The famous ‘‘1917 paper’’ of Einstein on the Quantum Theory of Radiation is revisited. Emphasis is placed on the little-known bulk of the paper dealing with momentum balance. The most difficult part of the calculation is here simplified by regarding the ‘‘drag force’’ on a body moving within a blackbody cavity as due to the same quantized impulses that give rise to random recoil.
The famous ‘‘1917 paper’’ of Einstein on the Quantum Theory of Radiation is revisited. Emphasis is placed on the little-known bulk of the paper dealing with momentum balance. The most difficult part of the calculation is here simplified by regarding the ‘‘drag force’’ on a body moving within a blackbody cavity as due to the same quantized impulses that give rise to random recoil.
ABSTRACT\nUsing Brownian's motion, Maxwell-Boltzmann' s molecular energy distribution, bohr postulates and Einstein's theory on quantum theory of photon radiation due to the interaction between photons and atoms/molecules accuring at thermal equilibrium, the Einstein's theory on stimulated emission by an exited moving atomic ensemble has been investigated. The modified spectral energy density p of the inducing photons appearing in the plank's law of black body radiation with an additional drag coefficient 7L which accommodates recoil effect of atoms/ molecules when the inducing photons hit them has been derived giving the form\nB":\thv\t\tand .[R„ R,1hv° [1\t1 dln(p) \nB\np(v) =\te v \t\nC2\t3 d In( v)\ne\t—B:\nB:\nThe modification steps which have been done based on momentum equilibrium, have improved the Einstein's theory on stimulated emission semiclassically.\n\nKeywords : stimulated, momentum-equilibrium, black body radiation, drag coefficient, photon spectral energy.
In 1916, A. Einstein developed a model of the absorption and emission of radiation from which he derived M. Planck’s radiation law. He postulated light-induced (stimulated) emission, because within the framework of classical physics an oscillator can, depending on the phase difference, both extract energy from the electromagnetic field and transfer energy to it. In a non-coherent field, α = β should hold, where α denotes the kinetic constant of absorption and β that of stimulated emission. This assumption is indispensable for deriving the radiation law from his model. In this context, it is problematic that a certain degree of field coherence follows necessarily from his model, which implies that α ≠ β. Moreover, the model cannot readily be generalised to fields of arbitrary coherence. An alternative model for the absorption and emission of radiation by matter is therefore developed here. On the one hand, it is based on the assumption that, within a blackbody, quanta of different energies may recombine freely; on the other hand, it employs the “pairwise interference model of quantum theory” (PIMOQ). The alternative model of the interaction between light and matter allows the radiation law to be derived for thermal equilibrium in a non-coherent field, under which conditions, according to the model, no stimulated emissions occur. It also describes the behaviour of systems with a coherent field (interference experiment, laser). Furthermore, considerations are presented regarding the energy distribution within a blackbody and the explanatory scope of A. Einstein’s model in this respect.
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 phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
Modern attempts to understand light go back to Newton who considered light to be particles, the so called corpuscular theory, and the other school of Huygens, Young and others. Huygens and Young viewpoint emphasised the wave property. This difference of opinions persisted for close to two centuries till Maxwell theory solidly established light as a wave phenomenon associated with Electromagnetism. A serious schism so to speak was introduced into the theory of light with the understanding of "Light gas", the so called Black Body radiation. Einstein's photon hypothesis and Bose's successful derivation of the Planck spectrum put the corpuscular theory back in place, while classical description continues to be used as well. One may then wonder if this being a classical limit may have to be corrected when dealing with quantum phenomena. To most people's surprise, the classical description was in fact a subset of the full quantum description, and the classical states of light could be shown to be subsumed within the fully quantum description without having to take the limit of Planck's constant h going to zero. This was the resolution provided by E. C. G. Sudarshan's Diagonal representation as the most general formalism for dealing with light.
The two-level atom problem formulated in energy space by Warwick (Astrophys. J. 121,190,1955) and Thomas~ (Astrophys. J. 125, 260,1957) may be demonstrated to be incapable of exact formulation. Three difficulties of principle are encountered: (1) the inability to distinguish between photon numbers and photon energy; (2) the introduction of normalized Einstein coefficients which in turn violate the Einstein relations; and (3) an erroneous treatment of stimulated emission, which when properly accounted for, does not permit an angular dependence in the scattering term. The basic difficulty arises from the fact that non-LTE is unable, in principle, to account for finite linewidths. Some of these difficulties appear to be eliminated if the non-LTE problem is formulated in momentum space rather than the customary energy space.