ASPDEN PAPER 1987o

PAPER NO. 1987o

TESTS OF PHOTON THEORY IN TERMS OF PRECISION MEASUREMENT

Copyright © Harold Aspden, 1987

This paper was presented at a conference held at the University of Gdansk, Poland 21-25 September 1987. It appears at pp. 353-373 in the proceedings of that conference under the title 'Problems in Quantum Physics; Gdansk '87' published by World Scientific (Singapore, New Jersey, Hong Kong) as ISBN 9971-50-449-9.

TESTS OF PHOTON THEORY IN TERMS OF PRECISION MEASUREMENT

H. ASPDEN
Department of Electrical Engineering,
University of Southampton,
Southampton SO9 5NH, England.

ABSTRACT

The author's photon theory, which gives a theoretical value of the reciprocal of the fine-structure constant as 137.0359148 for actions in space undisturbed by matter is extended to the material environment. It is shown that effects related to our motion through the cosmic reference frame can account for the part-per-million discrepancies between the above theoretical value and that measured. The photon theory is further supported by a phenomenon connected with resonance effects in an interaction between atomic electrons and the natural oscillations of the space medium, which are at a frequency involving resonant interaction with the gravity field. This concerns the extreme scarcity of the element promethium.

INTRODUCTION

The study of the photon usually involves the formal methods of quantum theory and their application to experimental data that essentially concern the qualitative features of interactions. Yet one of the most direct indicators of the true nature of the photon is that provided by the quantitative value of the Planck constant h. This constant features prominently in one of the most basic dimensionless constants of physics, namely the fine-structure constant et, which is a pure number representing 2πe²/hc, where e is electron charge and c the speed of light in vacuo. Historically, there have been several attempts to derive this constant on pure theoretical grounds. See the review by Eagles [1] which draws attention to the early proposals of Eddington [2], the more recent proposals of Wyler [3] and refinements by Vigier [4], but, more particularly, the theory of this author (Aspden [5]).

This approach to understanding the photon by calculating the precision value of a is viewed with some measure of scorn by many physicists working in this field, because it tends to be seen as a game of playing with numbers, rather than true physics [6]. Some physicists rely on the 'Anthropic Principle' and see a need for the 'Large Number Hypothesis', looking for answers in some grand philosophical scheme, rather than probing the causal physical basis for individual constants.

Yet, the very reason for measuring certain physical constants with high precision, which is a serious pursuit in national physical laboratories concerned with standards, is recognized [7] as necessary in order to test theories via the accuracy of their numerical predictions. Tests of QED, the theory of quantum-electrodynamics, rely on the progressive advances in the measurement field, which then stimulate further theoretical refinement, followed by a new onward stimulus to perform more accurate tests. However, what has been lacking in this pursuit is the interest in relating the measured values of the fine-structure constant with a recognized theory for the photon. This is no doubt due to the unwillingness by zhose involved in such measurements to recognize that there is a viable photon theory of record that gives a sufficiently definitive estimation of the expected value of a.

The object of this paper is to show that there is good reason for looking at the precision measurement of the fine-structure constant as a means for learning more about the photon. The following discussion will also show that some very fundamental issues come under scrutiny in this exercise, notably the possibility of detecting a preferred frame of cosmic reference. It will also be shown that there is independent evidence supporting the author's photon theory, which comes from resonance features, one relevant to the QED properties of the electron and one which concerns the atomic element spectrum and accounts for the extreme scarcity of the element promethium.

THE NATURE OF THE PHOTON

The full details of the author's photon theory were summarized in the paper presented at the NATO Advanced Research Workshop on Quantum Violations at Bridgeport University, Connecticut, USA in 1986 [8]. The progressive development of the theory is of long-standing record, culminating in 1972, when, in collaboration with Dr. D. M. Eagles of the National Measurement Laboratory in Australia, the definitive resonance condition which determines the precise free-space value of a was discovered [9]. Since then the author has published a full account of the photon analysis in book form [10]. A brief summary analysis in a scientific paper of easy reference [11] dates from 1984.

Essentially, the author's analysis treats the vacuum itself as having the properties we associate with quantum oscillations in an ordered electron gas in which the oscillations are harmonic and confined to two dimensions. The vacuum oscillations are at the Compton electron frequency and, as with any linear dynamic system sustaining synchronous oscillation modes, disturbances store potential energy and dynamic energy in equal measure. However, because of the two-dimensional character of the oscillation modes, the effect of feeding a quantum of energy E into the vacuum field is that a related quantum of angular momentum is also fed into the field. The reaction by which angular momentum is balanced involves a spin structure of the vacuum field which perturbs the surrounding field at a frequency proportional to the spin speed of this structure. Accordingly, if this frequency υ is that of the photon, we see that it must be proportional to E, so determining Planck's constant h in a way which is connected with the configuration of the field spin structure.

