Classical electromagnetics in free space leaves no room for accommodation of a light particle. To underline this, it is sufficient to remember that Einstein in order to reach his lightquantum (energy-quantum) hypothesis had to mix classical theoretical physics with a piece of experimental information that defies description in classical terms. In his 1905-paper Einstein concluded [60]:Monochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as though it consisted of a number of mutually independent energy quanta of magnitude hν. The introduction of light quanta in the Wien regime (the high-frequency part of the Planck blackbody radiation law) is the first step toward the concept of electromagnetic radiation as a Bose gas of photons [180, 39, 68, 69]. Although a photon gas obeys Bose-Einstein statistics for all frequencies the statistical independence assumed by Einstein in 1905 is not true in general. Einstein used Boltzmann statistics when he conjectured the existence of light quanta. In the Wien regime Boltzmann and Bose-Einstein statistics lead to the same conclusion since the mean number of particles (photons) with a given energy is much less than one. The circumstance that the light quanta are not statistically independent in Bose-Einstein counting finds its explanation in quantum mechanics. Hence, the statistical correlation is induced by the requirement of totally symmetric wave functions.
Classical electromagnetics in free space leaves no room for accommodation of a light particle. To underline this, it is sufficient to remember that Einstein in order to reach his lightquantum (energy-quantum) hypothesis had to mix classical theoretical physics with a piece of experimental information that defies description in classical terms. In his 1905-paper Einstein concluded [60]:Monochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as though it consisted of a number of mutually independent energy quanta of magnitude hν. The introduction of light quanta in the Wien regime (the high-frequency part of the Planck blackbody radiation law) is the first step toward the concept of electromagnetic radiation as a Bose gas of photons [180, 39, 68, 69]. Although a photon gas obeys Bose-Einstein statistics for all frequencies the statistical independence assumed by Einstein in 1905 is not true in general. Einstein used Boltzmann statistics when he conjectured the existence of light quanta. In the Wien regime Boltzmann and Bose-Einstein statistics lead to the same conclusion since the mean number of particles (photons) with a given energy is much less than one. The circumstance that the light quanta are not statistically independent in Bose-Einstein counting finds its explanation in quantum mechanics. Hence, the statistical correlation is induced by the requirement of totally symmetric wave functions.
Planck’s 1900 introduction of the “energy elements”, i.e., electromagnetic radiation quanta of energy hν each, for founding his radiation law marks the origin of quantum theory and is discussed in all courses on this subject. Surprisingly, the question whether Planck really implied quantisation is debated among historians of physics. We present a simplified account of that debate which also sheds light on the issue of indistinguishability and Einstein’s light quantum hypothesis. Here, the relevance of the notion ‘(in)distinguishability’ is often overemphasized. It has to be treated together with ‘equality’, ‘identity’, and ‘interchangeability’, where the latter one is the decisive notion in this context. As a result, the difference between Planck’s and Einstein’s concepts of ‘light particles’ becomes more easily to grasp. For that and many other reasons, we believe that the teaching of quantum physics benefits from including the material presented here, and that beyond the demand of historical completeness. Nevertheless, for the sake of our readers’ convenience, we almost completely reprint Planck’s former students Hettner’s remembering of Planck’s way to his radiation law, together with its translation into English. It seems that Planck has not really done the calculations described in his December 1900 lecture. For this, following Becker, we show how to overcome the difficulties over there, and we sketch his simplifying approach in his subsequent 1901 article. Strangely enough, in his 1906/07 lectures on the theory of heat radiation, Planck deviates from those calculations and obtains a non-extensive entropy. This, too, is most easily analyzed using Bach’s three-level scheme ‘configuration. occupation. occupancy’ for the counting combinatorics involved. Boltzmann’s 1877, Planck’s 1900, Einstein’s 1905, Bose’s 1924, and other treatments are systematized using that scheme
At the beginning of the century doubts were growing about the whole edifice of classical physics, including the laws of mechanics in their Lagrangian and Hamiltonian forms, of statistical thermodynamics, as formulated by Boltzmann and Gibbs, and of optics, namely Maxwell’s and Fresnel’s theory. Einstein proposed that electromagnetic radiation exists in discrete quanta whilst propagating in space as well as during the emission or absorption processes. Scattering by free electrons is a common interaction connected with the absorption of electromagnetic radiation. If the electromagnetic energy is large compared with the ionization energy, the atomic electron can be treated as free. The characteristic features of the scattered radiation have been explained by Compton, on the basis of an elastic collision of a photon with a free electron, where both energy and momentum are conserved. The concept of the matter wavelength holds for both relativistic and non-relativistic particles, provided that the appropriate form of momentum is used.
