Copyright Harold Aspden, 1987


This is an article by H. Aspden which appeared in The Toth-Maatian Review, v. 5, No. 4, January 1987 at pp. 2827-2833.

Abstract: One of the most basic questions in physics is whether there is a degenerate form of the electron, a charge of smaller mass than that of the electron. If there is then it is likely to be a primary constituent of the background field medium we recognize as sustaining electric displacement, namely the aether. This paper discusses the evidence indicative of the existence of such a particle, a sub-electron, having an effective mass 1/24.52 that of the electron.


If there is a charged particle of smaller mass than the electron why has it not been discovered? Can it be that it exists, but is only evidenced indirectly? We believe that an aether exists, but cannot grasp hold of it. Its existence is inferred by indirect evidence, such as the need to explain electric displacement current and energy storage in a vacuum field. Perhaps the aether is elusive because it is composed of something equally elusive. The sub-electron may be the primary constituent of the medium permeating all space, set in a lattice array in a continuum charge of opposite electric polarity so as to constitute a medium neutral overall. If this is so, then what are the properties to be looked for in order to confirm this hypothesis?

Firstly, one must expect the space metric to have a structure and determine, by its geometry, the value of the dimensionless fine-structure constant 2(pi)e2/hc. Here e is the electric charge of the sub-electron and c is the speed of light, a property accepted as set by the vacuum medium. Logically, therefore, the constant h, Planck's constant, which combines with e and c to give a dimensionless quantity, becomes a likely candidate for interpretation in terms of vacuum structure indicative of the existence of the sub-electron.

Secondly, if the electron can become degenerate and transform into a sub-electron, the reverse process should be possible. Therefore, we should be open to the possibility that an electron might exchange its energy with that of the sub-electron, so that, in effect, they change places spontaneously. This is a process which conserves energy and involves no electrodynamic disturbance, but their centre of mass is changed so there is an inertial effect. If the sub-electron is a hidden particle in the vacuum metric then this action would constitute a vacuum fluctuation and the process would soon be repeated in the reverse sense to preserve equilibrium.

All this is hypothetical until we can build some substance into the argument and show, for example, that several different phenomena can all be explained by appeal to the sub-electron and that the quantitative features of these phenomena all indicate the same mass property for the sub-electron. It will be seen that the sub-electron can be justified by diverse physical argument and that the evidence supports it having an effective mass 1/24.52 times that of the electron. Its mass mo is, therefore, 0.0408m, where m is electron mass.


When a spherical particle is in an incompressible medium of fluid form and has exactly the same mass density as that medium, its motion through the medium involves a kinetic energy corresponding to it having an effective mass of half its intrinsic mass. This is standard hydrodynamics. One cannot expect the vacuum to comply with hydrodynamic theory in every respect, but it is a guide to a possible property of the sub-electron. If this sub-electron is degenerate in form it will be in equilibrium with the surrounding medium, meaning that its pressure developed by repulsion of its charge will be uniform both inside the charge body of the sub-electron and in the surrounding space. Our expectation is that, unlike normal matter particles, the sub-electron will exhibit only half the mass derived from the E=Mc2 formula. In terms of its effective mass mo, this allows us to write E=2moc2 for the sub-electron, because its mass in a non-pressurized medium or true vacuum would be 2mo.

The argument just presented warrants investigation to see if the anomalous factor of 2 governing the gyromagnetic ratio of certain fundamental particles in spin is attributable to a similar process set up by a local equilibrium in the self-radiation field of the particle. In a sense 'spin' may mean a confined motion of the charge centre in relation to a standing wave energy set up in the local field, with the result that translational motion exhibiting mass M may correspond to a spin motion of effective mass M/2. The magnetic moment developed by a given spin angular momentum will be double that exhibited by a motion of the full mass M. The anomalous gyromagnetic ratio of 2 need not be quite so mysterious as we are led to believe from conventional Dirac theory based on relativistic formalism.

Readers interested in taking these thoughts further may find it useful to refer to Honig's recent discussion of the fluid model electron [W.M. Honig, 'The Quantum and Beyond', Philosophical Library, N.Y., pp. 87-93; 1986] or the electromagnetic reaction theory for the factor 2 proposed by Aspden ['Electromagnetic Reaction Paradox', Lett. Nuovo Cimento, v. 39, pp. 247-51; 1984] and further supported by analysis of the first principles of charge interaction in a later work [H. Aspden, 'Unification of Gravitational and Electrodynamic Potential Based on Classical Action-at-a-Distance Theory', Lett. Nuovo Cimento, v. 44, pp. 689-693; 1985].


