Hi All!

Allow me to raise a most important issue in quantum mechanics, namely the stability of the electron and the nature of its mass. QED postulates the electron as a point-particle of a size smaller than 10^-18 metres; yet the extremely successful calculations in Quantum ElectroDynamics or QED are required to 'scale up' the electron to its 'classical' size of so 3x10^-15 metres.

Postulating a 'Dirac Sea' of 'virtual particles' within this classical electron radius Re=ke²/mec²; the electron should be unstable due to the repulsion of the 'virtual electrons' of that 'uncertainty soup'.

The following references to the Canadian phycisist Vesselin Petkov further detail the scenario and its avenue of resolution in the form of a correct calculation of the electromagnetic mass of the electron.

I highly recommend the two papers, as they also describe the equivalence principle between gravitational- and inertial mass and should put to rest the 'varying c' lightpath questions which Petkov nicely analyses in the original 'Einstein Elevator' thought experiment in the 'Acceleration-paper'.

I shall then add and show that what the experimenters measure as the restmass of the electron is actually a REDUCED EFFECTIVE electronmass.

So the electron's mass is purely electromagnetic and via the equivalence principle it links the classical electron radius to its self-energies of its electric field and its magnetic field.

Finally, a relationship to the string parameters in Quantum Relativity shall show that in those parameters, the stability of the electron is assured in the electron's energy incorporating the experimental mass defect in the (v/c) ratio assuming its unitary value.

In other words, the higher dimensional electron is gauge-photonic, so always moving at lightspeed c, say as manifested in its spin angular momentum h/4π=λo/4πe*c=λo/8πRec³=360.10^-10/8π.c³.

This last expression is highly significant in Petkov's side-notes below and seems to relate to a so called 4-atomism advanced concept of the discretization of spacetime.

"Such a possibility follows from a work [37] which has received little attention so far. By bringing the idea of atomism to its logical completion (discreteness not only in space but in time as well - 4-atomism), it is argued in that work that a quantum-mechanical description of the electron itself (not only of its state) is possible if
the electron is represented not by its worldline (as deterministically described in special relativity) but by a set of four-dimensional (4D) points (modeled by the energy-momentum tensor of dust - in this case a sum of delta functions) scattered all over the spacetime region in which the wave function of the electron is different
from zero. The 4-atomism hypothesis gives an insight into two questions relevant to the issues discussed here:
(i) how an elementary charge can have ”parts” and still remain an elementary charge, and

(ii) why there is no stability problem despite that the ”parts” of an electron repel one another. Since, according to the 4-atomism hypothesis, for 1 second an electron is represented by 10^20 4D points (the Compton frequency) at one instant the electron exists as a single 4D point carrying a greater (bare) charge, but for one second, for example, there will be 10^20 such points occupying a spherical shell that manifest themselves as an electron whose effective charge is equal to the elementary charge. If we can observe the electron without interacting with it for, say, 10^-9  s the electron will appear to us as a spherical shell since during the observation time (10^-9 s) the electron is represented by 10^11 4D points appearing and disappearing on the spherical shell. Each charged 4D point feels the repulsion from other previously existing constituents of the electron, but cannot be repelled since it exists just one instant.

Therefore, such a spherical distribution of the electron charge appears to be stable. This hypothesis also appears compatible with the scattering experimental data - the dimensions of the constituents of the electron (its 4D points) can be smaller than 10^-18 m. The 4-atomistic model does not lead to the difficulties of a purely particle and a purely wave models of the electron and may be a candidate for what Einstein termed ”something third” (neither a particle nor a wave).

The electron here actually represents 10^11 4D-points which in a 'bosonic unification' time of order a nanosecond (10^-9 s) would constitute the electron as the Re shell, which is stable.

Our description of the higher dimensional electron justifies this in rendering lightspeed c intrinsic to the action quantum being FINESTRUCTURED in h=λo.10^10/2Rec³ and with λo.10^10/360=10^-22.10^10/360=10^-12 /360=Re describing precisely this 4-atomisation introduced by Petkov.

I shall continue after the Vesselin Petkov references.

Did 20th century physics have the means to reveal the nature of inertia and gravitation?

Abstract: At the beginning of the 20th century the classical electron theory (or, perhaps more appropriately, the classical electromagnetic mass theory) - the first physical theory that dared ask the question of what inertia and mass were - was gaining momentum and there were hopes that physics would be finally able to explain their origin. It is argued in this paper that if that promising research path had not been inexplicably abandoned after the advent of relativity and quantum mechanics, the contemporary physics would have revealed not only the nature of inertia, mass, and gravitation, but most importantly would have outlined the ways of their manipulation. Another goal of the paper is to try to stimulate the search for the mechanism responsible for inertia and gravitation by outlining a research direction, which demonstrates that the classical electromagnetic mass theory in conjunction with the principle of equivalence offers such a mechanism.

Acceleration-dependent selfinteraction effects as a basis for inertia

Vesselin Petkov

Physics Department, Concordia University
1455 de Maisonneuve Boulevard West
Montreal, Quebec H3G 1M8
vpetkov@alcor.concordia.ca
(or vpetkov@sympatico.ca)

http://arxiv.org/abs/physics/9909019

[18] In order to account for the stability of the classical electron Poincar´e [8] assumed that part of the electron mass (regarded as mechanical) originated from forces (known as the Poincar´e stresses) holding the electron charge together and that it was this mechanical mass that compensated the 4/3 factor (reducing the electron mass from 4/3m to m). However, the 4/3 factor, as discussed above, turned out to be an error in the calculations of electromagnetic mass as shown in [10]-[15]. As there remained nothing to be compensated (in terms of mass), if there were some unknown attraction forces (the Poincar´e stresses) responsible for holding the electron charge together, their negative contribution to the electron mass would result in reducing it from m to 2/3m.

