Abstract
It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrödinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrödinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.
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Acknowledgements
This is a belated, second response to John Bell's critique8 of my 1966 treatment of the statistical interpretation6. In my first and rather unsatisfactory response9, written after Bell's death but in the light of conversations with him, I interpreted his position as being based, at least in part, on the theme expressed in the opening paragraphs of this paper. I am indebted to David Mermin for advice and for posing pointed questions. This work is supported in part by the National Science Foundation.
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Gottfried, K. Inferring the statistical interpretation of quantum mechanics from the classical limit. Nature 405, 533–536 (2000). https://doi.org/10.1038/35014500
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DOI: https://doi.org/10.1038/35014500
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