---

This is a reproduction of the text of a booklet written by the author in 1959, published early in 1960. This continuation comprises Chapters 8 and 9 of that work. In the light of his 1998 perspective, some 38 years on from that 1960 effort, the author has added several notes bearing the symbol . These may interest science historians who, hopefully, one day will seek to track how the author’s theory developed over time.

---

8

THE GRAVITATIONAL DEFLECTION OF LIGHT

Preliminary Note
The explanation of the deflection of stellar light by the solar gravitational field involves a consideration of a critical field phenomenon predicted by this aether theory.

The energy of a photon may be transmitted as a forced vibration in the aether. This vibration is set up by imparting the energy h to an aether particle by the action of a force equal to -m(d²x/dt²) which persists while x changes from 0 to x_o, where x is x_osin2. The photon energy velocity is c and as this force does work at the rate -mc(d²x/dt²) the energy of the photon quantity may be found by integrating this expression from t=0 to t=1/4. In this way the photon energy is found to be 2mcx_o. However, this is h, so x_o is found to be h/2mc.

Evidently x_o is a fundamental constant independent of photon frequency. It represents the amplitude of the displacement of an aether particle as it transmits the photon energy. For the particle acceleration to be equated to the photon driving force the photon field V must balance the electrostatic restoring action due to the displacement of the particle in the continuum. The equation of balance is:

If x is limited to the value x_o = h/2mc, V has a limiting value V_o equal to 4x_o or 2h/mc.

This aether theory therefore leads to the prediction of a critical field strength which cannot be exceeded in a wave propagation. The critical electric field becomes, from equation (14), hc/16er², and this may be evaluated from the data presented in Chapter 3. The value of this critical field is 2.21×10¹³ cgs esu.

This critical electric field is very important in wave-propagation phenomena.

---

At this point I need to clarify what was in my mind when I wrote this chapter 8. I had come to realise that, in writing about the theory of gravitation, I was trepassing on territory that had been claimed by Einstein enthusiasts. there was zero tolerance of intruders who thought they could contribute to the theory of gravity without building on the Einstein foundation.

I was also, by then, not a part of the academic world, having ventured into employment in industry at the close of my six years at university. My priorites concerned my career and the technological scene. In October 1959 I had committed to conclude my service contract with my employer, giving three months notice, prior to moving to a managerial appointment with IBM. I had three months in which to write The Theory of Gravitation and get it ready for publication prior to shelving my theoretical research interest and concentrating on my task ahead with my new employer.

I knew that academia would show no interest in what I was about to publish, but it gave me satisfaction to get the work on public record.

To head off possible criticism on the point that Einstein’s theory offered an explanation of the solar deflection of starlight, whereas my theory offered no such explanation, I addressed that issue as Chapter 8. I was confident that my theory for the photon was sound. I had explained the relationship between the energy quanta and frequency that one sees as a photon ‘event’. I had derived a formula for Planck’s constant, the constant that governed that link between photon frequency and energy. I had not explained how a photon moves at the speed of light to convey that energy and so, in its transit from a star, grazing past the sun as it converged on body Earth, came to suffer deflection in its transit.

The first thought here was rather obvious. If energy has mass then that photon must exhibit mass and so be subject to gravity. If, as a kind of particle, it travels in close passage as it navigates the region of space occupied by the sun, then it must be deflected. Travelling at the speed of light it would, even by Newtonian theory, be deflected slightly and one could calculate that deflection. It is precisely half the value indicated by einstein’s theory. Were photons to travel at half the speed of light, then Newton’s theory would suffice. Eddington it seems had championed Einstein’s theory owing to the fact that Eddington had made the decisive measurements pertaining to that deflection of satrlight by the solar mass.

Concerning photons I submit that we do not really know how they travel or even if they travel at all. A photon is an event, a transaction occurring at a point in space when a package of energy changes its state in the aether, especially where the transaction involves energy exchange between matter and aether. We know that electromagnetic waves travel at the speed of light but such a wave is a ripple of the sea of energy in the aether so where does the photon feature as motion?

The answer seems to be that it exhibits its presence as a transfer of momentum as if its energy E exerts momentum E/c, where c is the speed of light. Physicists today would do well to wake up to the fact that a photon is an ‘event’, that the aether is real and that it can be involved in transactions involving momentum and, indeed, angular momentum, but that the deflection of light rays by a gravitational field depends upon the speed of light being affected by the presence of such a field. Einstein says that the speed of light is constant in the vacuum and Einstein then asks us to distort the vacuum so that straight paths of light bend to conform with the distortion of the space metric.

I was somewhat enthusiastic in developing this chapter 8 as part of that effort back in 1959. It was an interesting exercise, but it too was later replaced by something more logical, as one can see from my later publications. All I can add here is to say that I am left with the thought that there may be some maxiumum field intensity that the aether can tolerate before its structure collapses. I now think that has some connection with the very slight radial displacement of aether particles needed to justify the integer nature of the critical number 1843 mentioned in TUTORIAL NOTE No. 8, but I do not see that leading to a breakdown electric field intensity as being as high as the 2.21×10¹³ esu cgs deduced in this Chapter 8. That is an energy density of 1.94×10²⁵ ergs/cc, equivalent to a mass energy density of 21,600 gm/cc. I point out, incidentally, that if you believe Einstein’s theory and subscribe to the belief in Black Holes, then you are in the realm of believing that space (or aether) can tolerate field intensities that transcend even higher levels of concentration of energy density.

---

Analysis of Electromagnetic Wave-front Energy

An electromagnetic wave, however established, carries energy. If the wave is a plane wave the wave energy per square cm. of the wave must be constant.

Consider two plane boundaries in the wave and separated by a distance T. Field flux, whether electric or magnetic, does not cross these boundaries. Thus, if V is the electric field intensity between the boundaries:

A similar equation involving the magnetic field intensity H also applies.

The field energy per square cm. of the wave is a function of V, H and T, and the externally induced electric and magnetic fields in which the wave moves. Let F be the externally induced electric field component in the direction of V and M be the externally induced magnetic field component in the direction of H. Then the field energy E of the wave per square cm. between the boundaries of spacing T is:

If equations (40) and (41) are differentiated with respect to a parameter y, noting that E is a constant, and that in an electromagnetic wave V=H, it may be verified that:

This equation shows that if the fields F and M are uniform T is constant and the wave will therefore not be deflected. However, if F or M varies with y, T varies with y, showing that in moving a distance T the wave is deflected away from the y direction through an angle d equal to (u/T)d(T)/dy in time dt, where u is the velocity of the wave. The rate at which the wave is deflected in a non-uniform field is therefore given by combining this result with equation (42) to obtain:

If M is zero or uniform and the field F is strong enough
to polarize the wave, the direction of V may be expected to vary in the plane of the wave so that F is in fact the full intensity of the externally-induced electric field and the energy given by equation (41) is then a minimum. This further means that the vector fields F and V are opposed, and if this fact is applied in the foregoing analysis equation (43) becomes:

If F decreases with increasing y the wave is deflected into
the stronger parts of the field.

Deflection of Plane Wave in Passing an Electric Source

Consider the motion of a plane wave past a relatively weak electrostatic charge Q at a point 0. Imagine a point P in the wave travelling in a straight line distant Y from 0. In this case the direction y is as indicated in Fig. 2(a) in the plane of r and P. F at P is:

and dF/dy is equal to dF/dY, which is found noting that in the plane of the wave front X is constant. Equation (44) shows that the total deflection is:

where the integration is from minus infinity to plus infinity, udt being dX. When is evaluated it is found to be 2Q/VY².

Deflection of Plane Wave in Passing a Magnetic Source
Imagine the plane wave just considered to pass at a distance Y from a current element idl at 0 as shown in Fig. 2(b). Let be the angle between idl and OP, where P is a point in the wave front. At P the magnetic field due to idl is:

and in this case may be evaluated as:

Note that mod(-) implies the modulus or amplitude of a quantity, regardless of its positive or negative significance.

It is of interest to apply this expression to the problem of light deflection by solar gravitation. The effective value of mod(idl) is that attributable to the small gravitational charges orbiting in planes approximately parallel with the earth’s planetary orbit. The condition shown in Fig. 2(b) then applies to a ray of light grazing past the sun if Y is the solar radius and mod(idl) is GM_s, where M_s is the solar mass. The mean value of mod(sin is 2/. Thus is equal to 2GM_s/VY². Taking V as equal to the critical field parameter V_o as already evaluated, 2.21x¹³ cgs esu, G as 6.66×10^-8 cgs, M_s as 2.0×10³³ gm, r as 6.95×10¹¹ cm, is found to be 9.68×10^-5 radians or 2.00 seconds of arc.

This result is in agreement with the majority of the results derived from observations during eclipses.

