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.
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.
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.
This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
Abstract With the failure of classical physics to explain the experimentally observed black body radiation spectrum, the photoelectric effect and the existence of narrow spectral lines in the light emitted by excited atoms, physicists were forced to reach out for new ideas. Following Planck’s initial “drastic hypothesis” of light “quanta”, Einstein led the way in exploring some of the myriad implications of this idea. In particular, the study of fluctuations led to a new understanding of the interaction of electromagnetic radiation with atoms. Einstein invented the photon by showing, through fluctuation studies, that light emitted by atoms must be in the form of plane waves. These ideas led to the first notions regarding the quantization of matter and its dynamics.
This chapter starts with the historical development of quantum mechanics and explanations of key concepts behind fundamental discoveries such as Planck's hypothesis, the photoelectric effect, Bohr's atomic model, Compton scattering, the de Broglie hypothesis, the Pauli exclusion principle, the Schrödinger equation, Heisenberg quantum mechanics and the uncertainty principle, the Born interpretation of wave function, the Davisson and Germer experiment, and Dirac relativistic quantum mechanics, which made important contributions to the foundation of modern quantum mechanics. Concepts like the particle properties of radiation, the wave properties of matter, quantized energy and momentum, and the idea that one can no longer know exactly where a single particle like an electron is at any instant of time are brought out clearly through this chapter. A list of important quantum mechanical parameters along with solved examples and unsolved exercises on the key concepts are included towards the end.
Light quanta The history of the corpuscular and wave controversy in optical theory is well known. At the end of the last century physicists had no doubt as to the wave character of light, and the acceptance of the wave theory meant the rejection of the corpuscular theory. The possibility of both being correct and helpful to one another had not been much thought about and still less explored. At about this time Planck's quantum theory appeared and was soon followed in 1905 by Einstein's theory of ‘light quanta’ to explain the photo-electric effect, for which the wave theory alone had utterly failed to account. Einstein assumed that radiation exists in discrete ‘quanta’ of energy hν , where ν is the frequency; thus a quantum is a separate thing, like a corpuscle, and has a frequency associated with it, like a wave. There was a blend of the two older theories involved. This idea has been generalised by the speculations of Louis de Broglie, who pointed out the important clue given by the theory of relativity, namely, that of the identity of mass and energy, so that the conservation of mass is therefore also the conservation of energy. This suggested to him that all forms of energy (including radiation) should have an atomic structure, like matter; and that the atoms of energy are grouped round certain singular points, forming electrons, light quanta, and the like.