The more direct evidence of the sub-electron mass property comes from the derivation of the relationship:

hc/2πe2 = 216π(mo/m)1/2 ..........(1),
(m/2mo)3 = 1843 ...........(2),
From this hc/2πe2 is found to be 137.0359 and mo/m is 0.04078.

A recent derivation of equation (1) was presented by Aspden ['Boson Creation in a Sub-Quantum Lattice', Lett. Nuovo Cimento, v. 40, pp. 53-57 (1984)] and the earlier computations proving equation (2) were reported by Aspden and Eagles ['Aether Theory and the Fine Structure Constant', Physics Letters A, v. 41, pp. 423-424 (1972)]. Essentially, equation (2) arises from a recognition that the space occupied by a sub-electron must be an odd multiple of that occupied by the electron. The mass of the electron is inversely proportional to its charge radius and the corresponding 2mo term for the sub-electron is similarly proportional to charge radius. For a suitable transformation in which the volume displaced by charge is conserved it takes 1843 electrons and positrons to fill the volume of one sub-electron, meaning that electron-positron creation demanding the energy quantum of the order of that of the proton mass is needed to achieve such a resonant transformation.

The 1843 number is the nearest odd integer that assures a non-negative potential in the dynamic state of the structured vacuum medium. This is the subject of the paper by Aspden and Eagles just referenced. So far as equation (1) is concerned this is easily derived. The outline method involves taking the Planck radiation formula E=hf as a contracted statement of two equations. One equation says that, because the vacuum has the properties of a two-dimensional linear oscillator and stores energy E in proportion to angular momentum, there has to be something spinning to balance this angular momentum. The other equation relates this angular momentum to the moment of inertia of the spinning unit of the structured lattice and says that waves are set up as the unit rotates, the waves having the frequency f, which is indirectly proportional to energy E. The natural oscillation frequency of the vacuum medium is that at which electrons and positrons materialize, namely mc2/h. The derivation of equation (1) comes from determining the form of the spinning unit as the smallest symmetrical three-dimensional unit of a cubic lattice, with a sub-electron at its lattice sites and at its centre.

The author's theory of the photon is of long standing, but it is not well known. It is inappropriate to dwell upon it here, in view of the referenced publications, but it is mentioned that it was presented to a recent NATO Advanced Research Workshop on Quantum Theory [H. Aspden, 'The Theoretical Nature of the Photon in a Lattice Vacuum', NATO Advanced Research Workshop on Quantum Mechanics, Proceedings of Conference at Bridgeport, Connecticut, June 23-27, 1986, published in NATO ASI Series B: Physics Vol. 62 by Plenum (1987) at pp. 345-360] and the fact that the theory gives a theoretical value for hc/2πe2 to one part per million precision accord with its measured value was the subject of a recent comment in a review by Petley [B. W. Petley, 'The Fundamental Physical Constants and the Frontier of Measurement', Adam Hilger, Boston, pp. 161-163 (1985)]. The theory forms the basis of the statement that the mass of the sub-electron is 0.04078 times that of the electron. This paper now addresses other evidence of the sub- electron mass.


The energy needed to remove the electron from the lowest K orbit in the hydrogen atom is well known from physics texts to be equal to its kinetic energy E in a Bohr orbit, which is:

E = α2mc2/2 .......... (3),
where α is the fine structure constant (1/137), the reciprocal of the expression formulated in equation (1) above. This energy is 2.18x10-11 ergs, equivalent to a temperature T found by dividing by Boltzmann's constant, 1.38x10-16, to be 158,000 K.

If, however, we admit that the natural collision processes which occur in hydrogen under intense pressure and high temperature reduce this temperature threshold, then the Sun's temperature of about 6,000 K becomes explicable. This is somewhat hypothetical. It is, however, quite interesting to imagine the process discussed above, where it is suggested that an electron and a sub-electron might exchange places transiently. Putting mo into equation (3) instead of m, reduces T by the factor 24.52, from 158,000 K to 6,400 K, a quite representative value of the Sun's temperature. Accordingly, indirectly, we have evidence here that the sub-electron might exist and could play a very fundamental role in stellar properties.


To support what has just been said we will now consider an unexplained but curious fact of astrophysics. Wesson [P. S. Wesson, 'Clue to the Unification of Gravitation and Particle Physics', Physical Review D23 (8), pp. 1730-1734 (1981)] has established empirically that astronomical bodies obey the formula relating angular momentum J and their mass M and given by:

J = pM2 ............ (4),
where p is a constant of approximately 8x10-16 in cgs units. Strictly, this expression seems to apply where two similar bodies form together as a kind of binary pair.