Wave Deflection in the Atom

It is possible to apply equation (44) in an atomic system. Let the atomic number of the atom be Z so that the nuclear charge is Ze. An electron in the K shell will, by simple theory, have an associated orbital radius of r_H/Z where r_H is the radius of an electron orbit in a Bohr Hydrogen Atom. Let u be its associated wave velocity. Thus the angular velocity d/dt of the electron waves in the K shell is given by:

The electric field intensity caused by the charge Ze at the wave orbital radius:

and the parameter y is distance in a radial direction from the nucleus. Thus:

From equations (44), (45) and(46):

or:

The significance of this equation is not immediately apparent. It becomes apparent if one can impose an upper limit on the maximum field intensity of an electromagnetic wave. To fix such a limit will impose a limit on Z. Following this arbitrary suggestion let V_o be the maximum possible value of V and Z_max the maximum possible value of Z. Then, subject to any refinements which a full analysis on Quantum Theory might impose on equation (48):

From known data:

Also:

When evaluated from these data and equation (49) Z_max is found to be 86.5. This is very little different from the maximum value of Z found in atoms.

---

Although not related to gravitation, one interesting result of this aether theory is the explanation of the anomalous factor 2 found in gyromagnetic phenomena.

Consider the effect of a magnetic field of true strength H in the aether. For simplicity imagine this to be parallel with the axes of rotation of the aether particles and continuum. (The result to be derived may be proved to apply also in a general case.) The field H has the following effects on the radii r and R of the particle and continuum orbits respectively; it causes one radius to increase and the other radius to decrease. Thus:

w being the angular frequency of the aether system.

Evidently, in terms of a basic radius r_o, and a small increment r:

and:

where:

The energy involved in the disturbance caused by H is almost wholly kinetic energy and is equally shared between the particle system and the continuum system. It is mw²(r)² ergs for each element of space including one aether particle. In ergs/cc the energy is found by multiplying by /e. Substituting for r from (50) and m from (14) then shows that the magnetic field energy is:

Now, the true field H is the difference between the induced field H_i and the aether reaction field H_r. The value of H_r is readily found as 4 times /e times the magnetic moment of the elemental space including one aether particle. This is twice that of one particle because the continuum makes an equal contribution. Let the accepted law of the magnetic field induced absolutely by a current be assumed to be in error by the factor K. By accepted law the magnetic moment of the particle will change by (e/c)(w/2)r². From this:

From (14), (50), and (51):

The directly induced field H_i arising from a current in an electrical apparatus, say, is therefore:

it is knownthat the magnetic energy accompanying the induced field H_i is (H_i)²/8 ergs/cc. This is also H²/32 ergs/cc. Evidwently H_i is H/2 and K is 2.

It may be concluded that an has, when in orbital motion, twice the magnetic moment normally attributed to it, but when detected as a magnetic field this moment is effectively halved by aether reaction. However, the magnetic moment is not halved in its relation with angular momentum. Hence the anomalous factor 2 of gyromagnetic phenomena.



---

This note concerning the gyromagnetic ratio has no special connection with the theory of gravitation. I included it because it was my starting point in developing my aether theory. I knew that the inductance energy stored in a magnetic field in a vacuum was recoverable and there just had to be a physical explanation, not one based on empirical formulations which merely recognized the reality of the phenomenon. Physicists had rejected the aether and then had discovered an anomalous factor of 2 in their experimental research concerning angular momentum quanta, electron reaction and ferromagnetic gyromagnetism. I discovered that the factor of 2 was direct evidence of a reaction by something real in the aether and so there was my conviction that the aether was essential as the provider of the storehouse for inductance energy and much more. So I documented this as Chapter 9, and later to simplified the analysis for presentation in my later writings.

---

[1] CAMPBELL, N. R. Modern Electrical Theory, 2nd Ed. (Camb. Univ. Press), pp.387-8, 1913.
[2] VERONNET, A. Comptes Rendus, v. 188, pp.1380-1, 1929.
[3] WHITTAKER, SIR E. History of the Theories of Aether and Electriciy (Classical Theories) (Nelson), pp.84-7, 1951.
[4] DIRAC, P. A. M. The Principles of Quantum Mechanics, 4th Ed. (Oxford: Clarendon Press), 1958.
[5] NIELSON, C. E. See Appendix III of book by G. Gamow and C. L. Critchfield, Theory of Atomic Nucleus and Energy Sources (Oxford: Clarendon Press), 1949.
[6] EOTVOS, R. v., Math. u. Nat. Ber. aus. Ungarn, viii, p.65, 1891.
[7] ASTON, F. W. Mass-spectra and Isotopes, 1st Ed. (Arnold, London), 1933, pp. 101-2.
[8] CLEMENCE, G. M. Rev. Mod. Phys., v. 19, p.361, 1947.

---



---

This is a reproduction of the text of a booklet written by the author in 1959, published early in 1960. This continuation comprises Chapters 4 to 7 of that work. In the light of his 1998 perspective, some 38 years on from that 1960 effort, the author has added several notes bearing the symbol . These may interest science historians who, hopefully, one day will seek to track how the author’s theory developed over time.

---

4

THE FORCE OF GRAVITY

Preliminary Note
An important question concerning gravitation is, “Does all mass gravitate?” Mass has inertial and gravitational properties, but is the inertial mass of a body exactly equal to its gravitational mass? The Theory of Relativity requires the answer to this question to be definitely affirmative and, indeed, this was the conclusion reached as early as 1891 by Eotvos [6]. However, in accepting this as an established fact, those who attempt to explain gravity by the relativistic approach are ignoring a discrepancy found in highly accurate experiments by Aston [7].

These experiments have pointed to a difference between the ratios of the inertial masses and gravitational masses of the preponderant isotopes of hydrogen and oxygen. Aston detected a difference 0.00004+/-0.00002 between the mass number and chemical atomic weight of hydrogen on the oxygen scale and wrote, “This is a serious discrepancy…. It must be concluded that the discrepancy between the isotopic weights of hydrogen and oxygen is at present unaccountable and further work upon the matter is desirable.”

This discovery of Aston hints at the possibility that the fraction 0.00004 of the atomic mass of hydrogen may be nongravitating in character. Perhaps the hydrogen atom contains a non-gravitating particle of mass equal to this fraction of the mass 1.673×10^-24 gm. of the atom. Allowing for the limits of error in Aston’s experiments the mass of this particle will be between 3.3×10^-29 gm. and 10^-28 gm., a range which includes the value m of this theory.

There is the hint of a suggestion that the neutrino is gravitationally neutral as well as electrically neutral, and this is coupled with a suggestion that there is a neutrino in every hydrogen atom. The implications of this lead directly to the quantitative evaluation of the Universal Constant of Gravitation.



---

Reading the above after some 40 years since it was written, I now wonder whether what I quoted from the Aston book (1933 date) was overtaken by the discovery of the heavier isotopes of hydrogen, namely deuterium and tritium. Obviously, a point of such a nature by such an authority, would have attracted much attention in later years, if the problem did persist. So we shall move on here without further regard to this indirect experimental implication of a mass unit corresponding to that of the aether particle of my theory.

This Chapter describes how I first came to see the aether continuum of charge density as being the seat of gravitational action. The action had to be that of electric charge in motion but yet that of an electrically neutral unit having a mass property. A hole in the charge continuum neutralized by a balancing charge in orbit within the bounds of that hole gave the parameters needed to develop a quantitative and qualitative connection between the force of gravity and electrodynamic action.

The result was captivating. It represented progress and that gave one something on which to build, something far removed from wandering in a wilderness looking for a new equation that might provide a unifying link between the symbols used by the physicist versed in Relativity. Equation (24) seemed to be the answer I was seeking because it was not ‘discovered’. It simply emerged from analysis which recognized how electrodynamic action could develop a mutually attractive force in a universal omnipresent medium agitated by the mass property of matter.

Once I had the result which equation (24) offered, I was ready to move on to see if I could go further and deduce the proton/electron mass ratio by pure theory. I had been inspired by Eddington’s efforts in that regard.

In the event, however, I was later to discover that much of what I describe in this chapter 4 is best forgotten. It was later replaced by something truly wonderful as a theory for G and M. Indeed, only the feature of that dynamic mass balance involving ‘gravitons’ embodied in the charge continuum as the seat of gravitational action was to remain as the basis on which to build the final theory.

That said, however, there remains a lingering doubt concerning what is described by reference to Fig. 1, as I shall explain in the note at the end of this chapter 4.

---

The Gravitational Mass Unit

Ideally all massive bodies may be regarded as consisting
of units of a fundamental mass quantity which will be denoted
M. This ideal will be reviewed in a later chapter, and the value of M of such a unit will be calculated by applying this theory, but, for the present purpose, it suffices to accept this simple hypothesis.

An examination of the converted photon system having the neutral particle of mass m and velocity moment 2cr shows that in spite of the momentum balance there is a dynamic out-of-balance. A dynamic balance can be obtained without upsetting the analysis of the momentum balance or the evaluation of the magnetic moment er provided a relatively heavy particle acts as a counter-balance to the neutral particle of mass m. This heavy particle of mass M is regarded as disturbing the continuum to produce at its mass centre a concentrated portion of the continuum within a spherical hole left by the charge so concentrated. This simple hypothesis leads immediately to the gravitation constant. Logically, the centre of this hole will be the centre of gravity of M and m and the radius of the hole will be the radius of the orbit of M. Thus, as M is balancing a mass m moving at velocity c/2 at radius 4r:

(1) The position of the mass M is not fixed in the inertial frame but describes a circular orbit of radius 4r(m/M) with a velocity V=(c/2)(m/M).
(2) The particle will exhibit zero net electrostatic effect at points remote from the hole because the charge of the particle balances the charge missing from the hole.
(3) The position of the hole is fixed in the inertial frame of reference, which means that the hole itself gives rise to no negative magnetic effects.
(4) The particle M has a charge (denoted q) of (4/3)(4rm/M)² and the motion of this charge gives rise to a magnetic field and an associated magnetic force between M and all other units M and charges in motion.

