A simple proof of Born’s rule for statistical interpretation of quantum mechanics

Journal for Foundations and Applications of Physics 4 (1):24-30 (2017)
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Abstract

The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers have carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function.

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References found in this work

Quantum Theory of Probability and Decisions.David Deutsch - 1999 - Proceedings of the Royal Society of London:3129--37.
Measurement outcomes and probability in Everettian quantum mechanics.David Baker - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):153-169.
Quantum probability and many worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.