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International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE)

On the reduction of free photons speed in modeling of their propagation in space by the wave function in coordinate representation

Alexandr Petrovich Davydov, Tatiana Pavlovna Zlydneva

Published Oct 1, 2016• 6 citations
Publisher

Abstract

The main principles of photon quantum mechanics describing its single-particle states by means of the wave function (wave packet) in the coordinate representation are given. The results of modeling of the propagation in space-time of wave packet with a Gaussian distribution of the momentum of a photon corresponding to femtosecond laser radiation are discussed. On the basis of the general ideas about the evolution of this packet and within the framework of constructed photon quantum mechanics, the quantum-mechanical explanation of the experimentally registered (previously) reduction of speed of the free photons, “structured” in the same way as the light in Bessel and Gaussian beams, is proposed. It is emphasized that in fact the photon is not a some formed quantum corpuscle, but it is a quasi-particle, which is the result of propagation of spin wave in physical vacuum, the nature of which should be considered at the Planck distances simultaneously with structure of fundamental particles.

DOI
10.1109/apeie.2016.7806458

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The main principles of photon quantum mechanics describing its single-particle states by means of the wave function (wave packet) in the coordinate representation are given. The results of modeling of the propagation in space-time of wave packet with a Gaussian distribution of the momentum of a photon corresponding to femtosecond laser radiation are discussed. On the basis of the general ideas about the evolution of this packet and within the framework of constructed photon quantum mechanics, the quantum-mechanical explanation of the experimentally registered (previously) reduction of speed of the free photons, “structured” in the same way as the light in Bessel and Gaussian beams, is proposed. It is emphasized that in fact the photon is not a some formed quantum corpuscle, but it is a quasi-particle, which is the result of propagation of spin wave in physical vacuum, the nature of which should be considered at the Planck distances simultaneously with structure of fundamental particles.
On the base of the photon’s wave function (wave packet) in Schrodinger coordinate representation developed in previous papers the modeling of the propagation in space and in time of a wave packet of the photon corresponding to a separate laser impulse of radiation of femtosecond diapason is carried out. The development is proceeded from single-particle approach with the usage of the basis eigenfunctions of energy, momentum and helicity operators in continuous momentum spectrum case. The wave packet is constructed in the form of superposition of these eigenfunctions as the integral over the all momentum space. In the case of Gaussian momentum distribution the character of an extension of a form of this wave packet is established. The essence of wave-particle duality of light and microparticles is specified. The hypothesis is formulated, however, that the photon is a quasi-particle corresponding to the propagation of spin wave in physical vacuum. It is claimed that this question is related to the structure of the leptons and other particles on the Planck distances.
The basic principles of quantum mechanics of the photon, describing its single-particle states by means of the wave function in the coordinate representation are given.This wave function is a wave packet constructed by the superposition of the basic bivectors which are eigenfunctions of the operators of energy, momentum and helicity.The results of modeling in the space-time of such wave packet with a Gaussian distribution on the momentum of the photon corresponding femtosecond laser radiation are discussed.On the basis of the general ideas about the evolution of this packet and within the framework of the constructed photon quantum mechanics the quantum-mechanical approach is proposed to explain the wave phenomena exhibited by light such as the light interference in Young's experiment.It is emphasized that actually the photon isn't some "created" quantum corpuscle, but it's a quasi-particle that is a result of the propagation of spin waves in physical vacuum, the nature of which should be considered at the Planck distances simultaneously with the structure of the leptons and other fundamental particles.
The main principles of the previously constructed photon quantum mechanics allowing one to calculate the probability density of detection of the photon using the its wave function in the coordinate representation both in classical experiments and in experiments with single photons are presented. The theory is supplemented by solving the Cauchy problem for the corresponding equation, to which the photon wave function satisfies. The results of modeling the photon wave function with Gaussian pulse distribution for femtosecond laser radiation are presented. It is concluded that for well-polarized radiation the probability density of photon detection is proportional to the envelope of the square of the “electric field strength”. The Young's interference experiment is explained from the point of view of photon quantum mechanics. It is claimed that the coherence of the radiation should be consistent with the “separation” of the wave function of the photon falling on the beam splitter in experiments with single photons. This statement substantially weakens the dilemma of wave-particle duality, but it sets new challenges for the further development of physics. It is emphasized that for their solution the new experiments are needed to identify the properties of the physical vacuum. The physical nature of the photon is discussed as a result of the propagation of a spin wave with Planck parameters in a physical vacuum.
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.
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.
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.