As with the aether particle system all the units M will, by virtue of their electrical character, their mutual reaction and their reaction with the aether particle system, move in synchronism with one another. The force of magnetic attraction between all pairs of particles of mass M will be q²V²/c² at unit separation distance. The value of the universal constant of gravitation G is therefore given by:

Substituting the values of q and V just presented:

M is taken to be of the order of the mass of the hydrogen atom 1.673×10^-24gm, m is 3.714×10^-29 gm., r is 1.93×10^-11 cm., c is 2.998×10¹⁰ cm/sec, and is 1.857×10²¹ esu/cc. Using these values in equation (23) gives the known value of the constant G.

It is to be noted that there will be no unidirectional mean force between the mass units and aether particles because they are not moving in synchronism; the aether particles orbit at four times the frequency of the mass units. The magnetic moment of the mass unit M is very small, as may be verified from the data given; it will not produce a measurable magnetic effect.

It is a matter of algebra to show that equation (23) can be presented in the form:

This equation involves only experimental quantities. Using the known values:

The equation is satisfied for a value of M of 1.67525×10^-24 gm.

The Evaluation of M

The fundamental unit of gravitational mass M is closely equal to the mass energy of an electron-positron pair oscillating to have a magnetic field angular momentum of h/.

Consider an electron-positron pair formed by charges +e and -e moving in generally inclined directions at the same velocity v. It can be shown that the magnetic field of this system has a definite angular momentum which ranges from zero when the motions are parallel or anti-parallel to a maximum when they are directed at right angles to one another. For unit quantization of field angular momentum the smaller the inclination between the motions of the electron and the positron, the greater their kinetic energy. For least energy they will move at right angles to one another. Such a system will now be considered with reference to Fig. 1. The system comprises the two charges +e and -e rotating in a common circular orbit of radius r with velocity v and an angular displacement in the orbit of 90^o.

If one charge has been accelerated from rest after the other has acquired its steady velocity v, the magnetic field of the newly-accelerated charge is bounded by a boundary which spreads outwards at the speed of light and it is possible to show that this requires a transfer of the original field energy of the system in an angular sense about an axis perpendicular to the plane of the charge orbit.

This is readily understood from a consideration of Fig. 1. Let the velocity of the charge -e have been established after that of the charge +e and imagine the magnetic field wave boundary to be at the position shown. The magnetic field energy denmsity at a point P will be given by an expression such as (1/8)(H₁+H₂)², whereas that at Q will be given by an expression such as (1/8)(H₁-H₂)², where H₁ and H₂ are the field components due to +e and -e respectively. The energy expressions apply within the wave boundary. Before the boundary reached P or Q the corresponding energy density at P and Q was simply (1/8)H₁².

It is therefore evident that in passing through P and Q the wave causes a transfer of energy between P and Q because P gains energy density by an amount (1/8)(2H₁H₂+H₂²) and Q loses energy density by an amount (1/8)(2H₁H₂-H₂²). The quantity of energy (1/4)(H₁H₂) is transferred from Q to P by the passage of the wave, and this transfer must presumably occur around the wave region. This transfer of energy gives rise to a field momentum.

Since, using the symbols shown in Fig. 1, H₁ and H₂ are:

respectively, and cos=sincos, it may be proved that:

A resolution of the energy density velocvity moment about the orbital axis of the charges is achieved by multiplying this expression by u(OP)cos, where u is the perihpheral energy speed paramter in the wave boundary at P or Q about the orbital axis.

When averaged for all values of , cos² becomes 1/2, and the energy velocity moment of an elemental portion of the boundary region is found by further multiplication of the expression (25) by 2(OP)sin, (OP)d and cdt to obtain:

Here cdt is a measure of the radial thickness of the wave front. It may be shown that u is (OP)2/dt because 2 is the angle through which energy is exchanged. Thus the magnitude of the net velocity moment becomes:

Here the integral is between 0 and /2.

This expression is independent of OP and therefore does not depend upon time. This represents angular momentum when divided by c². Thus the field angular momentum is:

and we take this to equal h/ to obtain the basic quantum condition:

Consider now the energy of the system. The masses of the electron and positron are both equal and denoted m_e. The kinetic energy of the system is therefore m_ev², having a mass equivalent m_e(v/c)² or, from (28):

By applying equation (1), the magnetic energy of the system may be shown to be (ev/c)²[1/(2r)]. The electrostatic energy is -e²[1/(2r)]. The value of r, using that of the aether particle orbit, is h/4m_ec, giving the magnetic field energy as:

or, in terms of equivalent mass, 2m_e(v/c)²(2e²/hc), which is simply:

The corresponding mass equivalent of the electrostatic energy is:

Finally, to derive the total mass of this field angular momentum quantized electron positron pair it is necessary to add 2m_e as the basic rest mass of the pair. Thus the total mass M becomes:

This aether theory has accounted for the value of hc/2e², and thwerefore the ratio M/m_e is derived from pure theory. Its value, for hc/2e² of 137.0377, is 1839.57, whichm, for the known value of m_e of 9.1085×10^-28 gm, gives M as 1.67557×10^-24 gm. this differs from the value required to explain gravity by the arguments leading to equation (24) by only one part in 5,000.



---

Although I have abandoned the last section of this Chapter 4, as I review it now after some 40 years since I did the calculations, I still find that the argument has some appeal. I recall that I had read somewhere that a star might acquire its spin by having radiated angular momentum and, knowing that electrons and positrons exist in paired association in the theory of QED (quantum electrodynamics), I set about the task of checking to see if, perchance, each member of the electron-positron pair could acquire, by radiation reaction, an angular momentum quantum of Bohr’s theory of the hydrogen atom.

When I discovered that the analysis based on conventional Lorentz field theory justified this proposition, albeit by theory involving superluminal spin velocities, and further that it implied a mass energy corresponding to that of the nucleus of the hydrogen atom, I was convinced that my hypothesis had merit.

However, key to that analysis was the assumption, a standard assumption adopted by physicists, that a discrete electric charge in motion produces a magnetic field in its immediate vicinity. That was the basis on which J J Thomson had determined the theoretical formula for the electromagnetic mass of the electron.

As I later found, that assumption is erroneous. A discrete electric charge in motion cannot, of itself, develop a magnetic field conforming with the Lorentz prescription. Indeed, it needs two oppositely-charged particles moving in opposite directions to set up the action which gives basis for the Neumann potential, which in turn can guide one to formulate the force equations that include the derived force law prescribed by Lorentz. An electron-positron pair moving in the manner illustrated in Fig. 1 above cannot develop magnetic field effects of the kind formulated by reference to that figure.

When one learns about electromagnetism in one’s teaching, the teachers do not go back into the history of the subject to introduce what was known as the Fechner hypothesis, a topic mentioned in Clerk Maxwell’s treatise. That is a precursor of a relevant aspect of QED. The starting point instead is usually linked to the consequences of transformation theory which complies with Einstein doctrine and merely smears all action of moving electric charge into a form indistinguishable from the field action of a section of an infinitely long straight current element. The mutual gravitational action as between two elements of mass moving in a common straight line cannot be explained as a magnetic force by unified field theory unless one is wrong in thinking that there is no magnetic field active at the seat of either charge. Yet the Lorentz doctrine tells us that the magnetic field is zero in the line of the vector motion of a discrete electric charge.

So, in summary, as one can see particularly by reference to the papers in the Appendix to my book Aether Science Papers, notably papers 6 and 14, [1988a] and [1995e] in the bibliography section of these web pages, I had to abandon the magnetic field theory leading to equation (29) in the section of Chapter 4 of this discussion. The proton mass was destined to emerge from the onward development of the theory when the creation of mesons and their presence in a virtual form in the aether came to light.

In contrast, the next Chapter, Chapter 5, holds its ground as firmly as it did on the day it was first discovered. It is at the very heart of this whole theory and it has spin-off features which hold promise for advances in technology by which to harness aether energy. However, in the 1950s when the theory was first discovered such a thought was undreamed of and beyond contemplation.

---

Preliminary Note

As the aether has a physically-conceived structure we are able to “see” what happens to it when a part of it is caused to rotate, as with the earth, for example. Here, we find an advantage not shared with the Theory of Relativity. We can immediately deduce that an electrical property of the aether manifests itself when the aether is set in rotation.

