Title

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

Abstract

In the end of 19^th 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.

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Contact

• raffaele.pisano@univ-lille.fr