nature of quantum phenomena.