The Effect of Aether Rotation

Consider what happens when a large volume of the aether is rotating bodily. The continuum and particle system rotate together. There will be no resultant magnetic moment unless the particle distribution is disturbed. An evident disturbance is the centrifugal effect arising from aether rotation, but for angular velocities of the magnitude found in the solar system this effect is of negligible consequence. A much more important effect arises from the synchronizing interaction between particles in the rotating volume. This requires that the particles shall move about their neutral points at the same angular velocity. Thus if a particle is to have a velocity component V directed in the plane of its orbit, whilst retaining a mean velocity c/2, its speed along its orbit must be of the form c/2+Vcos, where is the angle subtended by a line joining the particle and the centre of its orbit relative to a fixed reference datum in the inertial frame. To satisfy the above requirement the centre of the orbit cannot be the neutral point. Evidently the particle is distant from this neutral point by r+(2VR/c)cos. As V is much less than c the effect of this is that the particle is moving around a circular orbit whose centre has been displaced a distance 2Vr/c perpendicular to V in the plane of the orbit. If V is x cosA, where is the angular velocity at which the aether rotates, x is the distance of the aether particle from the axis of rotation, and A is the angle of tilt of the axis to the common axial direction of the aether particle system, this displacement distance is 2xrcosA/c.

Consider a disc-like section of the rotating aether of radius x and unit thickness. Then, the effective charge displacement arising from the effective physical displacement of the particles is

The disc has acquired a uniform charge density of 4r.cosA/c esu/cc. The polarity of this charge depends upon the direction of rotation of the aether.

When evaluated from the aether data already presented the charge density is found to be:

This charge density represents a charge component which rotates with the aether. In the next chapter it will be shown that an aether which moves as well as rotates contains free particles which, though free to position themselves to minimise electrostatic energy, have a constrained motion which prevents them from rotating with the aether. In practical cases these free particles are found to be so abundant that the electrostatic effect of the charge given by equation (30) is wholly cancelled. However, the magnetic effect of this charge density is not cancelled, and it is therefore of particular interest to calculate the magnetic moment that such a charge rotating with the earth would produce.

The Calculation of the Geomagnetic Moment

For the earth, w is 7.26×10^-5 rad/sec and A is 23.5 degrees. Thus the carth’s charge density is, from (30), 0.000319 esu/cc. The rotation of this charge gives rise to a magnetic moment of:

where R is here the radius of the earth’s aether. If R is greater than the radius of the earth (6.378×10⁸ cm) by a small factor k, the earth’s theoretical magnetic moment becomes (1+5k)(6.8)x10²⁵ emu. This may be compared with the measured value of the earth’s magnetic moment of 8.06×10²⁵ emu.

This result is significant in that it shows that k is small and thus indicates that the limits of the earth’s aether are close to the earth’s surface. It also leaves room for some modest ferromagnetic effects in the carth’s core so that irregularities in the earth’s field may be explained. An upper limit Of 0.035 is imposed on k, suggesting that the earth’s aether terminates at a mean height of about 140 miles above the earth’s surface.

This suggests that the ionosphere may be a phenomenon arising at the aether boundary. It should be noted that it could be that the aether boundary is graded and occurs in stages, corresponding to the different ionosphere levels. These levels are at mean altitudes of 45, 75, 105 and 155 miles respectively.

It may be asked: “Will the above explanation explain the dipole character of the geomagnetic field?” The probable answer is negative, but the theory is amenable in this respect because it is found that the actual magnitude of the effective particle displacement in the earth’s aether matrix caused by the earth’s rotation is very much less than the interparticle spacing. On this basis it is clear that the charge effect caused by the rotation may merely amount to the displacement of charge to the aether boundary. When this is interpreted in the terms of magnetic moment it is found that the magnetic moment of the boundary charge is exactly twice that of the distributed charge and acts in opposition. The result is a net magnetic moment equal in magnitude to that already estimated, but the magnetic field distribution becomes more nearly that of a dipole.

Although not related to gravitation the explanation of geomagnetism provided by this theory lends extremely strong support to the theory upon which the understanding of gravitation is founded, and its inclusion in this work is considered pertinent. This chapter will have also proved of interest to those familiar with the Schuster-Wilson Hypothesis.



---

The above account was greatly extended in the second edition of The Theory of Gravitation published in 1966 and further reported in Modern Aether Science (1972).

Apart from the theory offering a better explanation of geomagnetism than that provided by magnetohydrodynamic theory, its quantitative significance pointed to there being a spherical boundary enclosing aether sharing the Earth’s motion through space and sharing the Earth’s spin motion within that boundary. Here was a prediction of a zone of transition seated above Earth in ionospheric regions.

That then became the focus of attention as I moved on to write Chapter 6 because, by an analogy with the Newtonian dynamics of the pendulum bob, I could see scope for introducing a cyclical fluctuation into the angular momentum of a planet in its motion around the sun. I suspected that could affect the rate of perihelion advance of body Earth in the orbital motion around the sun and, knowing of Einstein’s triumph in declaring that such perihelion motion offered support for his General Theory of Relativity, I just had to explore this avenue of research based on the spherically-bounded aether of body Earth.

---

6

THE PERIHELION MOTION OF THE PLANETS

Preliminary Note

To proceed to explain the anomalous perihelion motions of the planets it is necessary to consider the momentum conditions of an aether lattice having a translational motion.

In the introductory chapter it has been suggested that elements at the front of a moving aether lattice are continually breaking away and reforming behind the moving aether system as part of the fixed lattice of surrounding aether. This involves a continuous counter motion of free aether particles through the moving lattice. A system may be envisaged in which some of the aether particles retain their harmonious orbital motions but disturb the aether a little as they migrate at a fairly high speed (probably of the order of the speed of light) in an opposite direction to the lattice movement.

Analysis shows that for such a system the net linear momentum is at all times zero, but that this is not true with regard to angular momentum unless some additional compensating effect can be introduced.

Analysis of an Aether Momentum Effect

For linear motion, let the free particles move with velocity v in the opposite direction to the velocity V of the moving lattice. The uniform nature of the aether requires that as many particles move forward as backward. Thus for every bound lattice particle there are V/v free lattice particles and as their velocities are opposite in direction and related in the corresponding ratio v/V an exact linear momentum balance exists.

Next consider a rotational motion of a spherical aether lattice about a remote axis. Rotation about its own axis has been treated as an independent consideration in the preceding section. For the present purpose the attitude of the lattice is regarded as fixed in the inertial frame, its ‘centre of gravity’ moving with angular velocity Q around an orbit having polar co-ordinates, R,. The simple dynamics of this system show that the lattice has an angular momentum of R² times the net mass of its bound particles. Now, the free particles in the lattice have a constrained component of motion; they are obliged to move at right angles to the radius vector. Their angular velocity about the remote axis is -Z, where there are Z bound lattice particles for every free particle. This component of motion gives rise to an angular velocity moment about the remote axis of

where k is the radius of gyration of the moving particle system about an axis through its own ‘centre of gravity’ parallel with the remote axis. This has involved the application of the Parallel Axis Theorem. The corresponding angular momentum is obtained by multiplying:

by the net mass of the free particles, which is 1/Z times the net mass of the bound particles. Denoting this latter mass M, the net angular momentum of the moving particle system is therefore:

or -Mk².

Evidently, the orbital angular momentum of the aether particle lattice of a planet is not zero.

Now, in considering the photon and the problem of gravity, it has been assumed that the angular momentum of the aether particle system (or, in equivalence its magnetic moment and consequent magnetic energy) is at all times conserved. It is only logical that we should look for an aether lattice angular momentum which can balance at least the variable component of the momentum -Mk². Steady momentum components are of little consequence; an exact momentum balance may only be possible in terms of considerations extending throughout the whole universe or, at least, throughout the whole solar system. However, short-term variations of momentum must be balanced locally, and as P varies whilst a planet describes its orbit there must be another variable acther particle angular momentum associated with a planet’s motion.
A planet rotates about its axis at a steady velocity. The extent of its aether boundary is evidently determined by factors which ensure that the boundary occurs at a quite small but definite distance from the planet’s surface. The general aether of the planet cannot therefore be expected to have a variable component of angular momentum.

To meet the requirements of a conserved angular momentum of the aether particle lattice, it will be supposed quite arbitrarily that the main aether of the planet is surrounded by a spherical shell of aether which can oscillate about an axis at right angles to the orbital plane of the planet. It will further be supposed that the angular velocity of this shell varies between zero and the steady angular velocity w of the planet. This supposition is reasonable; if there is to be an oscillation, then this is the form of oscillation involving least energy exchange. The variations are such as to provide a balance component of angular momentum equal to -Mk².

Let R_P denote the radius of a planet, R_A/ denote the radius of its main aether boundary and R_S denote the outer radius of its spherical aether shell. The value of k² is therefore (2/5)R_S⁵. Let w(t) be the variable angular velocity component of the shell. Then the angular momentum of the shell is:

where is the mass density of the aether. is m/d³ in terms of the fundamental aether constants already evaluated. From this data may be shown to be 143.6 gm/cc. For angular momentum balance, as M is (4/3)R_S³:

Here (t) is the variable component of and, from the theory of planetary orbits, has a range of approximately 4e_o, where e is the eccentricity of the planetary orbit and _o is the mean value of . By the original assumptions this range is equal to the appropriate factor given by equation (31) times the range of w(t), which is w. Thus:

The continuum itself will now be considered. The continuum behaves, at least in response to weak disturbances, as if it is an incompressible fluid, and, in view of this, the bodily displacement of an aether region causes a reverse flow of continuum around the region. However there can be no ‘cross motion’ of the medium as in the case of the acther particle system. The net momentum both linear and angular about a remote axis must at all times sum to zero. The only uncompensated variable momentum in the continuum system is due to the oscillation of the spherical shell of the planet’s aether. It is evident that since the mass densities of the aether particle system and the continuum are equal there is a residual angular momentum having a time dependent component equal to:

It is this residual angular momentum which gives rise to the anomalous advance of a planet’s perihelion.

