Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of "photon oscillations".
Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of "photon oscillations".
Two-slit experiments performed earlier by Tsuchiya et al. and recently by Afshar et al. demonstrate the joint wave-particle properties of the single indiviual photon, and agree with Einstein’s argument against Complementarity. These results cannot be ex-plained by conventional theory in which Maxwell’s equations serve as a guiding line and basis. On the other hand a revised quantum electrodynamic theory based on a nonzero electric field divergence in the vacuum yields results which appear to be consistent with the experiments. A model of the individual photon is thus deduced from the theory, in the form of a wave packet behaving as a single entity and having simultaneous wave and particle properties. 1
In this paper using the Clifford bundle formalism we show how starting from the photon concept and its relativistic Hamilton-Jacobi equation (HJE) we immediately get (with a simple hypothesis concerning the form of the photon canonical momentum) Maxwell equation (ME) satisfied by a null 2-form field F which is a plane wave solution (PWS) of ME. Moreover, we show how introducing a potential 1-form A such that F=dA we can see how a duality rotation changed in a \ spatial rotation transformation besides showing how i=−1 enters Maxwell theory thus permitting the writing of a representative of ME as Schrödinger like equation which plays a key role in answering one of the main questions addressed in this paper, namely: is there any sense in talking about photon trajectories in de Broglie-Bohm like theories? To this end we investigate first the nature of the energy-momentum \emph{extensor} field of the Maxwell field T(n) in some special situations showing that for some of those cases T0=T(γ0) even cannot describe the flow of energy. A proposed solution is offered. We also prove that there exists a pulse reshaping phenomenon even in vacuum. Finally we discuss the Schrödinger equation for a photon that follows from quantum field theory and investigate solutions that some authors think imply in photon localization. We discuss if such an idea is meaningful. Moreover, we show that for such solutions it is possible (once we accept that photon wave functions are extended in the space and also in the time domains) to derive a generalized HJE containing a quantum potential and which may lead to non lightlike photon trajectories in free space. We briefly discuss our findings in relation to a recent experiment.
Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations. Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.
In this paper, a Unitary Quantum Relativistic Theory was developed. The wavy nature of a quantum particle involves the relativistic dynamics of the wave packet of this particle, and a field of interaction described by Lorentz’s force and three of the four Maxwell equations: the electromagnetic induction law, and the flow laws of the electric and magnetic fields. These equations arise from the group velocity, which is of the form of the Lagrange equation, and from a relativistic principle for wave functions, which asserts that in any system of reference, a wave function has a bounded spectrum with a velocity limit c. When a magnetic circuit law is considered for a field interacting with a quantum particle, this is an electromagnetic field, propagating with the velocity c. This means that the limit velocity c of a quantum particle according to the theory of relativity is also obtained as a necessary condition of quantum dynamics. The relativistic particle wavefunctions considered in this framework, describing finite distributions of densities in the two conjugated spaces of the coordinates and momentum, provide a better description of a collisional phenomenon, in a finite volume occupied by these particles and the photon mediating this collision according to Quantum Electrodynamics.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed mch (m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.
Aims/ objectives: The consideration of the three tasks, formulated below, is the aim of the given work. The first task of the paper presented is to analyse the existing viewpoints and to give the conclusion on the real photon status. To represent the clear and understandable explanation of the nature of the corpuscular-wave dualism and to give an insight into physics of the photon absorption process is the second task of the given review. The third task of the paper presented - to give the experimental proof for the Dirac theoretical conclusion, that the transitions of the quantum system from an equilibrium state to an excited state are not instantaneous and that a part of the time, related to a duration of the stay between the states can be determined. Study design: The theory of quantum Fermi liquid, the developed Dirac quantisation method, the theory of quantum Rabi oscillations and experimental results of the stationary electron spin resonance (ESR) spectroscopy were used. Place and Duration of Study: Heat-Mass Transfer Institute of National Academy of Sciences of RB, Belarusian State University and M.V.Lomonosov Moscow State University, between January 2014 and July 2014. Methodology: We have used the quantum 1D Fermi liquid model for the description of 1D correlated electronic systems, elaborated in the application to the quantised electromagnetic (EM) field, the Jaynes-Cummings model (JCM) of quantum Rabi oscillations, new Slepyan-Yerchak- Hoffmann-Bass model of propagating quantum Rabi oscillations and new fully quantum space-time quantisation method. Results: The status of the photon in the modern physics is analysed. In the physics of elementary particles the photon is considered to be the genuine elementary particle. The development of the viewpoint of the experts in the quantum electrodynamics theory is considered. It was established its change from the opinion, that the description of the photon to be the particle is impossible to the viewpoint on the photon to be the particle, that is, coinciding with the viewpoint, represented in the Standard Model of the physics of elementary particles. The quantized Maxwellian EM-field represents itself, according to the new conceptual model reviewed, the sets of 1D rays, the own structure of each ray is discrete - 1D-lattice of spin-1 bosons. Therefore, the structure of EM-field in boson model resembles the structure of the carbon frame of organic polymers like to trans-polyacetylene in the matter. Photons in the given concept are the corpuscles, propagating along EM-field boson-”atomic” chains. In other words, EM-field boson- ”atomic” chains represents themselves the medium for the photons’ propagation. In the structural aspect photons in usual conditions are chargeless spin 1/2 topological relativistic solitons of Su- Schrieffer-Heeger family. Spinless charged solitons of the same family can also be formed in socalled ”doped” EM-field structure. The origin of waves in the EM-field boson-”atomic” structure is determined by the mechanism, being to be quite analogous to the formation of Bloch waves in the solid state of condensed matter. The expression for the corresponding wave function representing itself the set of Bloch-like waves is given. Just, the given function allows to describe correctly the wave properties of the light, including the interference. Corpuscular properties of EM-field including those ones by its interaction with matter are described by independent scalar field function obtained from the solution of Schr¨odinger equation [nonstationary in general case] and usually called wave function. The term ”wave” seems to be incorrect in application to the given function and has to be corrected in all literature on quantum theory, including textbooks. The physics of quantum absorption process is analysed. It is argued, in accordance with Dirac guess, that the photon revival takes place by its absorption. It is concluded, that after the energy and impulse transfer to the absorbing system the photon state is a pinned state, in which it possesses the only by spin. The reviewed rather unusual spectroscopic electron spin resonance absorption characteristics of carbon nanotubes and superconducting ceramics, obtained with the participation of the authors and of the other research groups and being earlier unexplained, were correctly interpreted within the frames of the phenomenological model of the spectroscopic transition dynamics with finite time of the transfer of absorbing systems in an excited state. Moreover, it was established, that the time of the transfer of absorbing systems in an excited state governs the characteristics of the stationary ESR signal registered in the carbon nanotubes and superconducting ceramics. Conclusion: To describe correctly the EM-field properties including corpuscular-wave dualism [which is explained in a natural way] it is necessary to use the full variant of Schr¨ odinger’s theory, taking into consideration two scalar functions. The result, that the time of the transfer of absorbing systems into an excited state governs the characteristics of the stationary ESR signal is significant for the stationary spectroscopy at all, since the transfer of absorbing systems in an excited state is considered in the stationary spectroscopy at present to be instantaneous.