2017/04/03 by Joy Christian, Christian, Joy
Physics and Astronomy · Arts and Humanities · Computer Science · #Quantum Mechanics and Applications #Philosophy and History of Science #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.1704.02876
We show that the respective oversights in the von Neumann's general theorem\nagainst all hidden variable theories and Bell's theorem against their\nlocal-realistic counterparts are homologous. Both theorems unjustifiably assume\nthe additivity of expectation values within hidden variable theories to derive\ntheir respective conclusions. However, for non-commuting observables, the\nequivalence of a sum of expectation values and the expectation value of the sum\nof measurement results, although respected within quantum mechanics, need not\nhold for hidden variable theories, regardless of specific characteristics such\nas local realism they may respect. Once this oversight is ameliorated from\nBell's argument and local realism is implemented correctly, the bounds on the\nCHSH correlator work out to be \±2\√(2) instead of \±2, thereby\nmitigating the conclusion of Bell's theorem. Consequently, what is ruled out by\nthe Bell-test experiments is not local realism but the additivity of\nexpectation values.\n