Einstein never deviated from his belief in the reality of light quanta. In 1909, he published a remarkable paper in which he showed that fluctuations in the intensity of black-body radiation consisted of the statistical sum of the wave and particle properties of light. Following the 1911 Solvay conference, most of the participants were converted to the existence of light quanta. Bohr first applied the concepts of quanta to the structure of atoms. The experiment which finally convinced everyone of the light quantum hypothesis was Compton's demonstration of the energy change of X-rays in their scattering by electrons. This resulted in the concept of the wave-particle duality of light, one of the major foundation stones of quantum mechanics.
According to modern quantum field theory all elementary particles are quantum excitations of an underlying quantum field. In the case of the photon the underlying field is the electromagnetic field. In photon wave mechanics the photon concept was reached by a reinterpretation of the physical meaning of the free classical electromagnetic field. Such a reinterpretation does not give us a quantum theory of light quanta because the elementary quantum of action is foreign to classical physics. Although Planck’s constant does occur in the various Schro¨dinger-like wave equations we have presented in Part III it just plays the role of a multiplicative factor, see e.g., Eq. (10.36). The “justification” for bringing ~ into the formalism is the wish to make contact to the Einstein-de Broglie relations [Eqs. (10.40) and (10.41)]. In a sense one may call the light particle appearing from classical electrodynamics the classical photon.
This work examines the physical and conceptual evolution of the light quantum from Planck's blackbody theory to the theoretical and experimental developments that led to the quantization of the electromagnetic field. The present study shows that the decisive transition occurred in Einstein's quantum theory of radiation (1916-1917). Absorption, stimulated emission, and spontaneous emission were formulated as elementary probabilistic mechanisms whose statistical balance alone reproduces the blackbody spectrum. In particular, spontaneous emission requires the emission of a light quantum, thereby implicitly proving its physical necessity before its theoretical status was clarified. At the same time, the already existing term photon began to acquire a stable usage following Lewis's 1926 proposal and became increasingly associated with Einstein's light quantum. By the mid-1920s, the central problem had shifted from whether light quanta were physically required to how radiation could be incorporated into the emerging quantum-mechanical formalism. This transition marks a key stage, illustrating how initial debates about the existence of light quanta gave way to their integration into a comprehensive theoretical structure. The resulting asymmetry between the novel quantum description of matter and the still-classical description of radiation, called into question by the phenomenon of spontaneous emission, identifies the physical problem that led to the quantization of the electromagnetic field.
The Planck’s law of blackbody radiation is derived in several methods in this paper. The original Planck’s derivation in his 1900 paper, the derivation by Einstein, and another derivation based on the Bose-Einstein statistics are reviewed with comments on each derivation. Statistical properties of radiation are briefly reviewed in the second part of the paper. Different concepts of photon statistics are applied on the thermal (chaotic) light and laser light. Nonclassical properties of light that manifest its quantum nature are briefly highlighted with a short review of the experimental evidence embodied in ……….. 1-Introduction and historical perspective It was Robert Kirchhoff who first argued in 1859 that the thermal radiation of the blackbody was of a fundamental nature.1 Since that time, several attempts were made to derive a precise relation that matches the experimental results. Wien, suggested that the radiation density per