Article ID: CBB981997087

The Bose-Einstein statistics: Remarks on Debye, Natanson, and Ehrenfest contributions and the emergence of indistinguishability principle for quantum particles (2020)

unapi

The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning. The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly. Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized. The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) 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 (1902/1981), which in a way obscures the indistinguishability of the particles involved. It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function. 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. The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB981997087/

Similar Citations

Article Arias Vila, Nelson; Baracca, Angelo; (2006)
¿Quién propuso la fórmula de Rayleigh-Jean? (/isis/citation/CBB000930261/)

Article Duncan, Anthony; Janssen, Michel; (2008)
Pascual Jordan's Resolution of the Conundrum of the Wave-Particle Duality of Light (/isis/citation/CBB000933674/)

Article Enric Pérez Canals; Gonzalo Gimeno; Mercedes Xipell Gómez del Moral; Marià Baig i Aleu; (2020)
La mecánica ondulatoria llega a España: Schrödinger en la Universidad Internacional de Santander, agosto de 1934 (/isis/citation/CBB717742451/)

Article Kojima, Chieko; (2008)
Marcel Brillouin's Wave Concept and Its Influence on Louis de Broglie (/isis/citation/CBB000930012/)

Article Pérez, Enric; Sauer, Tilman; (2010)
Einstein's Quantum Theory of the Monatomic Ideal Gas: Non-Statistical Arguments for a New Statistics (/isis/citation/CBB001022007/)

Article Enric Pérez; Blai Pié i Valls; (2016)
Bohr and Ehrenfest: Transformations and Correspondences in the Early 1920s (/isis/citation/CBB429800364/)

Article Lunteren, Fran H. van; Hollestelle, Marijn J.; (2013)
Paul Ehrenfest and the Dilemmas of Modernity (/isis/citation/CBB001321213/)

Article Schirrmacher, Arne; (2003)
Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics (/isis/citation/CBB000641699/)

Article Pérez, Enric; (2009)
Ehrenfest's Adiabatic Theory and the Old Quantum Theory, 1916--1918 (/isis/citation/CBB000932074/)

Article Duncan, Anthony; Janssen, Michel; (2007)
On the Verge of Umdeutung in Minnesota: Van Vleck and the Correspondence Principle. Part One. (/isis/citation/CBB000773023/)

Article Brush, Stephen G.; (2007)
How Ideas Became Knowledge: The Light-Quantum Hypothesis, 1905--1935 (/isis/citation/CBB000700576/)

Article Montgomery, H. E., Jr.; Pupyshev, V. I.; (2013)
On Lower Bounds for Polarisability (/isis/citation/CBB001320786/)

Article Bustamante, Martha Cecilia; (2002)
Rayonnement et quanta en France: 1900--1914 (/isis/citation/CBB000502757/)

Article Boughn, Stephen; Reginatto, Marcel; (2013)
A Pedestrian Approach to the Measurement Problem in Quantum Mechanics (/isis/citation/CBB001320783/)

Article Monaldi, Daniela; (2009)
A Note on the Prehistory of Indistinguishable Particles (/isis/citation/CBB000933687/)

Article Guzmán Diaz, Ricardo; Cervera Jiménez, José Antonio; (2006)
Origen, ascenso y muerte de la hipótesis del éter y el ojo crítico de Paul Ehrenfest (/isis/citation/CBB000930264/)

Authors & Contributors
Pérez, Enric
Janssen, Michel
Duncan, Anthony
Nagasawa, Nobukata
Moral, Mercedes Xipell Gómez del
Blai Pié i Valls
Concepts
Quantum mechanics
Physics
Electromagnetic waves; radiation
Statistics
Waves
Scientific priority
Time Periods
20th century, early
21st century
20th century, late
Places
Spain
France
Institutions
Universität Göttingen
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment