Abstract The general results of constructing and modeling the photon wave function in the coordinate representation in the framework of quantum mechanics are presented in order to explain single-photon interference phenomena, in particular Young’s experiment. The relevance of this function is emphasized in connection with modern single-photon and two-photon experiments. The necessity of replacing the explanation of obtaining coherent light sources using the concept of a train of supposedly real electromagnetic waves emitted by one atom, by the conditional emission by this atom of the photon wave function in the coordinate representation, which then experiences diffraction and interference, is substantiated. A single-photon wave function is simulated based on the consideration of the electric dipole radiation of an atom in classical electrodynamics, and a conclusion is drawn on the possibility to explain Young’s experiment. It is argued that although the photon wave function (as well as of particles having mass) is not a physical object, the application of this function significantly weakens the problem of wave-particle duality of light. It is assumed the “nature” of this function reflects the properties of a physical vacuum, but new experiments are required to clarify it.
Abstract The general results of constructing and modeling the photon wave function in the coordinate representation in the framework of quantum mechanics are presented in order to explain single-photon interference phenomena, in particular Young’s experiment. The relevance of this function is emphasized in connection with modern single-photon and two-photon experiments. The necessity of replacing the explanation of obtaining coherent light sources using the concept of a train of supposedly real electromagnetic waves emitted by one atom, by the conditional emission by this atom of the photon wave function in the coordinate representation, which then experiences diffraction and interference, is substantiated. A single-photon wave function is simulated based on the consideration of the electric dipole radiation of an atom in classical electrodynamics, and a conclusion is drawn on the possibility to explain Young’s experiment. It is argued that although the photon wave function (as well as of particles having mass) is not a physical object, the application of this function significantly weakens the problem of wave-particle duality of light. It is assumed the “nature” of this function reflects the properties of a physical vacuum, but new experiments are required to clarify it.
The main principles of photon quantum mechanics describing its one-particle states with the help of the wave function in coordinate representations are given.This wave function (packet) is the superposition of the basic bivectors that are generalized eigenfunctions of energy, momentum, and helicity operators.The quantum-mechanical approach is offered for an explanation of the interference Young's experiment.This explanation is especially important for new interpretation of the non-laser method of obtaining the interference by the amplitude division, as in this case it is traditionally assumed that the radiation of one light train of a single atom interferes with itself.In our explanation, not both "halves" of some real train ("scrap") of the electromagnetic wave interfere with each other, but the both terms of the photon's wave function do this.Nevertheless, the wave function is not directly measured by experience, and therefore it does not exist as a physical object.The attraction of the wave function to the explanation of single-photon interference obtained "by the division of the wave front" is obviously also necessary.Therefore, the situation for the photons emitted by individual atoms (and also, obviously, by laser), is absolutely similar to the situation with the particles having mass, whose distribution in space is described by wave function in coordinate representation.It is pointed out that in fact the photon is not some "formed" quantum particle, but it is a quasi-particle arising when a certain spin wave propagates in a physical vacuum at Planck distances.
The two-photon interference appearing in a mental experiment similar to the Young’s experiment as a result of simultaneious emission of two photons by (two) independent point sources under the assumption that their radiation is described in the electric-dipole approximation in the classical electrodynamics is simulated within the framework of the photon quantum mechanics by using a six-component photon wave function in the coordinate representation and, for comparison, in the proposed “quasi-classical” approach by using the one-component photon wave function. The relevance of introduction of the photon wave function is emphasized in comparison to the concept of the photon being a “train” of real electromagnetic waves. The task of setting up new experiments that could initiate the analysis of the physical nature of quantum phenomena that occur in the physical vacuum and are formally described by the wave function in the quantum mechanics or by transition amplitudes in the quantum electrodynamics is proposed.
