The concept of hidden variables in quantum mechanics refers to the idea that the behavior of quantum systems is determined by unknown or unobserved variables that exist alongside the wave function. These hidden variables would supposedly provide a complete and deterministic description of the system, similar to classical mechanics.
However, the notion of hidden variables was addressed by a famous result known as Bell's theorem, which demonstrated that certain predictions of quantum mechanics are incompatible with any theory based on local hidden variables. Local hidden variables are the idea that the properties of a particle are determined by variables that exist independently of any measurements and that these variables cannot be influenced instantaneously over long distances.
Bell's theorem, formulated by physicist John Bell in 1964 and subsequently tested experimentally, shows that quantum mechanics can produce correlations between entangled particles that cannot be explained by any theory based on local hidden variables. These correlations have been confirmed in numerous experiments and are inconsistent with the idea that the particles possessed preexisting well-defined properties before measurement.
In quantum mechanics, when two particles become entangled, their states become intertwined in such a way that they cannot be described independently of each other. The properties of the entangled system are only determined when measurements are made on the individual particles, and the correlations between them are observed. This behavior, known as quantum entanglement, has been experimentally verified and is a fundamental aspect of quantum mechanics.
The violation of Bell's inequalities by entangled particles implies that there is no underlying reality of preexisting properties that is simply revealed upon measurement. The behavior of quantum systems is inherently probabilistic, and the outcomes of measurements are fundamentally uncertain until the moment of measurement itself. This probabilistic nature is a distinctive feature of quantum mechanics that sets it apart from classical mechanics and rules out the possibility of hidden variables providing a complete deterministic description of quantum phenomena.
While alternative interpretations of quantum mechanics have been proposed that reintroduce hidden variables, they generally involve abandoning either locality or realism (the idea that physical properties exist independently of observation) or both. These interpretations remain highly debated and have not gained wide acceptance within the scientific community, as they often face challenges in explaining and reproducing the full range of observed quantum phenomena.