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14. History of Physics [Prof. Pisano, France/Australia]

Start Date:
5. June 2017, 14:45
Finish date:
5. June 2017, 15:45
LILLIAD, Lille University



On the Black Body Radiation & the Birth of Quantum Mechanics. An Interplay between Physics and Mathematics



In the end of 19th century, foundational problems produced a scientific incertitude climate within physics and mathematics disciplines both for inquiring mathematical–geometrical description interpretation and for the inquiring physical phenomena themselves. For example among them, the development of Lagrangian mechanics (included vincula) with respect to Newtonian (deterministic) one, the classical thermodynamics, the new analytical and statistical theories, the electromagnetism and the birth of Non–Euclidean geometries, etc. Thus the space in physics could be not Euclidean, too. The Black Body and its Radiation is an idealized physical object that absorbs the incident electromagnetic radiation and in all frequencies. Crucial problems crossed the composite story (1859–1907) of black body radiation. Which are the magnitudes for interpreting this phenomenon? If one consider a cavity-body at temperature T (> T–environment, frequencies/temperatures) its cavity-wallets emits both extern and interne, so cavity-body become full electromagnetic radiation (until thermal equilibrium). What kind of mathematical-physical universal function u(v,T) in order to describe the radiation-energy emitted by a rigid-wallet cavity per unit of surface? How can one mathematically determinate distribution–in–all–requencies of electromagnetic radiation?  Thus, which color should be the light emitted by a black body conserved in T-constant temperature? How can we be sure for the independence from the nature of cavity-wallet in thermal-equilibrium conditions? What is its relationship physics–mathematics? Etc. It seems that in 1862, Gustav Kirchhoff (1824–1887) firstly used the term black body along his researches on (1859–) on spectroscopic exams of the light. Then, we mainly had: Stefan–Boltzmann law (1879), Boltzmann studies on Stefan’s law (1884), Michelson’s analyses on Boltzmann’s results by means of calculus of probability (1887), Weber proposed (1879) an hypothesis on a correlation between frequency and curve of temperature obtained, Wien established (1893–1896) his “displacement law” within a similitude idea between the u(v,T) and distribution in speeds of gas-molecules, Rayleigh (1900)–Jeans (1905) law in agreement with wavelengths, but strongly disagreed at short wavelengths (high frequencies), Einstein studies on the corpuscular of the matter and his hypothesis ad hoc, et al. Finally, the three main Planck’s hypotheses (1897–1899/1900) on the body–wallets permitted to well determinate (1900) the new mathematical form of the universal function. The latter, in an attempt to explain the radiation emitted by a black body, introduced the concept of quantization of the energy of electromagnetic radiation according to which energy can assume only whole multiple values ​​of a fundamental value, called quantum. Finally, not only the transfer was quantized, but also the radiation – a priori – done by quanta.  After Black Body Radiation and quanta, the 3–formulations of the Quantum mechanics (20s-35s) was carried out respectively by Heisenberg, Schoredringer and Bohr. Black Body Radiation is complex modelling as interplay among thermodynamics, statistical mechanics electromagnetism applied to kinetic modelling of gas. The Quantum mechanics is a foundational consequence of Black Body Radiation, but it cannot be considered as part of it. In my talk, I will present a story of black body theory taking into account historical mathematical–physical foundations and the change of the relationship physics–mathematics until the birth of quantum mechanics.



