Derivation of Bose-Einstein statistics from the uncertainty principle

• URL: http://arxiv.org/abs/2308.02069v3
• Date: Mon, 9 Sep 2024 08:41:25 GMT
• Title: Derivation of Bose-Einstein statistics from the uncertainty principle
• Authors: Paul Tangney,
• Abstract summary: The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. I prove that if the same lower bound applied to every degree of freedom of a sufficiently cold classical dynamical system, the distribution of the system's energy among its degrees of freedom would be a Bose-Einstein distribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. Since infinitely precise measurements are impossible, a measurement can, at best, constrain the location of this point to a region of phase space whose area is finite. This paper explores the implications of assuming that this finite area is bounded from below. I prove that if the same lower bound applied to every degree of freedom of a sufficiently cold classical dynamical system, the distribution of the system's energy among its degrees of freedom would be a Bose-Einstein distribution.

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