To test the sub-electron theory we take the temperature T of 6,400 K as giving the mean energy (3/2)kT of the free electron, k being Boltzmann's constant. Then we argue that at the moment when two spherical bodies of mass M and radius r separate, their distance between centres is 2R. Therefore, the balance between gravitational attraction GM2/(2R)2 and centrifugal force MV2/R gives GM4 as equal to 4(MVR)2(M/R), so that:

J = MVR = pM2 ............(5),
p2 = G/4(M/R) ............(6).

To find M/R we note that free electrons, like molecules in a gas, have three degrees of freedom and that their mean energy is (3/2)kT. In relation to the excitation energy of the hydrogen atom we used kT because there are only two degrees of freedom and because hf, as the energy quantum, is found empirically to relate to kT in the exponential distribution formulated by Planck.

Provided an astronomical body composed of hydrogen has a temperature less than T=6,400 K, there should be no free electrons to be driven off by their thermal agitation. Above this temperature the energy (3/2)kT of the electrons can overcome the gravitational potential GMm/R, where m is electron mass, and move well away from the body, leaving it with a positive charge. This prevents the escalation of this process but it also arrests the build-up of the body to larger size, because protons in the surrounding plasma are repelled by the charge and the effect overcomes gravitational attraction. We see, therefore, that M/R is fixed as (3/2)kT/Gm and put this into equation (6) to find Wesson's constant p. Thus:

p = G(m/6kT)1/2 ........... (7)

To calculate p, we now put G=6.67x10-8, m=9x10-28, k=1.38x10-16 and T=6,400. The resulting value of p is 8.7x10-16, which is virtually the empirical value discovered by Wesson, thereby confirming our theory.

The theory has the further merit of explaining why the two bodies separate. As a binary star system they may heat very slightly above the critical temperature and acquire strong mutual repulsion owing to their positive charge and electron emission. The effects of gravitational attraction are weakened by this and the system acquires a kind of stability, but the mass and angular momentum of each body is unaffected.

However, our objective of deriving some evidence for the properties of the sub-electron is met, even in these remote cosmological systems. Our attention now turns to the microcosmic world of elementary particles.


To the author the neutral pion is somewhat of an enigma. The author has developed a theoretical basis for the muon, the pion, the kaon and other mesons, explaining their mass ratios in terms of electron mass. Also the proton, neutron and deuteron have yielded to the theory, but the neutral pion, which is 264.1 times as massive as the electron has been a mystery. Relevant references are [H. Aspden, 'The Mass of the Muon', Lett. Nuovo Cimento, v. 38, pp. 342-344 (1983)], ['The Nature of the Pion', Spec. Science and Tech., v. 8, pp. 235-239 (1985)]. [H. Aspden, 'The Theoretical Nature of the Neutron and the Deuteron', Hadronic Journal, v. 9, pp. 129-136 (1986)] and [H. Aspden, 'Meson Production based on the Thomson Energy Correlation', Hadronic Journal, v. 9, pp. 137-140 (1986)].

It is therefore interesting to find that the neutral pion has revealed itself in the following theoretical analysis. The argument begins by considering the interchange of energy and so, state, between the electron and the sub-electron and looking for a standing wave resonance mode that develops between the two particle forms. Then we specify that a pair of oppositely charged particles can have a quasi-stable but short-lived interaction with the electron and the sub-electron. Together they form a neutral entity, which we shall find we can identify as the neutral pion.

As mentioned already, the earlier theory indicated that the spherical volume of the sub-electron charge was 1843 times that of the electron. This means that its radius is (1843)1/3 times that of the electron. Now, from independent theory concerned with wave resonance effects [see, for example, H. Aspden, 'The Muon g-factor by Cavity Resonance Theory', Lett. Nuovo Cimento, v. 39, pp. 271-275 (1984)], there is reason to suspect that standing wave conditions can be set up around the charge periphery and develop resonance as between charges connected with disturbances propagating around the charge at the speed of light.

The task, therefore, was to find the likely resonance as between the electron and the sub-electron. The method adopted is to suppose that there are X standing wave nodes on the electron charge taken around a circle centred on the charge. Then, in traveling through N wave nodes around the electron, a disturbance will take N/X units of time. The resonance requires this to equal the time required by a disturbance traveling through Y wave nodes around the sub-electron, which has N standing wave nodes.

