Bell's inequality is a mathematical expression that relates to the correlations between the measurements of physical properties in certain quantum systems. It provides a criterion to test whether these correlations can be explained by local hidden variables, which would imply a classical explanation of quantum phenomena.
The Einstein-Podolsky-Rosen (EPR) paradox is a thought experiment proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935. It highlights a perceived inconsistency in the completeness of quantum mechanics, particularly with respect to the principle of locality and the concept of entanglement.
Entanglement refers to a quantum phenomenon where two or more particles become interconnected in such a way that their states become correlated, even if they are spatially separated. According to quantum mechanics, measuring one entangled particle can instantaneously affect the state of the other, regardless of the distance between them.
Bell's inequality and the EPR paradox are connected in the following way:
EPR Paradox: The EPR paradox challenges the completeness of quantum mechanics by suggesting the existence of hidden variables that determine the outcomes of measurements on entangled particles. These hidden variables would provide a classical explanation for the correlations observed in entangled systems.
Bell's Inequality: In 1964, physicist John Bell derived an inequality known as Bell's inequality that serves as a test to determine whether the correlations observed in entangled systems can be explained by local hidden variables or require a non-local explanation.
Bell's inequality is a mathematical inequality that imposes constraints on the correlations between measurements of certain properties in entangled systems. Violation of Bell's inequality implies that the correlations observed cannot be explained by local hidden variables and necessitates a non-local, quantum mechanical explanation.
Experimental tests based on Bell's inequality, such as Bell tests, have been conducted, and the results consistently show violations of the inequality. These violations support the predictions of quantum mechanics and provide evidence for the non-local nature of entanglement.
In summary, Bell's inequality is a mathematical criterion that tests the local hidden variable explanation of correlations in entangled systems. Its violation, as confirmed by experimental results, supports the existence of entanglement and challenges the classical notion of local realism proposed by the EPR paradox.