This made the stability problem even more puzzling - on the one hand, a spherical electron tends to disintegrate due the repulsion of the different parts of the spherical shell; on the other hand, however, an assumption that there is a force that prevents the electron charge from blowing up leads to a wrong expression for its mass.

Obviously, there is an implicit assumption in the classical model of the electron that leads to such a paradox - it is assumed that at every instant the electron charge occupies the whole spherical shell (see [20]).
[19] D. J. Griffiths, Introduction to Electrodynamics, 2nd ed., Prentice Hall, New Jersey, 1989, p. 439.

[20] It is not impossible for an elementary charge to have a spherical but not continuous distribution. Such a possibility follows from a work [21] which has received little attention so far.

Such a possibility follows from a work [37] which has received little attention so far. By bringing the idea of atomism to its logical completion (discreteness not only in space but in time as well - 4-atomism), it is argued in that work that a quantum-mechanical description of the electron itself (not only of its state) is possible if
the electron is represented not by its worldline (as deterministically described in special relativity) but by a set of four-dimensional (4D) points (modeled by the energy-momentum tensor of dust - in this case a sum of delta functions) scattered all over the spacetime region in which the wave function of the electron is different
from zero. The 4-atomism hypothesis gives an insight into two questions relevant to the issues discussed here:
(i) how an elementary charge can have ”parts” and still remain an elementary charge, and

(ii) why there is no stability problem despite that the ”parts” of an electron repel one another. Since, according to the 4-atomism hypothesis, for 1 second an electron is represented by 10^20 4D points (the Compton frequency) at one instant the electron exists as a single 4D point carrying a greater (bare) charge, but for one second, for example, there will be 10^20 such points occupying a spherical shell that manifest themselves as an electron whose effective charge is equal to the elementary charge. If we can observe the electron without interacting with it for, say, 10^-9  s the electron will appear to us as a spherical shell since during the observation time (10^-9 s) the electron is represented by 10^11 4D points appearing and disappearing on the spherical shell. Each charged 4D point feels the repulsion from other previously existing constituents of the electron, but cannot be repelled since it exists just one instant.

Therefore, such a spherical distribution of the electron charge appears to be stable. This hypothesis also appears compatible with the scattering experimental data - the dimensions of the constituents of the electron (its 4D points) can be smaller than 10^-18 m. The 4-atomistic model does not lead to the difficulties of a purely particle and a purely wave models of the electron and may be a candidate for what Einstein termed ”something third” (neither a particle nor a wave).

What is promisingly original in the 4-atomism hypothesis is its radical approach toward the way we understand the structure of an object. The present understanding
is that an object can have structure only in space. The 4-atomism suggests that an object can be indivisible (structureless) in space (like an electron) but structured in time. Whether or not this hypothesis will turn out to have anything to do with reality remains to be seen, but the very fact that it offers conceptual resolutions to several open questions and goes beyond quantum mechanics (which cannot be discussed in this paper) by predicting two new effects that can be tested makes it a valuable candidate for a thorough examination.

CALCULATION OF THE ELECTRONMASS

The magnetic energy stored in a magnetic field B of volume V for a (n-turn toroidal) current inductor i  for velocity v and selfinduction L is:

Um=½Li²=½(μon²v)(B/μon)²=½B²V/μo and the Magnetic Energy Density per unit volume is then Um/V=½B²/μo.

Similarly, the Electric Energy density per unit volume is: Ue/V=½εoE² say via the Maxwell equations and Gauss' law.

By the Biot-Savart and Ampere Law: B=μoq.v./4πr² and εo=1/c²μo for the E=cB foundation for electrodynamic theory.

So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:

Um=∫{μoq²v²/8πr²}dr = μoq²v²/8πRe.

Similarly, Ue=∫dUe=q²v²/8πεoRe =kq²/2Re=½mec²  as per definition of the classical electron radius and for the total electron energy mec² set equal to the electric potential energy. We term me here the EFFECTIVE electronmass and so differ it from an actual 'bare' restmass mo.

We now define the electric electromagnetic mass as:

melectric=kq²/2Rec²=Ue/c²=½me and consider the electric electron energy to be half the total energy (akin the virial theorem for PE=2KE, say in the Bohr atom's PE=(-)ke²/RBohr = e²/4πεoRBohr = (2)e²/8πεoRBohr =2KE).

mmagnetic=μoe²[v/c]²/8πRe==melectric.(v/c)²=½me.(v/c)² and which must be the KE by Einstein's c²dm=c²(me-mo) and for the relativistic electronmass m=mo/√(1-B) for B=(v/c)².

But we can see, that should one use the measured electron mass from the Re-definition as the electron's restmass, that mmagnetic+melectric=me{½+½(v/c)²}<me, because of the mass-velocity dependency factor B and the groupvelocities v<c.

So we introduce the relativistic restmass mo and set  Constant Amo=μoe²/8pRe  for AB=1/√[1-B] -1.

This concludes this introduction to the electron's missing restmass.

Tony B.