  • Boltzmann L (1895a) On Certain Questions of the Theory of Gases. Nature 51:413–415.
  • Boltzmann L (1895b) On the Minimum Theorem in the Theory of Gases. Nature, 52:211.
  • Boyer TH (1969) Classical statistical thermodynamics and electromagnetic zero-point radiation. Physic Review 186:1304–1318.
  • Boyer TH (1969) Derivation of the blackbody radiation spectrum without quantum assumptions. Physic Review 182:1374–1383.
  • Boyer TH (1978) A connection between the adiabatic hypothesis of old quantum theory and classical electrodynamics with classical electromagnetic zero-point radiation. Physic Review 18:1238–1245.
  • Boyer TH (2003) Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum,” American Journal of Physics 71:866–870.
  • Bussotti P, Pisano R (2014) Newton’s Philosophiae Naturalis Principia Mathematica “Jesuit” Edition: The Tenor of a Huge Work. Accademia Nazionale Lincei-Rendiconti Matematica e Applicazioni 25:413-44
  • Chandrasekhar S (1950) Radiative Transfer. Oxford, Oxford University Press.
  • Franck J (1948) Max Planck. Science 107:534-537.
  • Gillispie CC, Pisano R (2014) Lazare and Sadi Carnot. A Scientific and Filial Relationship. 2nd edition. Dordrecht. Springer.
  • Heilbron JL (1986) The dilemmas of an upright man : Max Planck as spokesman for German science. University of California Press, Berkeley.
  • Hermann A (1971) The Genesis of Quantum Theory. MIT Press, Cambridge–MA.
  • Kirchhoff G (1860a [27 October 1859]) Über die Fraunhofer'schen Linien. Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin: 662–665.
  • Kirchhoff G (1860b [11 December 1859]) Über den Zusammenhang zwischen Emission und Absorption von Licht und Wärme. Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, pp. 783–787.
  • Kirchhoff G (1860c) Über das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Annalen der Physik und Chemie 109/2:275–301.
  • Kirchhoff G (1860d) On the relation between the radiating and absorbing powers of different bodies for light and heat. Philosophical Magazine 4/20:1–21.
  • Kirchhoff G (1882 [1862]) Über das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Gesammelte Abhandlungen. Johann Ambrosius Barth, Leipzig, pp. 571–598.
  • Kirchhoff GR (1860) Über die Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Annalen der Physik 109:275–301.
  • Klein MJ (1962) Max Planck and the Beginnings of the Quantum Theory. Archive for History of Exact Sciences 1:459–479.
  • Klein MJ (1963) Planck, entropy, and quanta 1901–1906. The Natural Philosopher, I. Blaisdell Publishing Co., New York, pp. 81–108.
  • Kragh H (1999) Quantum Generations: a History of Physics in the Twentieth Century. Princeton University Press, NJ.
  • Kragh H (2000) Max Planck: the reluctant revolutionary. Physics World. December
  • Kuhn TS (1978) Black–Body Theory and the Quantum Discontinuity. 1894–1912. Oxford University Press, NY–Oxford.
  • Kuhn TS (1984) Revisiting Planck. Historical Studies in the Physical Science, 14:232–252.
  • Lorentz HA (1916) Les Théories Statistiques en Thermodynamique. Teubner–Verlag, Leipzig.
  • Lorentz HA (1952) The Theory of Electrons. Dover, New York.
  • Maxwell JC (1865) A dynamical theory of the Electromagnetic field. Philosophical Transactions of The Royal Society of London CLV:459-512.
  • Newton I ([1726] [1739-1742] 1822) Philosophiae Naturalis Principia Mathematica, auctore Isaaco Newtono, Eq. Aurato. Perpetuis commentariis illustrate, communi studio Thomae le Seur et Francisci Jacquier ex Gallicana Minimorum Familia, matheseos professorum. Editio nova, summa cura recensita. A. et J. Duncan. Glasgow.
  • Newton I (1746) Methodus fluxionum et serierum infinitarum, in Opuscula mathematica. Marcum Michaelem Bousque Lausanne et Genevae, I, 29-200.
  • Penrose R (2005) The Road to Reality: A Complete guide to the Laws of the Universe. Vintage Books, London.
  • Pisano R (2010) On Principles In Sadi Carnot’s Theory (1824). Epistemological reflections. Almagest 2/1:128–179.
  • Pisano R (2011) Physics–Mathematics Relationship. Historical and Epistemological notes. In: Barbin E, Kronfellner M, Tzanakis C (Eds). Proceedings of the ESU 6 European Summer University History and Epistemology in Mathematics. Vienna. Verlag Holzhausen GmbH–Holzhausen Publishing Ltd., pp 457–472
  • Pisano R (2012) Historical Reflections on Physics Mathematics Relationship in Electromagnetic Theory. In: Barbin E, Pisano R (Eds). The Dialectic Relation between Physics and Mathematics in the XIXth Century. Dordrecht. Springer, pp 31-57.
  • Pisano R (2013) On Lagrangian in Maxwell's electromagnetic theory. Scientiatum VI. História das Ciências e das Técnicas e Epistemologia. The Federate University of Rio de Janeiro. Rio de Janeiro University Press, pp 44-59.
  • Pisano R (2017) A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics. Transversal: International Journal for the Historiography of Science 2:166-203.
  • Pisano R (ed.) (2015) A Bridge between Conceptual Frameworks, Science, Society and Technology Studies. Dordrecht. Springer.
  • Pisano R, Agassi J, Drozdova D (Eds) (2017) Hypotheses and Perspectives in the History and Philosophy of Science. Homage to Alexandre Koyré 1964-2014. Springer. Dordrecht.
  • Pisano R, Anakkar A, Pellegrino EM, Nagel M (2018) Thermodynamic Foundations of Physical Chemistry. Reversible Processes and Thermal Equilibrium into History. Foundations of Chemistry (Springer) 10:1-27.
  • Pisano R, Bussotti P (2016a) A Newtonian Tale Details on Notes and Proofs in Geneva Edition of Newton’s Principia. BSHM-Journal of the British Society for the History of Mathematics 31/3:160-178.
  • Pisano R, Bussotti P (2017) The Emergencies of Mechanics and Thermodynamics in the Western Society during 18th–19th Century. In: Pisano 2015 (ed), pp 399-436.
  • Pisano R, Bussotti P (2017) The Fiction of the Infinitesimals in Newton’s Works: On the Metaphoric use of Infinitesimals in Newton. Special Issue Isonomia 9:139-158.
  • Pisano R, Capecchi D (2013) Conceptual and Mathematical Structures of Mechanical Science in the Western Civilization around 18th Century. Almagest 4/2:86-121.
  • Pisano R, Capecchi D (2015) Tartaglia’s science weights and Mechanics in XVI century. Selections from Quesiti et invention diverse: Books VII–VIII. Dordrecht. Springer.
  • Pisano R, Fichant M, Bussotti P, Oliveira ARE (Eds) (2017). The Dialogue between Sciences, Philosophy and Engineering. New Historical and Epistemological Insights. Homage to Gottfried W. Leibniz 1646-1716. The College Publications. London.
  • Planck M (1900a [1967]) Über eine Verbesserung der Wienschen Spektralgleichung. Verhandlungen der Deutschen Physikalischen Gesellschaft. 2:202–204. [On an Improvement of Wien’s Equation for the Spectrum. Pergamon Press, Oxford].
  • Planck M (1900a [1967]) Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum. Verhandlungen der Deutschen Physikalischen Gesellschaft 2:237. [On the Theory of the Energy Distribution Law of the Normal Spectrum. Pergamon Press, Oxford].
  • Planck M (1914) The Theory of Heat Radiation. Blakiston’s Son & Co, Philadelphia [1959. The Theory of Heat Radiation. Dover Publications, New York].
  • Planck M (1901) Über das Gesetz der Energieverteilung im Normalspektrum. Annalen der Physik 309/3:553–563. [On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik 4].