It is convenient to denote this residual momentum M_Ph, where M_P is the planet’s mass and is (4/3)R_P³ times the mean density _P of the planet. Thus:

M_Ph must be introduced into the momentum conservation of the Newtonian equation:

Here M_S is the mass of the sun and h is the moment of the planet’s velocity about the sun.

The corrected equation becomes:

When this equation is solved for h given by (33) it is found that it represents an elliptical orbit having a perihelion which advances rads/rev., given by:

where a and b are respectively the semi-major and semi-minor axes of the elliptical orbit. Taking R_A as closely equal to R_P we have, from (32) and (36):

The values of given by this equation are negligible for all planets except Mercury, Venus and the Earth. In the case of these three planets there is no disagreement between the result of equation (37) and the known anomalous rates of advance of perihelion. Unfortunately, available data do not allow an accurate comparison in the case of the planet Venus. However, Clemence [8] had deduced from observational data rates of advance of perihelion of 42.56 and 4.6 seconds of arc per century for the planets Mercury and the Earth respectively. These values can only be regarded as accurate to within about 2 seconds of arc per century. The fact that the General Theory of Relativity can explain an anomalous perihelion motion, and can be adapted to yield corresponding values of 43.03 and 3.83 seconds of arc per century for Mercury and the Earth respectively, has lent very strong support to Relativistic notions. However, now consider the values of given by equation (37).

For the Earth 4e_o/w is much less than unity. _P is 5.52, a and b are nearly equal and are 149,600,000 km, and R_P is 6,378 km. Thus, as is 143.6 gm/cc, as given by equation (37) is 5.2 seconds of arc per century. Bearing in mind the possible errors involved, this value is in very good agreement with the observed value of 4.6 seconds of arc per century.

For Mercury _o/w is unity, e is 0.2056, _P is 5.13, a is 57,000,000 km, b is 56,700,000 km, and R_P is 2,495 km. In this case the value of given by equation (37) is 44.3 seconds of arc per century. This result is in satisfactory agreement with the observed value.

These results are summarized in the table below:

It can be concluded that the General Theory of Relativity no longer retains the unique property of being able to explain the known anomalous perihelion motions of the planets.



---

I was destined to adhere to this theory for the anomalous motion of planetary perihelion for some 20 years until I heard of the contribution made by a German schoolmaster, Paul Gerber, dating from 1898. There was sense in his proposition, sense not to be found in Einstein’s method, namely that the transfer of energy as between sun and planet, where the planet describes an ellipse, takes time and that can account for the radial oscillation period differing slightly from the orbital period. This would cause the major axis of the ellipse to turn very slowly over the centuries and so account for a perihelion motion.

That unsettled my belief in my own aether-based account, especially as I was all too aware that the enclosing aether boundary of some planets would need to be slightly below the surface of the planet whilst in other cases, as for Mercury, it could be well above. The numerical data for Mercury, with its high eccentricity, and Earth, with its small eccentricity, happened to fit well, as the above Table shows. However, as I was unsettled by the Gerber interpretation and, though I knew Einstein was off track in his notions about space-time, I was not inclined to ignore the Gerber claim. Instead, as there was a small error in Gerber’s analysis, I set about correcting that, as can be seen from the subject of PHYSICS LECTURE NO. 2.

One can there see that by 1980 I had discovered a different way of explaining the anomalous perihelion motion of the planets. My result, as an equation of motion, was identical to that obtained by Einstein. However, I was using aether theory, whereas Einstein had rejected the aether notion and put us instead into an incomprehensible jungle of mathematics which claimed to intermesh what we understand as time and space.

Now that I have come to write this historical account I feel I can disclose something I have had in mind for quite a while, namely that both of my theories for the perihelion motion are correct. If that is the case, then it is the retarded energy transfer as between sun and planet that determines the anomalous component of the rate of perihelion advance of the planet, but that then in its turn constrains the aethereal constitution of the planet in such a way as to define the location of the spherical aether boundary enclosing the planet.

Even if this means that the aether boundary lies inside the body of the planet I see this as a possibility. Just as matter can move through aether, so aether can move through matter, and the two need not be rigidly coupled as one unit. The amount of energy associated with planetary motion is enormous and its action could be dominant in governing the aether-matter coupling involved. Moreover, if for Venus, this internal aether boundary is a serious consideration it suggests that a Michelson-Morley test performed with open apparatus on the surface of Venus, if that were ever possible, would be of special interest. My calculations, as reported in the 1966 second edition of The Theory of Gravitation (page 114), did show that the available data of the Venus anomalous perihelion advance corresponded to its aether boundary radius being 5,950 km compared with the radius of its atmosphere of 6,100 km. Developing on that theme one wonders if an artificial satellite set in a highly elliptical orbit around the sun would offer a platform on which a Michelson-Morley type test could be performed with the object of disproving Einstein’s theory, should that theory persist well into the future. Furthermore one can see purpose in bringing these thoughts to bear in connection with the observation of phenomena associated with comets.

---

7

THE UNIVERSAL CONSTANCY OF GRAVITY

Preliminary Note

Although the nature of the force of gravity has been explained in terms of the magnetic force of attraction between parallel moving charged particles associated with fundamental units of mass of 1.67525×10^-24 gm and the observed gravitation constant G has been correctly evaluated as applying between these units of mass, it still remains to explain why the same value of G applies to all matter. To acknowledge the universal constancy of gravity it is necessary to argue that every element of gravitational matter in the universe occurs in multiples of the mass M. This is apparently not quite so; the atomic mass of hydrogen on the oxygen scale is 1.008. Compare, for example, the following mass values:

M as calculated from this theory: 1.67557×10^-24 gm.
M as needed to explain value of G: 1.67525×10^-24 gm.
The known mass of neutron: 1.67474×10^-24 gm.
The mass of hydrogen atom: 1.67334×10^-24 gm.
Mass of oxygen atom: 16 times: 1.65981×10^-24 gm.

This difficulty is a problem which this theory has not yet resolved. Three approaches will be considered here.

Multiple Quantization of the Mass Unit M

In deducing the value of M in terms of the field angular momentum quantization of the electron-positron pair it was supposed that the angular field momentum was h/, this being twice the quantization h/2 applicable to one of the members of the pair in atomic theory. However, consider the effect of a quantization Nh/, where N is an integer.

An argument on these lines is consistent with a conception of an atomic nucleus having one neutrino only, regardless of the number N. This means that on the oxygen scale the inertial mass of hydrogen will be 15m/16 times greater than the gravitational mass, because the neutrino mass is non-gravitating. This result would have a bearing on the discovery of Aston mentioned in the preliminary note of Chapter 4.

The effect upon equation (28) is to increase v² in proportion to N, and this causes the value of M/m_e given by (29) to be very nearly increased in the same proportion. However, the small difference in proportion is inadequate to explain the difference shown above in the case of the oxygen atom.

Variable Orbital Radius of Electron-Positron Pair

If the orbital radius of the electron and positron increases above r when the unit mass system forms part of a cluster of atomic mass number N, M/m_e, for each unit mass system will be reduced below the value of M/m_e applicable when N is unity. If the radius becomes large in comparison with r, M/m_e may be shown to tend to the following limiting value:

This corresponds to a value of M/m_e of 1,820.8 N or a value of M of 1.6585Nx10^-24 gm. This result is of interest because it is in very close agreement with the mass of Chromium 52 when N is 52 and Chromium 52 has about the lowest ratio of mass to mass number.

This approach, while affording some understanding of the non-integral relationship between atomic masses, will probably upset the derivation of a universally constant value of G. It may therefore be necessary to resort to another alternative approach.

A Time-sharing Existence Hypothesis

According to this hypothesis an atom of mass number N is in reality composed of N fundamental mass units M part of any measurable time and N-1 mass units M the remainder of the time. The observed gravitational effects then only involve at any time actions between units of mass M and the gravitational constant G developed from the aether theory would, on this hypothesis, be a universal constant.

This approach has also interesting quantitative implications. Considering the range of energy exchange required to account for this time fluctuation of the real mass of an atom, it is evident that the least number of atoms or a minimum energy exchange range is involved when the atomic mass NM applies half the time and the atomic mass (N-1)M applies the other half of the time. This suggests that the most stable of all atoms is that for which the known atomic mass is (N-1/2)M. If Chromium 52 is regarded as the most stable atom in this sense it should have an atomic mass of 51.5M or 52 times 1.659×10^-24 gm.