Thus: XY becomes NZ(1843)-1/3. Note that XY has to be less than NZ in the ratio of the radius of the electron charge to that of the sub-electron. X, Y, Z and N are all integers and, in order to assure a definitive resonance state not conducive to setting up harmonics, it is stipulated that at least three of these numbers must be prime. The author has searched for the best combination of numbers giving close equality in the above equation and discovered that the best combination, without going to excessively high values, is X=19, Y=139, Z=1619 and N=20. This has the advantage also that, in the transition from electron to sub-electron, the number of standing wave nodes only changes by one.

It may be verified that this combination satisfies the equation to about 4 parts in a billion. The numbers 19, 139 and 1619 are all prime and 19 differs from 20 by unity. These resonance criteria will, therefore, be the most likely to prevail as between the two most fundamental particles in nature.

We now look for a particle that can exchange state transiently with the sub-electron so as to have ideally the same number N of standing wave nodes but which resonates with both the electron and the sub-electron in traversing XY wave nodes. This means that its radius (or the inverse of its mass) must be 1/Z times that of the sub-electron or N/XY times that of the electron. In other words, its mass must be XY/N times that of the electron mass m. This is (19)(139)/(20) or 132.05 units of m.

This state of affairs can be interpreted by saying that a charge pair of combined mass (264.1)m can exist and that it may transiently cycle between the two states as one member of the pair assumes the sub-electron form and the other member absorbs the balance of the energy. The result is a neutral entity of total mass (264.1)m, which happens to be exactly the mass of the neutral pion. Hence the theory is well supported.

Should the reader be sceptical, then we go a step further and explain the other property of the neutral pion using the same theory. Its lifetime is 8x10-17 seconds. The theory tells us that, because the neutral pion oscillates between two states, it presents, as a main target for decay, a volume some 1843 times that of the electron, the volume of the sub-electron charge, for half of any period of time, because it spends equal time in each state. Thus its lifetime will be 921 times shorter than that of the electron. Now, the electron is not believed to have a finite lifetime, but it does have one. It decays in 0.75x10-13 seconds. The lifetime has been rigorously calculated [H. Aspden, 'The Finite Lifetime of the Electron' , Spec. Science and Tech., v. 7, pp. 3-6 (1984)] using the same theoretical method as that involved in deducing equations (1) and (2) and found to be 0.75x10-13 seconds. It follows, therefore, that the same theory leads to a lifetime for the neutral pion of (2/1843) times this or 8x10-17 seconds, in full accord with observation.


The case for the sub-electron has been presented by showing how a number of phenomena lacking explanation in conventional physical theory, all become explicable with precise results on the basis of its assumed existence. It has an effective mass 0.04078 times that of the electron.

It is debatable whether the effective mass of positive holes in semi-conductors may in some way reflect the transitional states of electrons and sub-electrons. The latter belong to the unseen aether lattice and removal of a sub-electron might be manifested as a positive hole. Experiments on p-type germanium crystals have given effective masses m* of positive holes as m*/m=0.04 and m*/m=0.3, whereas n-type germanium was found to sustain values of m*/m=0.11 [W. Ehrenberg, 'Electric Conduction in Semiconductors and Metals', Clarendon Press, Oxford, pp. 145-146 (1958)]. In a sense, the semi- conductor lacks the simplicity of the isolated particle in the structured vacuum medium, so analysis of such data by the author's theory is unprofitable. Being unconventional in its technique it rests on the successful theoretical determination of precise values of measured quantities, some with part per million precision. Therefore, it has seemed best to seek out the indirect evidence of the existence of the sub-electron.

One question that the author has faced up to is why electrons exist all, if the sub-electron is the natural degenerate form. The answer to this is believed to be dependent upon the proton and the derivative atomic nucleus. Just enough electrons exist to keep a neutral overall balance with the positive charge in the proton form and atomic nuclei. The surplus energy that has not found a fully dissipated destiny in the vacuum lattice, the world of the sub-electron and the neutralizing vacuum background continuum, materializes as protons. Larger particle forms cannot be stable because they would soon encounter the sub-electron and they would have enough energy to generate 1843 electrons and positrons from the sub-electron. The ongoing annihilation of electrons and positrons causes the energy to start again in its effort to create protons, which are stable because their mass is 1836 times that of the electron, that is, below the threshold set by the 1843 factor.

Clearly, the theory outlined involves speculation and it gives plenty of scope for one's imagination. For this reason, and so as to follow a path which is meaningful and not fanciful, the author has taken it to be essential also for any idea to have more than one such outcome. This has been demonstrated above in discussing the Wesson constant, and in deducing the neutral pion mass and its lifetime. It is hoped that the reader will find interest in the case for the sub- electron and be stimulated to probe other secrets of Nature that might bear out the views offered in this paper.