Einstein explained the experimental characteristics of the photo-electric effect by the concept that the photon is a localized packet of electromagnetic radiation with the mechanism: photon + atom → emitted electron. A classical plane wave theory of light concluding that the photoelectric effect can be explained without localized photons is reexamined and found to have been flawed in predicting no time delay for photoelectron emission; this accords with Millikan's conclusion (based upon energy conservation) that a classical plane wave would entail a delay prior to emission of the order of hours. The quantification of Einstein's localized packet concept as a solitary wave one wavelength in length (one period long in time) predicts a delay of one period of the photon's oscillating field, which accords with the experimentally measured response time being a few femtoseconds.
Einstein explained the experimental characteristics of the photo-electric effect by the concept that the photon is a localized packet of electromagnetic radiation with the mechanism: photon + atom → emitted electron. A classical plane wave theory of light concluding that the photoelectric effect can be explained without localized photons is reexamined and found to have been flawed in predicting no time delay for photoelectron emission; this accords with Millikan's conclusion (based upon energy conservation) that a classical plane wave would entail a delay prior to emission of the order of hours. The quantification of Einstein's localized packet concept as a solitary wave one wavelength in length (one period long in time) predicts a delay of one period of the photon's oscillating field, which accords with the experimentally measured response time being a few femtoseconds.
According to an entropy approach and by reviewing the similarity between laws characterizing the flow of heat and electric charges, electric charges were defined as electromagnetic waves that possess an electrical potential or simply as ionized photons. Accordingly, the flow of electrons was defined as a simultaneous flow of particulate energy and wave energy. Such definitions led to clear the confusions of duality properties of electrons and light waves, conflicts in the SI system of units and to explain the difference between the calculated drift speed of electrons and the speed of electricity or charges in conductors. However, Einstein considered the electron to be a negative charge of unknown nature during his analysis of the photoelectric effect. Einstein presented his hypothesis that light may behave as a particle to find a plausible explanation of the photoelectric effect. He found the measured cutoff frequency of light below which light might not eject electrons from metal-surfaces in photocells regardless of how much light is shone on the surface as a proof of truth of his hypothesis. Such frequency may be explained also, according to the previously introduced definitions, as the minimum energy quanta that may gain a quantized potential in photocells. This explanation may find plausible explanations of the found measurements of the photoelectric effects for different metal surfaces, stopping voltages into photocells and the photoelectric effect of X-rays. Einstein’s hypothesis of the photoelectric effect failed to find plausible explanations of such measurement results. According to the principles of conservation of momentum, there is a minimum quantity of photons that may lead to bouncing an atomic electron out of its orbit. So, considering Einstein’s theory as a perfect hypothesis that explains the photoelectric effect may be a misconception.
The idea of the photon has stirred the imaginations of physicists ever since 1905 when Einstein originally proposed the use of light quanta to explain the photoelectric effect. This concept is formalized in the quantum theory of radiation, which has had unfailing success in explaining the interaction of electromagnetic radiation with matter, seemingly limited only by the ability of physicists to perform the indicated calculations. Nevertheless, it has its conceptual problems—various infinities and frequent misinterpretations. Consequently an increasing number of workers are asking, “to what extent is the quantized field really necessary and useful?” In fact the experimental results of the photoelectric effect were explained by G. Wentzel in 1927 without the quantum theory of radiation. Similarly most electro-optic phenomena such as stimulated emission, reaction of the emitted field on the emitting atom, resonance fluorescence, and so on, do not require the quantization of the field for their explanation. As we will see, these processes can all be quantitatively explained and physically understood in terms of the semiclassical theory of the matter–field interaction in which the electric field is treated classically while the atoms obey the laws of quantum mechanics. The quantized field is fundamentally required for accurate descriptions of certain processes involving fluctuations in the electromagnetic field: for example, spontaneous emission, the Lamb shift, the anomalous magnetic moment of the electron, and certain aspects of blackbody radiation. (The Compton effect also fits here, but see later under references 8b and c.) Here we will outline how the photon concept originated and developed, where it is not required and is often misused, and finally where it plays an essential role in the understanding of physical phenomena. In our discussion we will attempt to give a logically consistent definition of the word “photon”—a statement far more necessary than one might think, for so many contradictory uses exist of this elusive beast. In particular consider the original coining of the word by G. N. Lewis: “[because it appears to spend] only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains an important structural element within the atom…, I therefore take the liberty of proposing for this hypothetical new atom which is not light but plays an essential part in every process of radiation, the name photon!” (our exclamation point). Clearly the present usage of the word is very different.