As atomic mass increases there comes a condition for which the atomic mass is very nearly equal to (N-1)M, and thereafter the atom may consist of N mass units M part of the time and N-2 mass units M the remainder of the time. It appears that instability occurs when the N-2 condition applies all the time. Instability sets in when the atomic mass is (N-2)M, or, on the oxygen scale, (N-2)x1.67557/1.6598 or 1.0095(N-2). This value of atomic mass is reached when N is 222 to give a theoretical mass of 222.090 on the oxygen scale, which compares with the corresponding observed mass of Ra 222 of 222.09116.

The whole of this approach would be inapplicable if the theoretical value of M had not proved greater than the mass of any known fundamental particle.



---

The fact that G is constant regardless of the size of the elements of matter which interact gravitationally is a very formidable problem confronting any would-be theorist who seeks to unravel the secrets of gravitation.

One would like to divide all matter into mass units of identical value and then derive G in terms of the force acting between two such units. However our knowledge of atomic structure kills that thought. Yet there has to be some such answer if the force of gravity is to make sense in terms of G as a constant.

My approach along the three lines of enquiry as presented in the above Chapter 7 was relying on the earlier analysis of that 1959 text. I changed course once I decided to seek evidence that the seat of gravitational action lies in the charge continuum and not in the matter system proper. So it was that I eventually took the bold step of saying that the mass of matter is collectively balanced by a local deployment of virtual leptonic charge forms, existing in equal numbers in positive and negative forms, but having an effective mass that comes in units and having a charge volume that, in conjunction with the amount of charge continuum thereby displaced, represents minute units of electrodynamic action as ‘unit’ holes in a moving charge continuum.

Elsewhere in these web pages there is reference to ‘gravitons’ which exist in that sea of continuum charge and define unit quanta which provide the parameters linking G and the charge/mass ratio of the electron in quantitative terms. The mutually parallel motion of those gravitons, whose collective mass matches and dynamically balances the matter mass exactly, is the source of the mutual electrodynamic attraction we see as gravity. Just as two parallel wires carrying electric current in the same direction pull together as if mutually attracted so that same phenomenon applied to the discrete graviton-continuum charges sets up attractive forces in measure related to the product of the masses for which they provide dynamic balance. An insight into this is provided by Tutorial Note No. 4.



---

---

This is a reproduction of the text of a booklet written by the author in 1959, published early in 1960. In the light of his 1998 perspective, some 38 years on from that 1960 effort, the author has added several notes bearing the symbol . These may interest science historians who, hopefully, one day will seek to track how the author’s theory developed over time.

---

This work presents a theory of gravitation which will either come to be accepted as a correct account of the nature of gravitational phenomena or, failing that, will stand as a record of perhaps the greatest of all coincidences in physical theory because the theory relates, by a common simple factor, six basic phenomena in physics and further provides exact quantitative support in each case.

The theory presents a challenge to the General Theory of Relativity and, if accepted, should release the physicist from further need to apply himself to understanding the very complex General Theory of Relativity and thereby enable him to divert his efforts to more fruitful fields of research. This is perhaps a more important consequence of this work than the satisfaction of man’s natural curiosity to understand the nature of gravitational force.

This privately published work is little more than a collection of the author’s abridged notes, but if the reader has the interest to grasp the basic notions presented and judge these in the light of all the results they yield, he will undoubtedly share the author’s enthusiasm.

Harold Aspden
22nd November, 1959.

---

1 INTRODUCTION
2 THE AETHER
3 THE PHOTON
4 THE FORCE OF GRAVITY
5 THE GEOMAGNETIC FIELD
6 THE PERIHELION MOTION OF THE PLANETS
7 THE UNIVERSAL CONSTANCY OF GRAVITY
8 THE GRAVITATIONAL DEFLECTION OF LIGHT
9 THE GYROMAGNETIC RATIO
10 REFERENCES

---

Although modern physical theory, which consists essentially of Quantum Mechanical and Relativistic notions, ostensibly precludes further creative thought on classical lines, it is nevertheless built up around a series of natural laws developed solely by the classical method. To deny scope for further thinking along classical lines is to accept that the set of natural laws existing 30 years ago, when these modern theories became established, is complete.

This work is founded upon the conviction that the classical method was not a spent force 30 years ago, and that it can produce further data which will provide new starting points for advances in theoretical physics. One fruit of this conviction is the derivation of a valid relationship between the Universal Constant of Gravitation and the fundamental atomic constants, and incidental to the derivation of this relationship is the understanding of the very nature of the force of gravity, Newton’s Law of Gravity and, indeed, the minor inadequacy of Newton’s Law in explaining the perihelion motions of the planets.



---

I

INTRODUCTION

Preliminary Note

Quantum Mechanical Theory and the Theory of Relativity each overcome a fundamental difficulty facing classical theory. The problem of the negative result of the Michelson-Morley Experiment is met by Relativity and the quantization problem of the Bohr atom is met by Quantum Mechanics. By their premises these theories avoid the need to provide a physical account for these two problems, and in consequence the theories miss the benefits which such a physical account may confer. These modern theories have left a vast field of theoretical physics wide open for exploration by the classical method and, as will be shown, the explanation of gravitation lies in this field.

The Michelson-Morley Problem
The result of the Michelson-Morley Experiment did not disprove the existence of an aether. A positive result would have confirmed the prevailing notions of a simple universal, homogeneous aether. The negative result provided definite proof that the earth has an aether of its own, a medium which moves with the earth through some surrounding medium. As Campbell [1] puts it:

“If we speak of ‘aethers’ and not ‘the aether’ all our experiments prove is that the particular aether with which we are concerned in any case is that which is at rest relatively to the source and may be regarded as forming part of it. This is the simple way out of the difficulties raised by the Michelson Morley experiment. If from the beginning we had used a plural instead of a singular word to denote the (aether) system … those difficulties would never have appeared. There has never been a better example of the danger of being deceived by an arbitrary choice of terminology. However, physicists, not recognizing the gratuitous assumptions made in the use of the words ‘the aether’, adopted the second alternative; they introduced new assumptions.”

In 1929 Veronnet [2] suggested that the aether was permeated with electrically charged particles having a magnetic moment equal to the Bohr Magneton. This conception can be applied to the understanding of the quantization problem of the Bohr atom and goes a step in advance of the premises of Quantum Mechanics because it affords a physical picture of a space filled with charged particles moving harmoniously in equal circular orbits. In addition to this orbital motion of each particle an extensive matrix of particles can itself rotate. Thus, the earth may well be regarded as having its own matrix of particles rotating with the earth about the carth’s axis of rotation. As this matrix would be the frame of reference for physical measurements on earth no motion of the earth can be detected without reference to something outside this matrix. Also, the earth’s aether particle matrix may evidently move freely through surrounding aether, which it can do if the forward boundaries of the aether matrices of the earth and its surroundings can break up and transmit the freed particles to the rearward boundaries where the matrix is being reformed.

This hypothetical picture readily lends itself to a remarkable quantitative explanation of the principal outstanding fundamental physical phenomena.

The Perihelion Motions of Planetary Orbits

The explanation of these motions provides the greatest support for the General Theory of Relativity, but the aether just envisaged provides a simple alternative explanation. The motion of a planet in its orbit is accompanied by a reverse motion of the freed particles. If the orbit is elliptical and the orbital velocity of the planet accordingly varies, the number of free aether particles in the planet’s local aether will vary and will be balanced by a fluctuation of the number of bound aether particles forming the local aether matrix. Indirectly, as the aether has mass properties, this gives rise to a variable component of angular momentum which has an effect on the planet’s motion. Exact calculation of the effects is possible, and the results establish that the hypothetical aether picture involved is essentially valid.

The Features of a Veronnet-type Aether

The harmonious rotation of a number of identical electrical particles in identical orbits defines, in conjunction with a consideration of electrostatic force action between the particles:

(1) a system in which all the particles are at any instant moving parallel to one another,
(2) a system having a fundamental rotation frequency which is fixed through all space,
(3) a system of particles having a common direction for their rotation axes, and
(4) a system of particles having quantized momenta.

Gravity

The basic explanation of gravitational force stems immediately from the fact that at every instant the electrical particles in the aether move in parallel directions.

The electromagnetic force of attraction between two electrical particles in motion has never been measured. Such forces have been measured only between current systems of which one current flows in a completely closed circuit and the formulation of a general law of force between two current elements has only been required to conform with experimental observation. The simple law is well known but there is a complex law which, although it represents a correct and full interpretation of the experimental data available on the subject, has not come into general or even specialized use because all practical applications involve closed current circuits and the more simple law suffices. The complex law is required to understand the mechanism of gravity.

The original formula of Ampere has been modified by Whittaker [3], who has shown that one of the most simple forms of the general formula is:

where F denotes the force acting on a current element ds’ due to a current element ds, r is the line from ds to ds’, and i and i’ denote their respective current strengths.

Evidently, for parallel current elements, with ds equal to ds’ the force acting between the elements is an attractive force acting directly between them, proportional to the product of their strengths, and inversely proportional to the square of the distance between them. This will yield a qualitative account of gravitation which may be tested by deducing the value of the Universal Constant of Gravitation once an association between a current element and mass has been recognized.

