The concept of hidden variables in quantum mechanics refers to hypothetical underlying properties that, if known, would fully determine the outcomes of quantum measurements. In other words, hidden variables would provide a complete description of a quantum system, allowing us to predict the results of measurements with certainty.
The existence of hidden variables was initially proposed as a possible explanation to resolve the apparent randomness and indeterminism of quantum mechanics. However, in the 1960s, physicist John Bell formulated a set of mathematical inequalities, known as Bell's inequalities, that could be tested experimentally to investigate whether hidden variables could account for the predictions of quantum mechanics.
In subsequent experiments, Bell's inequalities have been tested, and the results consistently violate the bounds set by these inequalities. This experimental evidence strongly suggests that hidden variables are ruled out in quantum mechanics. The violation of Bell's inequalities implies that the correlations between entangled particles cannot be explained by pre-existing, predetermined values of the measured properties.
The phenomenon of entanglement, where particles can be instantaneously correlated regardless of the distance between them, is a key aspect of quantum mechanics. It has been extensively tested and verified experimentally. The measurements on entangled particles are inconsistent with the idea that the particles possess predetermined values for their properties that we simply discover when we make the measurement. Instead, the outcomes of measurements are inherently probabilistic and governed by the fundamental principles of quantum mechanics.
Quantum mechanics introduces a fundamentally different understanding of reality compared to classical mechanics. It incorporates inherent uncertainty, wave-particle duality, superposition, and entanglement, which do not have classical analogs. While hidden variables were proposed as a potential explanation for the behavior of quantum systems, experimental evidence and theoretical arguments support the view that quantum mechanics does not allow for the existence of such hidden variables.