Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green's function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell's equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate.
Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green's function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell's equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate.
Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green’s function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell’s equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate. “But the real glory of science is that we can find a way of thinking such that the law is evident .” — R. P. Feynman
Preface. Introduction to the Conference. A Quantum of Light Shed on a Classical Problem C.K. Whitney. A Classical Photon Model R.J. Beil. Stationary Vacuum-Polarization 'P Fields': the Missing Element in Electromagnetism and Quantum Mechanics M.H. MacGregor. Electrons and Photons as Soliton-Waves G. Hunter. Topological Solitons in Non-Linear Electrodynamics G. Kalbermann. A Particle or a Photon in a Field T.W. Marshall, E. Santos. Could the Photon be Superfluous? M. Sachs. Fluctuation-Dissipation Quantum Electrodynamics G.F. Efremov, et al. Einstein-de-Broglie-Proca Theory of Light and Simultaneous Existence of Transverse and Longitudinal Photons S. Roy, M. Roy. Origin, Observation and Consequences of the B(3) Field M.W. Evans. Opto-Magnetic Effects in Non-Absorbing Media: Problems of Measurement and Interpretation S. Jeffers, et al. Generalized Equations of Electrodynamics of Continuous Media V.M. Dubovik, et al. Maxwellian Analysis of Reflection and Refraction R.D. Prosser, et al. Solutions of Maxwell Equations for a Hollow Curved Wave Conductor N. Bashkov, A. Tchernomorov. Maxwell's Equations Directly from the Dynamics of Point Particles G.N. Ord. Obtaining the Schrodinger and Dirac Equations from the Einstein/KAC Model of Brownian Motion by Projection G.N. Ord. Derivation of the Schrodinger Equation T.B. Andrews. An Appraisal of Stochastic Interpretations of Quantum Mechanics M. Baublitz, Jr. Compatible Statistical Interpretation of Quantum Beats M. Bozic. Stochastic Non-Markov Model of Quantum Mechanical Behaviour S.R. Vatsya. A Fundamental Force as the Deterministic Explanation of Quantum Mechanics B.J. Dalton. A Geometric Approach to the Quantum Mechanics of the Broglie and Vigier W.R. Wood, G. Papini. Stable Orbits as Limit Cycles S. Bergia. The Correspondence Principle: Periodic Orbits from Quantum Mechanics D. Provost. Neutron Interferometric Experiments on Quantum Mechanics G. Badurek. Enigmatic Neutrons V.K. Ignatovich. Experiments to Test the Reality of De Broglie Waves J.R. Croca. Preselected Quantum Optical Correlations M. Pavicic. Apparent Contradiction in EPR Correlations L.C. Ryff. The Wave- particle Duality E. Bitsakis. Quantum Mechanical Tunneling in a Causal Interpretation M. Clarkson. Quantum Uncertainty, Wave-particle Duality and Fundamental Symmetries P. Rowlands. On the Contradiction between Quantum Mechanics and Relativity: a Superluminal Quantum Morse Telegraph A. Garuccio. Incompatibility between Einstein's Relativity and Lorentz's Equations P. Marmet. On Self-Interaction and (Non-)Perturbative Quantum GRT H.-H. von Borzeszkowski. Classical Physics Foundations for Quantum Physics L. Motz, D.W. Kraft. Inertial Transformations: A Review F. Selleri. The Lorentz Invariance Revisited M. Surdin. A New Type of Massive Spin-One Boson: And Its Relation with Maxwell Equations D.V. Ahluwalia. Implications of Extended Models of the Electron for Particle Theory and Cosmology E.J. Sternglass. The Takabayasi Moving Frame, from the A Potential to the Z Boson R. Boudet. The Nature of the Cosmological Redshift M. Moles. A Quantum Digital Theory of Light N.V. Pope. Toward a Comprehensible Physical Theory: Gravity and Quantum Mechanics H. Yilmaz. Hidden Background Field and Quantum Non-Locality R. Ramanathan. Einstein-Podolsky-Rosen Correlations within Bell Region R. Horodecki. Electromagnetic Gauge as Integration Condi
Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.
Maxwell's equations describe the interactions of the electromagnetic field at a macroscopic level. In the 1920s, Louis DeBroglie demonstrated that every moving particle (including an electron) has a wave nature, and we know from Einstein that every wave has a particle nature, which we call the photon. Later in the 1930s, Paul Dirac's development of the famous Dirac equation showed the quantum nature of the electron at relativistic speeds. Then in 1948 Richard Feynman and Julian Schwinger extended these concepts in the development of quantum electrodynamics which gives a full accounting (although a very strange one) of how an electron can borrow energy from the vacuum of space and return it legally as long it does so within limits of the uncertainty principle.
Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, momentum spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Dirac equation the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors. In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In the presence of a potential the momentum components cease to commute with each other. To neutralize this effect, the Schrödinger equation is supplemented by several equations with mixed partial derivatives on coordinates. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant. This novel equation permitted the construction of an actually invariant procedure for the second quantization of the fermion field in spinor coordinate space. Furthermore, it is demonstrated that the field operators are a combination of plane waves in spinor or vector space, with the coefficients of which being pseudospinors or pseudovectors. Each of these pseudovectors or pseudospinors corresponds to one of the particles presented in the theory of electrodynamics. Furthermore, each plane wave possesses an additional coefficient in the form of a creation or annihilation operator. In vector space, these operators commute, whereas in spinor space they anticommutate. The paper presents the spinor and vector representations of the field operators in explicit form, comprising sets of 16 pseudospinors or 4 pseudovectors corresponding to particles represented in electrodynamics. An explicit form of the symmetric traceless tensor with spin two, zero mass and two polarizations is presented, which can serve as a model of the graviton. The results obtained may prompt changes in some aspects of the construction of Feynman diagrams. Among other things, it presents a purely mathematical derivation of Maxwell's inhomogeneous equations without reference to empirical data on the action of electric current, which is usually referred to when deriving equations. Section 4 presents Einstein's inhomogeneous equation, which features the Riemann tensor rather than the Ricci tensor, with the energy-momentum tensor of a charged particle having four indices rather than two. In the case where a particle of matter has a charge, another Riemann tensor is added to Einstein’s equation, in addition to the usual Riemann curvature tensor, which describes the additional curvature created for a charged particle by an electromagnetic field.