Geomagnetism

Geomagnetism arises from the rotation of the matrix of aether particles forming the earth’s local aether. The effect of this is to expand or contract the matrix to upset the normal aether balance. The electrical effects of this distortion of the aether matrix cannot be detected because the freed particles in the aether matrix which have the constrained counter motion in the earth’s orbit will position themselves to provide a compensating non-rotating charge effect. Nevertheless, the magnetic effect of the rotating electrical charge will manifest itself. It will be shown that this self-induction property of the aether by which a matrix of aether particles in rotation produces a magnetic field will provide an excellent quantitative account for the source of the geomagnetic field.

Dirac’s Continuum

The conception of holes in a continuum is envisaged in the implied aether of Dirac’s work in Quantum Mechanics [4], and the aether model of Veronnet can represent this if it consists of a myriad of identical particles in motion in Dirac’s ‘sea of opposite charge’.

This continuum of opposite charge balances the electrical effects of the aether particles. Mass disturbs the aether by selectively affecting electrically compensating charges to produce an unbalanced magnetic effect owing to a difference in their velocities, a magnetic effect which, for reasons which will become apparent in the following chapters, cannot be detected as such in present experimental work.



---

Readers who may have studied PHYSICS LECTURE NO. 2 will see that by 1980 I had discovered a different way of explaining the anomalous perihelion motion of the planets. However, there is something quite relevant and fascinating in the fact that my researches gave me two explanations for the same phenomenon. When one comes to study the relevant Chapter 6 of this 1960 booklet on The Theory of Gravitation it is seen that I had to introduce the bounding radius of the earth’s aether as a parameter in the analysis. I now (1998) believe that the 1980 version as published by the U.K. Institute of Physics 1980b is the governing formulation, but that the 1960 version provides the explanation of what it is that determines the position of the boundary as between aether rotating with the planet and the enveloping aether which does not share the planet’s rotation. This will be discussed in my notes as added to Chapter 6.

---

2

THE AETHER

Preliminary Note
The aether is regarded as consisting of particles of electrostatic charge e distributed throughout a continuum of opposite charge of uniform charge density a per unit volume. In this system the particles will, by mutual electrostatic repulsion, arrange themselves in a simple cubic lattice-like array to form a matrix whose inter-particle spacing (to be denoted d) is determined by the charge density of the continuum. Thus:

The aether cannot be at rest; it must convey the notion of time and must therefore have some motion. Electrical particles in motion set up magnetic influences and, as equation (i) is taken as fundamental, it must apply to the particles in the aether. This introduces a point which in itself is sufficient to justify the recognition of the aether model presented without recourse to the extensive support which follows. Equation (1) is typical of many capable of satisfying the experimental evidence, but it is the only possible equation capable of being fully consistent with Newton’s Third Law for any value of r. Compare the equation with Whittaker’s equation:

Experimental evidence is consistent with the first term having any numerical coefficient. However, although this equation (3) ensures that there is no out-of-balance of the forces acting between the two current elements there is nevertheless an out-of-balance couple in the general case. This may be compared with equation (1), which is formulated to ensure that there is no out-of-balance couple though there may be an out-of-balance force. Newton’s Third Law demands that force and couple balance are essential in a complete system. However, if the aether is present this may become a party to the system, and it is then useless to draw distinctions between equations such as (1) and (3) which both suffice to satisfy observation.

Consider now the aether particles. These are current elements, and they actually form the aether; when applied to these particles the magnetic force equation applies to a complete system. Equation (3) is inapplicable because it does not guarantee an elimination of the couples between the particles. Equation (1) ensures that the couples are eliminated, but there is only force balance for one condition; the motions of the particles must be parallel. Evidently, as Action and Reaction must always be equal and opposite for any complete system, charged particles forming the aether cannot move unless their motions are parallel.

An Analysis of the Structure of Undistorted Aether

The obvious conditions satisfied by the aether are:

(1) It is mechanically balanced.
(2) It is electrically balanced.
(3) It is magnetically balanced.

Also, as in any electrical system, there is the condition that:

(4) The electrostatic energy of the aether tends
to a minimum value.

The electrostatic energy of the aether can be written :

The factors 2 in the denominators are introduced because each interaction is counted twice in the summation or integration. In these expressions the summations apply to all the aether particles in an infinitely-extending cubic array, the integrals extend over the whole volume V of the aether, x denotes the distance between the element charges and denotes the intrinsic electrostatic energy of a particle. The interparticle lattice distance d is taken to be unity for this analysis.

Let:

m denote the aether particle mass,
denote the continuum mass density,
v denote the aether particle velocity,
u denote the continuum velocity,
r denote the radius of the particle orbit, and

R denote the radius of the continuum orbit.

The first three conditions just enumerated can then be formulated as follows:

(1) Mechanical balance

mv = udV …..(5)
v/r = u/R …..(6)

(2) Electrical balance

e = dV …..(7)

(3) Magnetic balance

evr = uRdV …..(8)

From (7) and (8) it is evident that vr=uR, and from (6) and this result it is further evident that v=u and r=R. Equation (5) then shows that m is equal to dV. The relative velocity between the particles and the continuum is therefore 2v.

When the aether is disturbed and the disturbance is propagated relative to the aether particle system or the continuum this velocity 2v will equal the propagation velocity c. Hence v is equal to c/2.

---

This latter statement needs some justification and this was presented in the 1966 second edition of this Theory of Gravitation text as well as in the author’s later works Physics without Einstein (1969) and Physics Unified (1980). The essential point is that the relative velocity between the system of aether particles and the medium constituting the background continuum is assumed to be the speed of light. The consequences of this assumption are the test of this, but one can appeal to logic and take note that the vacuum medium has somehow to have a property which determines the speed at which light propagates through it and, given that its components have a relative motion that has a universal value, it seems logical to take that as the speed of light.

It is noted here that the author, in reproducing this web page presentation, has retained the mathematical symbols as used in the original printed work. However, since such symbols are not, as yet, standard media features in Internet communication, this has been done by use of images which do not fit well together. This seems a better option than using a style of presentation which writes ‘pi’ for .

---

Next, consider condition (4). The electrostatic energy tends to a minimum. by differentiating equation (4) with respect to and equating to zero it is found that:

From equations (40 and (9):

Examination of (10) shows that the energy E_s is only finite per particle, as it must be, if:

and this agrees with the requirement that E_s tends to a minimum which is simply:

Evaluation of Aether Particle Mass

The condition demanded by (11) is only satisfied if the particle matrix is displaced in the continuum from its electrostatically-neutral position. the restoring force opposing such a displacement is 4e times the displacement. The displacement is clrealy r+R or 2r, and there is balance between the electrostatic force and the centrifugal force when:

From this:
mc² = 32er² …..(14)
The displacement gives rise to an electrostatic energy component 8er², and this enables equation (11) to be written in the form:

where the suffix N indicates that the expression is evaluated assuming that the particle system is in an electrostatically-neutral position in the continuum (the rest position).

The Evaluation of (e/x)dV – (e²/x)

This evaluation may proceed in three stages:

Stage 1: The evaluation of (e²/x) between one particle and the other particles.

Regarding d as a unit distance, the co-ordinates of all surrounding particles are given by l, m, n, where l, m, n may have any values in the series 0, +/-1, +/-2, +/-3, …. but the co-ordinate 0,0,0 must be excluded. Consider successive concentric cubic cells of surrounding particles.

The first shell has 3³-1 particles, the second 5³-3³, the third 7³-5³, etc. Any shell is formed by a combination of particles such that, if z is the order of the shell, at least one of the co-ordinates l, m, n is equal to z and this value is equal to or greater than that of either of the other co-ordinates. On this basis it is a simple matter to evaluate (e²/x) or (e²/d)(l²+m²+n²)^-1/2 as it applies to any shell. Denoting this summation when applied to the z shell S_z, it may be verified that:

By way of example, S₂ is the sum of the terms:
6/(4) +
24/(5) + 24/(6) + 12/(8) + 24/(9) + 8/(12)

Here, 6+24+24+12+24+8 is equal to 5³-3³.

Stage: The evaluation of components of (e/x)dV corresponding to the quantities S_z.

The limits of a range of integration which correspoonds with a z shell lie between +/-(z-1/2), +/-(z-1/2), +/-(z-1/2) and +/-(z+1/2), +/-(z+1/2), +/-(z+1/2). An integral of e/x over these limits is denoted ed²I_z. The expression I_z may be shown to be:

this integral being over the range 0 to 1.

Upon integration:

Within the I₁ shell there is a component I_o for which z in 9160 is effectively 1/8. Thus:

(e/x)dV – (e²/x) may now be evaluated. From (2) this expression becomes

This is equal to:

Stage 3: The correction for finite particle size and free particles.

