A simple derivation of Born's rule with and without Gleason's theorem

Alexia Auffèves; Philippe Grangier

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arXiv · 1505.01369

A simple derivation of Born's rule with and without Gleason's theorem

Alexia Auffèves·Philippe Grangier

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Abstract

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual quantum formalism, within a new conceptual framework that is discussed heuristically in details. The structure of Quantum Mechanics, from its probabilistic nature to its mathematical expression, appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities.

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Alexia Auffèves, Philippe Grangier. 2015-05-06. A simple derivation of Born's rule with and without Gleason's theorem. https://arxiv.org/abs/1505.01369

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