The photon is modeled as a monochromatic solution of Maxwell’s equations confined as a soliton wave by the principle of causality of special relativity. The soliton travels rectilinearly at the speed of light. The solution can represent any of the known polarization (spin) states of the photon. For circularly polarized states the soliton’s envelope is a circular ellipsoid whose length is the observed wavelength (λ), and whose diameter is λ/π; this envelope contains the electromagnetic energy of the wave (hv = hc/λ). The predicted size and shape is confirmed by experimental measurements: of the sub‐picosecond time delay of the photo‐electric effect, of the attenuation of undiffracted transmission through slits narrower than the soliton’s diameter of λ/π, and by the threshold intensity required for the onset of multiphoton absorption in focussed laser beams. Inside the envelope the wave’s amplitude increases linearly with the radial distance from the axis of propagation, being zero on the axis. Outside the envelope the wave is evanescent with an amplitude that decreases inversely with the radial distance from the axis. The evanescent wave is responsible for the observed double‐slit interference phenomenon.
This chapter comprises Einstein's explanation of the photoelectric effect, his analysis of the transition of electrons in atoms, his study of the behavior of bosons (named after their discoverer, Satyendra Bose), and his opposition to the standard interpretation of quantum mechanics. For the photoelectric effect, Einstein showed that light could behave as a particle, not only as a wave. Using this “photon” model, he explained how atoms absorbed and emitted light. He also predicted that a photon could stimulate the emission of many more, through (decades later) light amplification by stimulated emission of radiation. He studied bosons, particles that, unlike fermions (named after Enrico Fermi), such as electrons in atoms, had no “Exclusion Principle”: any number of them could “condense” into a single state. Finally, he opposed Bohr's “Copenhagen interpretation,” that a system such as an electron has a range of values for its properties such as spin, until a measurement is made, forcing it to choose one. Einstein argued for a “hidden variable theory” in which there was something deeper than quantum mechanics: that a system was in a specific state before a measurement. (He was wrong.)
The photoelectric effect, the Compton effects, and now anticorrelation experiments have been claimed to prove that light consists of particles flying through a void. However the particle model is decisively falsified by the known wave qualities of electromagnetic radiation. Quantum Electrodynamics also uses spreading wave amplitudes; not flying particles. The evidence indicates that light is a wave and electrons are electromagnetic wave-structures that absorb and emit light in discrete wave-packets. These wave-quanta are emitted directionally and then spread in space in proportion to their wavelength. Their waves superposition with all other waves in space. In low intensity experiments, the waves that an electron in a photodetector absorbs come from the superpositioning of the source wave-quanta and background radiation. The importance of background radiation is evidenced by "dark counts". Treating electrons and the quanta they absorb and emit as particles when they are composed of waves is the source of all the paradoxes, unreality and confusion in Quantum Mechanics. The word "photon" should be replaced by "quantum" in the description of this particular electronic process. The conceptual model presented here explains the known phenomena without producing paradoxes and unifies quantum and classical electromagnetics.
Light occupies a special position in our attempts to understand nature both classically and quantum mechanically. We recall that Newton, who made so many fundamental contributions to optics, championed a particle description of light and was not favorably disposed to the wave picture of light. However, the beautiful unification of electricity and magnetism achieved by Maxwell clearly showed that light was properly understood as the wave-like undulations of electric and magnetic fields propagating through space. The central role of light in marking the frontiers of physics continues on into the twentieth century with the ultraviolet catastrophe associated with black-body radiation on the one hand and the photoelectric effect on the other. Indeed, it was here that the era of quantum mechanics was initiated with Planck's introduction of the quantum of action that was necessary to explain the black-body radiation spectrum. The extension of these ideas led Einstein to explain the photoelectric effect, and to introduce the photon concept. It was, however, left to Dirac to combine the wave-and particlelike aspects of light so that the radiation field is capable of explaining all interference phenomena and yet shows the excitation of a specific atom located along a wave front absorbing one photon of energy. In this chapter, following Dirac, we associate each mode of the radiation field with a quantized simple harmonic oscillator, this is the essence of the quantum theory of radiation.