Transformation for the energy flux of the electromagnetic wave

Dmitri L. Khokhlov, R. Korsakov St

Published Jan 1, 2010• 1 citation

Abstract

The quantum mechanical model of electromagnetic waves is considered, in which the photon, as a particle, propagates with the speed of light, while the wave function of the photon spreads out with an infinite speed. The Lorentz transformation for the energy flux of electromagnetic wave is obtained while assuming the Galilei transformation for the space and time. The energy of the electromagnetic wave also follows the Lorentz transformation with the volume restricting the wave train not following any transformation.

Related papers

Linear relationship between frequency and energy of a wave train

Peifeng Wang

We demonstrate that, under Lorentz transformation, the frequency and the energy of an electromagnetic wave train form a linear relationship, emulating the equation of photon energy E = ℏ ω . This shows that wave-particle duality of light is compatible under space time transformation.

May 3, 20190 citations

Spatial wave functions of photon and electron

Dmitri L. Khokhlov

The quantum mechanical model of the photon and electron is considered. The photon is conceived of as a particle moving with the speed of light which is accompanied by the wave function of the photon spreading out with an infinite speed. The wave function of the electron is introduced in terms of virtual photons tied to the electron. A description of electrostatic and magnetostatic interactions is given through the wave functions of electrons. The approach provides an explanation of the results of recent experiments measuring the speed of propagation of the bound magnetic field.

Journal of Applied PhysicsDec 1, 20101 citation

Spatial and Temporal Wave Functions of Photon

Dmitri L. Khokhlov

The quantum mechanical model of electromagnetic waves is considered. The photon as a particle moves with thespeed of light with respect to the CMB frame. The spatial wave function of the photon is introduced as a waveaccompanying the photon, with an infinite speed of spreading throughout the whole space at some moment oftime. The temporal wave function of the photon emitted (absorbed) by the electron is defined through thetemporal wave function of the electron (virtual photon associated with the electron) at some point of space. TheMichelson-Morley experiment is studied with use of both the spatial and temporal wave functions of photon, andthe null result being obtained in both the cases.

Applied Physics ResearchOct 19, 20108 citations

Unitary Relativistic Quantum Dynamics and Electromagnetic Field

In this chapter, we consider a quantum particle wave function with a bound spectrum of velocity c, and obtain the relativistic momentum based on the group velocity of this wave function. With a space-time isometry condition, the Lorentz transformation and the relativistic dynamics were obtained. Considering a field interacting with a quantum particle as a four-vector conjugated to the space-time vector in the time-dependent phase, we obtain the Lorenz force and the Maxwell equations. It is interesting that only the Ampère-Maxwell equation of a magnetic circuit is specific to the electromagnetic field, while the other equations are general for a field interacting with a charged quantum particle. Considering the time-dependent phase of a quantum particle interacting with an electromagnetic field with a space-time homogeneity condition, we obtain Lorentz transformations for this field. For a quantum particle at a non-relativistic velocity, we obtain a wave function with a very rapidly-varying factor, of a frequency proportional to the rest energy of this particle. From the Schrödinger equation of a particle with a relativistic Hamiltonian, we obtain a split of the wave function into four components, describing a proper rotation of this particle with an angular momentum called spin (Dirac’s relativistic electron theory). Moreover, we also calculate electron potential in the magnetic field, and two-electron interaction potential.

BENTHAM SCIENCE PUBLISHERS eBooksMay 8, 20170 citations

Photon structure

Solomon Khmelnik

The so-called. wave-AND-particle - WAP, which is a standing wave in the volume of a cube. On the sides of the cube, the flux is zero, i.e. the cube does not emit energy. However, there are magnetic and electrical strengths on the sides of the cube. It is shown that such HIV, having received a quantum of energy, becomes a quantum of energy flow and flies at the speed of light. Such a representation allows one to remove the contradictions between Maxwell's equations and the quantization of the energy of electromagnetic radiation, associated, firstly, with the fact that the energy transferred from light to atoms depends only on frequency, and, secondly, with the fact that it is impossible to find the wave equation for a photon.

Nov 28, 20210 citations

Are Maxwell's Electromagnetic Equations Probabilistic?

Francesco R. Ruggeri

We have argued in previous notes (1) that the “wave” nature of quantum mechanics follows from the Lorentz invariant for a constant p: A= -Et+px which holds for both a particle with rest mass and a photon. In A, t and x are separated indicating independence which violates the Newtonian view x(t). “A” leads to dA/dx partial = p and dA/dt= -E. Creating eigenvalue equations yields: -id/dx exp(ipx) = p exp(ipx) and id/dt exp(-iEt) = E exp(-iEt). Thus, x and t may be separated. Given that exp(ipx) exists in all of space (because there is no time), it represents a somewhat spatially invariant probability. In the case of a photon, Maxwell showed one may write wave equations for the electric El and magnetic B fields using his electromagnetic equations with no charge or currents.. He showed the wave travels at the speed of light in a vacuum and thus characterized light as an electromagnetic wave. This is not the same statement as exp(ipx) which is a probability wave. One may note that Maxwell’s equations are Lorentz invariant, so the ideas of the first paragraph should hold. In this note, however, we consider the Poynting equation: d/dt partial (.5( eoElEl+1/uoBB)) + 1/uo grad dot El x B = function(charge and current). 1/uo ElxB is considered to be a momentum density. We note Maxwell’s equations contain d/dt partial and d/dx partial, so time and space are considered independent (unlike x(t)), and act on El and B. The presence of charge and current densities breaks spatial invariance i.e. creates local regions. We argue in this note that d/dx and d/dt are generators of translations in space and time. We further argue that Maxwell’s theoretical creation of a photon follows from introducing spatial invariance into the problem, i.e. removing all charge and current densities. Spatial invariance in Newtonian mechanics, however, is associated with a constant i.e. a constant speed and momentum and equal probability to be at any x. Given that d/dx and d/dt appear, one has a function of space and time which seems to be completely at odds with spatial invariance and the idea of a constant momentum. We have argued in (2), however, that constant motion, even though represented by v=constant, is associated with the force that created the momentum, and this manifests itself in a spatial density which is probabilistic. Thus the presence of d/dt and d/dx in Maxwell’s electromagnetic equations, even when charge and current densities are removed, implies the same thing. Thus we argue that Maxwell’s electromagnetic equations are probabilistic. We investigate these ideas in this note. We further argue that it is spatial invariance, together with the presence of d/dx partial which yields the periodic form exp(ipx). Thus it is not a coincidence that wave equations appear for El and B.

Jan 26, 20230 citations