Derivation of Bose-Einstein statistics from the uncertainty principle
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909829290786816 |
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| author | Tangney, Paul |
| author_facet | Tangney, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Derivation of Bose-Einstein statistics from the uncertainty principle Tangney, Paul Statistical Mechanics Quantum Physics 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. |
| title | Derivation of Bose-Einstein statistics from the uncertainty principle |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2308.02069 |