@article{Spałek_2020, title={The Bose-Einstein statistics: Remarks on Debye, Natanson, and Ehrenfest contributions and the emergence of indistinguishability principle for quantum particles}, volume={19}, url={https://ojs.ejournals.eu/SHS/article/view/7357}, DOI={10.4467/2543702XSHS.20.013.12569}, abstractNote={<p>The principal <em>mathematical</em> idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/<a href="https://www.mdpi.com/1099-4300/17/4/1971/pdf">2015</a>) and used by M. Planck (<a href="https://pl.booksc.xyz/dl/52730877/8bd1c3">1900</a>; <a href="https://ia802609.us.archive.org/28/items/vorlesungenberd04plangoog/vorlesungenberd04plangoog.pdf">1906</a>) to derive the frequency distribution of radiation (<em>Planck’s law</em>) when its discrete (quantum) structure was additionally added to the reasoning.</p> <p>The fundamental <em>physical</em> idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly.</p> <p>Here the role of P. Debye (<a href="https://booksc.xyz/dl/375637/2369bd">1910</a>), H. Kamerlingh Onnes and P. Ehrenfest (<a href="http://www.dwc.knaw.nl/DL/publications/PU00012735.pdf">1914</a>) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; <a href="http://matwbn.icm.edu.pl/ksiazki/pmf/pmf24/pmf2411.pdf">1913</a>) is emphasized.</p> <p>The reintroduction of this Natanson’s statistics by S. N. Bose (1924/<a href="https://books.google.pl/books?id=L01pDQAAQBAJ&pg=PA26">2009</a>) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/<a href="https://b-ok.cc/dl/454524/2eb884">1981</a>), which in a way obscures the <em>indistinguishability</em> of the particles involved.</p> <p>It was ingeniously reintroduced by P. A. M. Dirac (<a href="https://www.jstor.org/stable/94692">1926</a>) via postulating (imposing) the transposition symmetry onto the many-particle wave function.</p> <p>The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles.</p> <p>The last remark may serve as a form of the author’s <em>post scriptum</em> to the indistinguishability principle.</p>}, journal={Studia Historiae Scientiarum}, author={Spałek, Józef}, year={2020}, month={Sep.}, pages={423–441} }