In modern areas of photonics, the physical description of the interaction of photons with matter in the control, transmission and registration of single-photon and two-photon states implemented in practice is of great importance. An appropriate acceptable description may be faced with the need to take into account various kinds of interference effects associated with these states. Meanwhile, even the most “simple” case of single-photon interference in Young's experiment requires the use of a rather complex apparatus of quantum electrodynamics. This article explains one- and two-photon interference in Young's thought experiment based on the photon wave function (PWF) in coordinate representation. This explanation is illustrated by two examples of wavelengths: 10.6 μm and 1.5 cm. For both examples, two approaches to PWF modeling are used: “purely quantum-mechanical” and “quasi-classical”. In the first approach, a 6-component coordinate PWF is constructed using a spherically symmetric momentum distribution in a wave packet, followed by numerical and approximate analytical calculations. In the second approach, a one-component “quasi-classical” PWF is constructed, which corresponds to either electric dipole radiation or simulated spherically symmetric radiation. In all cases, the same pronounced interference pattern was obtained, which allows us to conclude that not only the quantum-mechanical coordinate PWF is able to explain the phenomena of one- and two-photon interference, but also a much simpler “quasi-classical” PWF. This conclusion sheds light on the theoretical interpretation of the measurement of the coordinate PWF in some recent experiments.
Introduction: In the rapidly developing areas of photonics associated with quantum teleportation of photons, quantum cryptography, and quantum computing, ideas are becoming increasingly relevant about the certain localized states of single or several entangled photons moving in space and time. As is known, in quantum mechanics, localized states of particles can only be described using wave functions in coordinate representation – the corresponding wave packets. Aims: To explain Young's one- and two-photon experiments using coordinate 6-component quantum mechanical and 1-component quasi-classical photon wave functions. Methods: The article outlines the method developed in authors' previous work in constructing the 6-component coordinate wave function of free photons in the form of the wave packet (an integral over the entire momentum space and sum over two possible values +1 and -1 of the helicity). The basis functions are the circularly polarized monochromatic waves, corresponding to certain values of the momentum, helicity, and photon energy operators and forming a complete orthonormal set of generalized eigenfunctions of these operators. This photon wave function (PWF) is normalized to the unit probability of finding the photon anywhere in space. Both the basis functions and the coordinate PWF satisfy a Schrödinger-type equation derived from the Maxwell-Lorentz equations written in quantum mechanical form first introduced by Majorana. Then the results of modeling and consideration of the space-time evolution of the wave packet with Gaussian momentum distribution corresponding to the directed photon emission for 80 fs are briefly presented. Further, in view of the possibility of constructing the coordinate PWF, the basic formula for the waveparticle duality of photons and particles is formulated. It is emphasized that the photon is fundamentally different from “ordinary” particles, since, according to the authors, the photon is the result of the propagation of a certain complex spin wave in a physical vacuum, the details of which can only be considered simultaneously with the study of the structure of the physical vacuum at Planckian distances. Results: Young`s one- and two-photon experiments are explained using various options for modeling 6-component coordinate PWFs, including approximate functions corresponding to spherically symmetric and electric dipole photon radiation. Conclusion: This explanation is illustrated using specific examples of radiation and, at the same time, is compared with numerical simulations for spherically symmetric radiation and the use of 1-component quasi-classical PWFs.
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.
Abstract The main provisions of the construction of the single-particle wave function of a photon in the coordinate representation are expounded and its application to the description of single-photon interference phenomena is discussed. The connection between the concepts of electromagnetic field strengths used in quantum electrodynamics and the characteristics of wave packets in photon quantum mechanics is substantiated. For illustration, we consider the relationship between the structure of the photon wave function in coordinate representation and the polarization of photon in the formalism of quantum transition amplitudes. The meaning of the concept of linear polarization of a photon in the state of a wave packet is explained. The wave function is constructed in the coordinate representation of the state of two entangled photons at the exit from a nonlinear crystal by modeling the polarization vectors and Gaussian momentum distribution for each of the photons.