The particles are not point charges as assumed at Stage 2. Also equation (2) is not strictly correct owing to the free particles in the aether matrix moving through surrounding aether. The latter effect is small, being only of the order of 10^-4 in the earth’s aether. The particle size correction is more important. As the exact nature of the particle is not known it is only possible to form a rough estimation of the necessary correction. Suppose, for example, that the particle is a hollow spherical shell of charge of radius a and that its electrostatic energy e²/2a is mc². Since mc² is
32er² from (14) or 32e²(r/d)²/d from (20), the radius a is found to be of the order d(d/r)²/64. The evaluation of (e/x)dV at Stage 2 then requires correction by subraction by the subtraction of:

the integration being from 0 to a, or 2a²e²/d³ to allow for the interaction between the particle charge and the continuum charge originally considered as occupying the space now occupied by the particle. the correction term is of the order of:

Neglecting this correction term, a substitution of the value 2.31456(e²/d) in equation (15) gives a value of r/d of 0.3035, as:

It is emphasized that the derivation of this correction term is based on mere hypothesis and it is therefore only safe to accept that the ratio r/d, though less than 0.3035, is probably not less than 0.3000.



---

The above calculations were later checked by a computer program, first in 1972 at a time when the doubts about the nature of the aether particle had been resolved (See Physics Letters paper 1972a) and again to allow verification of such a program by readers of TUTORIAL NOTE No. 7 in these web pages.

A weakness of the analysis of this chapter 2 is found in the notion of ‘magnetic balance’ as expressed in equation (8) and this equation does not feature in the author’s later work.

Aether, undisturbed by matter, does not exhibit a magnetic field, as such, though there is a gravitational feature which indirectly could be seen as a kind of magnetic state. The key which revealed the secret was the realisation that the system of aether particles constituted the electromagnetic reference frame. This meant that the aether particles, though sharing a universal jitter at least over vast regions of gravitationally-coherent space, in their synchronized motion in circular orbits in the inertial frame, did not produce a magnetic field. It was then seen that the continuum charge , though moving relative to the electromagnetic reference frame, could not produce a magnetic field. This was owing to its lack of presence as a concentrated charge form having collectively the same charge polarity, that of the continuum. I was later to discover that in this fact lay the true secret of what governed the force of gravitation. However, to proceed here, the result of this was that the step by which vr was shown to equal uR could not depend upon equation (8) originating from a so-called magnetic balance. Further research did clarify the situation. The answer was presented in the discussion on pp. 41-42 of the author’s 1975 book GRAVITATION.

---

3

THE PHOTON

Preliminary Note

On this theory the photon is regarded as a travelling disturbance which involves, at least occasionally, a discrete group of aether particles which is caused to rotate about a group axis, the particles still retaining an orbital motion and being kept in step with surrounding aether particles by a synchronizing electrical action. This particle group forms a tiny matrix akin to the larger matrix of a planet’s aether and this conception of a photon state is merely a logical extension of the ideas already developed in the Introduction. The axis of the particle group is fixed in the inertial frame, and the particles are supposed to retain their Bohr Magneton quantization; that is, their angular momenta are conserved. As a result the group rotation causes the orbital radii of the group particles to be modified. This involves energy. When this energy is evaluated it is found to be proportional to the photon frequency and, accordingly, the radiation law E=h is deduced. The theory can then be put to its first test as h can be evaluated theoretically.

Evaluation of the Fine Structure Constant

The energy of undisturbed aether has a minimum value, and a disturbance can only be brought about by an increase in the aether energy. If the disturbance involves a change in the orbital radii of the particles this change must increase the energy. Evidently r can only increase. Let the increment of r be . Then, if is much less than r, the energy of the disturbance will be 8er per particle. The kinetic energy of the disturbance will also be (m/2)(c/2r)²[(r+)²-r²], which from equation (14) reduces to 8er per particle. The net photon energy is therefore given by E_P, where:

The summation here extends over all particles forming the
rotating group.

The axis of group rotation is perpendicular to the planes of the particle orbits. This is essential for momentum balance. Let x be the distance of a particle orbit centre from the group axis. Then the net moment of velocity of the group rotation may be written x², where w is the angular frequency of rotation. The velocity moment of the particle orbit motion has changed by (c/2r)[(r+)², which, again neglecting ², is c. The total effect of this for the group is c, and for momentum balance this is equal to x². Accordingly:

In rotating, the particle group is in register with surrounding particles four times every revolution. The frequency , characteristic of the disturbance will be that of the fundamental frequency component of /, which is 4(_o/2), where _o is the mean value of _o. It follows from this and (17) and (18) that the mean value of E_P will be given by:

By analogy with the well-known radiation law E=h it is evident that Planck’s Constant h is:

The expression is conveniently written as:

There is no reason to suppose that e is not equal to the electrostatic charge of the electron unless one contemplates very minor effects due to the finite size of the aether particles. The expression in (20) may therefore be taken as representing 1/, where is the fine structure constant. To proceed to evaluate this constant theoretically the quantity x² must be assessed.

The rotating particle group will in all probability be a symmetrical 3-dimensional particle array having a particle at its centre. Furthermore it will have such a size that when a certain frequency is reached the relationship between photon energy and the particle group angular momentum will suit some physical transformation, because it is known that high energy photons can transform into particles. Consider, for example, the condition of the photon when its energy reaches mc², the mass energy of an aether particle. When the photon has this energy it may transform into a non-rotating matrix of particles by creating a particle of mass m. As an intermediate step the matrix may rotate as this involves very little energy, but the particle orbits may adopt their normal radii to transfer the main energy to the newly-created particle which will itself move to provide the balance of angular momentum. This has the following consequences:

(1) The created particle will have no electrical charge; it may be a neutrino.
(2) The particle will be created with a velocity ‘c if it has the same mass energy as an aether particle.
(3) From (I4) and (19) x² is 2rc, which means that the particle will move in an orbit of radius 4r if its velocity is c/2.

The photon particle group will have such a size that the radius 4r is as nearly equal to the group radius of gyration as possible. In terms of the interparticle spacing 4r is between 1.214d and 1.2d from the result of Chapter 2. Only one 3-dimensional symmetrical particle array has a radius of gyration of its photon moving particles between 1.1d and 1.3d. A simple 3x3x3 array has a radius of gyration of (1.5d) or 1.22d. For such a system the value x² is 36d². Thus, introducing this in (20) gives the following theoretical value:

As r/d is slightly less than 0.3035 is it deduced that:

is slightly less than 137.30. This compares well with the observed value of 137.038.

---

Concerning this figure 137.038, it is noted that when this 1959 text was written the value of the reciprocal of the fine structure constant, as measured, was recorded as being 137.0377. Sir Arthur Eddington, who championed Einstein’s theory, had attempted to explain this dimensionless constant of physics by pure theory at a time when it was believed that it might be an integer 137. See Eddington’s Unification of the Constants. His theory amounted to the summation of 1²+6²+10² and could hardly be classified as ‘physics’. It was more in line with the Einstein philosophy of seeking symmetries in multi-diemensional representations of abstract mathematical ideas. In the event, I comment on this here because the quantity, as measured in modern times, is 137.0359895(61), meaning that it is slightly larger than 137.0358 and slightly smaller than 137.0360. Any theory purporting to explain this dimensionless physical constant has to survive the very exacting test of giving that figure with such high precision. The onward development of this author’s theory can rise to this challenge, but here we are discussing its origins from that period in the latter part of the 1950s when the I first discovered the nature of the photon.

---

The Evaluation of r

A fourth consequence of the creation of the particle of mass m is that the magnetic moment of the particle group will not be compensated. This magnetic moment is 2rc(e/2c) or er. This is a fundamental unit of magnetic moment. It will be the Bohr Magneton he/4m_ec, where m_e is the mass of an electron.

It is to be noted that at this stage the Bohr Magneton is associated with an observed quantization phenomenon rather than the unobserved aether. This is a step away from the basic assumption in Veronnet’s Aether Theory.

From known data r may be shown to be 1.93×10^-11 cm.

The evaluation of d, and m

The correct value of r/d deduced from the experimental value of the fine structure constant using equation (21) is 0.3029. As r is known, d can be calculated. It is 6.314×10^-11 cm.

The continuum charge density is e/d³. The value of e is known to be 4.802×10^-10 esu. From these data is found to be 1.857×10²¹ esu/cc.

m can now be found using equation (14). c is the velocity of light 2.998×10¹⁰ cm/sec. m is found to be 3.714×10^-29 gm. This is about 1/25 of the electron mass m_e.

This latter result is interesting as there are 24 particles of mass m rotating with the photon matrix. Also, the result indicates a theoretical mass for the neutrino. Experimental evidence obtained by Nielsen [5] indicates that the mass of the neutrino is of the order of one-thirtieth of the electron mass, a result in agreement with this theory.

It will next be shown how the creation of the neutrino in a photon system guides us to an explanation of gravitation.



---

Equation (13) left me in no doubt that the mass of the aether particle has the value just derived, namely 3.714×10^-29 gm. I had suspected that the neutrino, or whatever is implied by that term, was a figment of scientific imagination devised to describe an artefact of the aether without admitting that the aether really exists. It therefore seemed logical at the time to seize on the Nielsen result for ‘neutrino mass’ as being an experimental pointer to the mass of the aether particle.

The role of the neutrino, its nature and even whether or not it can be said to have mass are all issues that are still debated as open questions and, for my part, it seems that the neutrino concept amounts to little more than a form of aether momentum arising from energy exchanges between aether and matter. See also Neutrino Mass and the notes I add when we come to Chapter 8 below.



---