Bell's theorem proves nonlocality in quantum mechanics from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
Bell's theorem is a significant result in the realm of quantum mechanics, shedding light on the concept of nonlocality. It addresses the issue of correlations between distant particles, challenging the classical notions of locality and realism. The theorem demonstrates that certain predictions of quantum mechanics cannot be explained by theories based on local hidden variables.
In the context of Bell's theorem, local hidden variables refer to hypothetical properties that determine the outcomes of measurements on quantum systems. These variables are assumed to exist independently of the measurements themselves, allowing for a deterministic explanation of the observed correlations. However, Bell's theorem shows that such explanations are incompatible with the predictions of quantum mechanics.
The theorem is based on the concept of Bell inequalities, which are mathematical expressions that place constraints on the correlations between measurements on entangled particles. Violations of these inequalities indicate the presence of nonlocal correlations that cannot be accounted for by local hidden variables. Experimental tests of Bell's inequalities have consistently shown violations, providing strong evidence for the nonlocal nature of quantum mechanics.
By ruling out the possibility of local hidden variables as a complete explanation for quantum phenomena, Bell's theorem highlights the inherent nonlocality of the quantum world. This concept has profound implications for our understanding of the nature of reality and the fundamental principles that govern the behavior of particles at the quantum level. Bell's theorem stands as a cornerstone of quantum mechanics, challenging our intuition and pushing the boundaries of our comprehension of the physical world.
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