A theory elaborated by the author on revised quantum electrodynamics (RQED) is elucidated in a condensed form on special important points. The latter concerns the basic electromagnetic field equations in a vacuum state, the connection of this state with the Zero Point Energy (ZPE), the procedure of quantization, steady states of particle models, the concept of the individual photon, and examples on experimental support of the theory.
A revised quantum electrodynamic theory (RQED) on the vacuum state has earlier been elaborated by the author, as described in a monograph [
The conventional electromagnetic field equations have been used as a guideline and basis for proper inter- pretation, also of a quantum electrodynamical approach as stated by Schiff [
The vacuum is however not a state of empty space. The solutions of the harmonic oscillator do not only lead to the Planck electromagnetic wave energy, but also to a lowest nonzero energy of one-half quantum per state, i.e. the Zero Point Energy (ZPE). The vacuum state therefore includes fluctuations part of which also carry electric charges, as pointed out by Abbott [
The low-frequency part of the ZPE fluctuations has thus to be accepted as an experimental fact, but there exists a problem with their high-frequency part. As demonstrated by Terletskii [
To overcome these difficulties, the author [
The restrictions and shortcomings of the conventional field equations governing the vacuum state can be eliminated by including the ZPE effects into the theoretical foundation, thereby breaking the symmetry between E and B, and introducing an extra source term. To preserve the Lorentz and gauge invariance at the same time, this is done by including a four-current
Since J has to vanish when there is no charge density, the final form of the four-current density becomes [
where c is a velocity vector having a modulus equal to the velocity constant c of light. In three-space the extended electromagnetic field equations of the vacuum state then become
where
The nonzero electric field divergence of Equation (6) acts here somewhat like a “hidden” variable, removing the condition
The solutions which come out of Equations (1)-(6) for models of particles and waves include nonzero integrated rest masses, net electric charges, and spin. There are thus configurations with nonzero local electric charge density which after spatial integration result both in nonzero and zero net electric charge, at the same time as both the local and integrated energy densities and corresponding masses become nonzero and finite.
To convert the present approach into a quantized electrodynamic theory, the quantum conditions could be included into the deductions already from the outset. Here we shall instead make a short-cut and simplification, by first determining the general solutions of the basic field equations, and then imposing relevant quantum conditions. This is at least justified by the fact that a quantization of the general electrodynamic field equations merely results into the same equations in which the potentials and currents are replaced by their expectation values as shown by Heitler [
Here we finally notice that the conventional symmetric field equations for an empty vacuum space lead to imposed restrictions which therefore cannot be removed by quantization.
A characteristic feature of RQED, not being available from conventional theory on the vacuum, is the steady states obtained from Equations (1)-(6) in the case of no explicit time dependence. This leads to models for particles being at rest. In the case of spatially limited axisymmetric configurations, spherical coordinates are then introduced, and the magnetic and electrostatic potentials as well as the charge density can all be derived from a generating function [
For a divergent radial part models can thus be elaborated in a spherical frame of coordinates
where
with
where
For a convergent radial part models can be elaborated for neutral particles, i.e. those with vanishing net integrated charge. This case does not require a revised renormalization procedure, and it is associated with a finite and defined characteristic radial dimension.
One example is given by the Z boson considered by the author [
The particle discovered at CERN [
At this stage it may be argued that this composite particle solution is not the particle observed at CERN, and that the latter also has been considered in terms of interactions with the quarks of other elementary particles. This leads to two points of discussion:
1) It may be questioned if there can exist two non-identical particles which still behave like “twins”, in possessing the same basic properties of vanishing charge and spin as well as rest masses of the same order of magnitude.
2) The present theory has so far been directed towards individual and free particles. Interaction with bound particles such as quarks, and the related strong forces, have not been considered. But in principle such consi- derations could equally well become applicable to the present composite model.
According to experimental experience, the individual photon is limited in its transverse directions, and it has a nonzero spin. This implies that a physically relevant photon model should have the form of a wave or wave packet of preserved and limited shape, propagating in an undamped way in a defined direction. A single plane wave has infinite spatial extensions and no spin, and is therefore hardly suitable for an individual photon model. This is instead the case of a cylindrical configuration.
Starting from the basic Equations (1)-(6), the velocity vector then has the form
in a cylindrical frame. For normal propagating modes varying as
Here the phase and group velocities are both equal to v. In terms of a generating function, the fields E and B are obtained from the basic equations. The normal modes are then superimposed into an axisymmetric wave packet of narrow line width, having a main wave number
and a frequency
and there is an equivalent “rest mass”
being associated with the transverse velocity component of C in Equation (10), and with a spin of the magnitude
These results are summarized as follows [
1) A nonzero spin does not have to be added to the system as an extra ad hoc assumption, but becomes an integrated property obtained from the field equations.
2) The concept of Lorentz invariance is extended to apply not only to a plane wave, but also to a cylindrical one. This is done by replacing the scalar velocity c by the velocity vector C.
3) The existence of a nonzero spin is obtained at the expense of a slight reduction in the velocity v of propagation, from c to
4) For relevant radial extensions of an axisymmetric wave packet, this reduction becomes extremely small. It is first appearing in the ninth or tenth decimal of v, as given by Equation (12).
5) A nonzero spin is related to a nonzero “rest mass”. But the latter does only need to become extremely small to satisfy relevant conditions on the present photon model.
6) The radial extensions of the photon model become limited. In its turn, this results in such properties as needle radiation and a combined wave-particle behaviour, as well as in increased understanding of the photoelectric effect and two-slit experiments.
The present RQED approach is likely to lead to several new possibilities within fundamental physics, being beyond the theories of the Standard Model, Dirac, and Higgs, and including more applications. Examples of consistency with experimental facts are as follows:
1) The present field equations result in steady particle models having nonzero electric charge, mass, and spin.
2) The electron is point-charge-like and has very small radial extensions.
3) The deduced minimum electric charge agrees with the observed elementary charge within an uncertainty of only a few percent.
4) The charged leptons are prevented by the included magnetic field from “exploding” under the action of their electrostatic eigenforce.
5) The deduced characteristic radial extension of the Z boson agrees with its so far estimated order of magnitude.
6) The composite unstable and electrostatic particle obtained from the present theory has at least the same basic properties of vanishing charge, vanishing spin, and order-of-magnitude mass as that detected at CERN.
7) The model of the individual photon has a nonzero spin. It also contributes to the understanding of the wave-particle nature, needle radiation, the photoelectric effect, and of two-slit experiments.
The future will show what is relevant and not relevant of these considerations.
BoLehnert, (2015) Some Elucidations of the Theory on Revised Quantum Electrodynamics. Journal of Modern Physics,06,1695-1700. doi: 10.4236/jmp.2015.611171