The Bell inequality is a fundamental concept in quantum mechanics that tests the limits of classical correlations in entangled systems. It was formulated by physicist John Bell in the 1960s and has since been experimentally verified, confirming the predictions of quantum mechanics.
To understand the Bell inequality, let's first define the terms "entangled states" and "separable states." In quantum mechanics, particles can become entangled, which means their properties are interdependent in a way that cannot be described by classical physics. Separable states, on the other hand, refer to a situation where the properties of individual particles can be described independently of each other.
The Bell inequality provides a way to test whether a given system exhibits correlations that are consistent with classical physics or if they violate the constraints of classical theories. It involves measuring correlations between the properties of entangled particles in different directions or settings.
Bell's inequality is typically derived based on the assumption of local realism. Local realism suggests that physical properties are pre-existing and independent of measurements, and that distant measurements cannot instantly influence each other. However, quantum mechanics predicts correlations that violate the inequality derived from these assumptions.
The violation of the Bell inequality implies that entangled particles cannot be described by local realistic theories. Instead, their behavior is fundamentally different from classical systems. This violation has been experimentally observed in various experiments, confirming the predictions of quantum mechanics.
In summary, the Bell inequality holds for entangled states but not for separable states because entangled states exhibit correlations that violate the constraints of classical physics and local realism. This violation is a fundamental aspect of quantum mechanics and has been experimentally confirmed.