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? __

(Submitted on 14 Dec 2000 (

v1), last revised 17 Dec 2000 (this version,
v3))

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.

Comments:

12 pages, LaTeX

Subjects:

Classical Physics (physics.class-ph)

__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 leads to the quadratic: B=([A-2]/2A)±√[A²+4A])={(½-1/A)±√(¼+1/A)}.**

**This defines a distribution of B=(v/c)² velocity ratios
in mo.AB=μoe²[v/c]²/8pRe.**

**mmagnetic=μoe²[v/c]²/8πRe=mo.AB=½me.(v/c)² then finestructures ****mmagnetic in
the relation moA=½me and allows correlation between
the relativistic and kinetic restmass mo and the effective electron groundmass me (say).**

**In particular me =2Amo and
is moA for A=½ AS the NEW minimisation condition.**

**In string parameters and with me in *units, the following is found:**

**moA=30e²c/e*=½me=4.645263574x10^-31 kg*.**

**This implies, that for A=1, mo=½me, where me=9.290527155x10^-31 kg* from the prequantum algorithmic associations,
based on the magnetic constant defining the Classical Electronic Radius.**

**As B≥0 for all velocities v, bounded as groupspeed (not
de Broglie Phasespeed always >c) in c for which B=1; a natural limit is found for the B distribution at A=½
and A=∞.**

**The electron's restmass mo so is binomially
distributed for the B quadratic.**

**Its minimum value is half its effective mass me and as given in ****melectric=kq²/2Rec²=Ue/c²=½me for A=½
and its maximum for A=∞ is the unity v=c for B=1.**

**The X-root is always positive in an interval from 0 to 1 and
the Y-root is always negative in the interval from -3 to 0. **

**For A=½: B=-3/2±3/2 for roots x=0 and y=-3;**

**for A=¾: B=-5/6±√(19/12) for roots x=0.425 and y=-2.092;**

**for A=1: B=-½± ½√(5) for roots x=X and y=Y;**

**for A=∞: B=½[-]±½[+] for roots x=1[-] and y=0[-];**

**Letting B=n, we obtain the Feynman-Summation and the Binomial
Identity gives the limit of A=½ in:**

**A=1/2 - B{3/8 - 5B/16 + 35B²/128 -...} and as the nonrelativistic
low velocity approximation of E=mc² as KE=½mov².**

**But the FRB or Functional-Riemann-Bound
in Quantum Relativity (and basic to the pentagonal string/brane symmetries) is defined in the renormalisation
of a wavefunction ****B(n)=(2e/hφ).exp(-alpha.T(n)),** exactly
about the roots X,Y, which are specified in the electron masses for A=1 in the above.

**The unifying condition is the Euler Identity: XY=X+Y=i² =-1=℮^iπ.**

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

**Tony B.**

**
**

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