The theory then concerns the calculation of this structural system and leads to a value for the free-space dimensionless fine-structure constant that is, in its reciprocal form, found to be 137.0359148, as shown in the 1972 paper [9]. This is in agreement with the measured value to within part per million precision. Yet, of itself, this has proved insufficient to command acceptance and has caused the author to seek the further substantiation presented in this paper.

Since the Bridgeport conference the author's attentions have focussed on two aspects of the theory. One is the theme touched upon in Bridgeport, concerning a possible second-order dependence of the photon theory upon frequency. This involved examining the additional energy needed to sustain the rotation of the spin field structure nucleating the reaction angular momentum for the brief period during which the photon wave train is generated. This energy is a kind of priming energy component that is left behind as the main energy E is dissipated by the photon in its emitting mode. The additional energy is of the order of one ten millionth of the photon energy E at optical frequencies. Some supporting evidence for this proposition has emerged, in that the model of interacting spin units of this kind, associated with a captured photon or standing wave resonance in the electron field, can account for the de Broglie wavelength of the electron. A report on this has already been published and so the subject will not be addressed further in this paper [12].

The other aspect of development is the subject now under discussion, namely the reason for the very slight discrepancies between the value of a as calculated and as measured. To explore this we need to look into the nature of the measurement.

THE QUANTIZED HALL RESISTANCE

It is significant that the most effective method nf measuring the fine-structure constant has proved to be one which simulates experimentally the two-dimensional charge oscillations in the author's 30-year-old model of the vacuum field system.

The experiment involves applying an intense magnetic field in a direction normal to the plane of a very thin film of conductive substance having a very low population density of charge carriers. This and the fact that the experiment is performed at low temperatures assures that collisions are less likely. The charge carriers are caused to convey current in one direction in parallel with the film and the related Hall voltage is measured at right angles to both the magnetic field and the current. The 'resistance' determined by the ratio of this induced voltage and the current, if expressed in electrostatic units, is found to be dependent solely upon the fine-structure constant.

The force balance on the charge carriers can be written as:
Ee = Beu/c ................. (1)
where e is the charge of a carrier, u is the carrier speed, E is the electric field intensity, B is the magnetic field intensity and c is the speed of light in vacuo.

The current I per carrier layer has the form:
I = neu/c .................. (2)
where n is the number of carriers in unit layer and unit length of conductor. The Hall resistance R per layer of width w is, therefore, wE/I or, from (1) and (2):
R = wB/ne ................... (3) wB/n is the flux quantum φ, found by supposing that the work done inductively by such flux quantum linking a circular loop described by a charge carrier in its reaction to the magnetic field is equal to the energy of a photon having the related frequency. To find φ we write:

φi = hυ ..................... (4) where the loop carrier current i is found from:
(2πr)i = ev/c .................... (5) and:υ = v/2πr .................... (6) Here, r is the radius of the charge circuit linked by the flux and formed by the charge e describing this circuit at speed v.

Combining these equations:
φ = hc/e .................... (7)
Then, since wB/n is φ, one finds, from (3), that:
R = hc/e² = (α^-1/2π) ................. (8) By measuring R (in electrostatic units) one has, therefore, a direct measurement of α, the fine-sutcture constant. Such measurements give α^-1 as close to 137.036, a typical measurement, recently reported [13], being 137.036012(11).

However, one of the problems being faced by the experimenters is that they cannot quite reconcile the values obtained at different times and at different locations with the standard error ranges involved. One wonders, therefore, whether some variable of a few parts in ten million is affecting their data.

THE COSMIC MOTION EFFECT

In order to compare the author's photon theory with measurements such as that just discussed, one needs to remember that the theoretical value of 137.0359148 was derived for free-space conditions. This concerns a vacuum field not disturbed by local matter or the state of motion of this matter.

When considering the release of an energy quantum to create a dispersing photon state in the field medium, one needs to think in terms of a photon being created where matter exists and then travelling out into the free-spac-. regions of the field. The frequency of the photon will not change in this process, apart from the apparent effects of Doppler action caused by relative motion. The energy released will go, in the main, into setting up the dispersing photon state carried at the photon frequency. However, some energy may go into an ancillary condition residual to the local field which shares the motion of matter at the photon source.

Now, it is not customary in modern physics to think in terms of a motion of a field, as opposed to a propagating disturbance of the field relative to an observer. Yet, if we think in classical terms and imagine that we are at rest in a preferred frame looking at matter moving, with its field system, through that preferred frame, we can ask the question as to how a photon sourced in that matter disposes of the energy component that the source matter has owing to its motion in that preferred frame. Considering the Earth's motion at a few hundred kilometres per second relative to the preferred frame (the background in which cosmic radiation is isotropic), we can take its speed, using a redesignated term v, as being such that v/c is very much smaller than unity. Then we can be sure that the energy component is one half of (v/c)² times the photon energy quantum E. This is merely the kinetic energy of the mass-equivalent of E. Looked at in the frame of reference seated in the field of matter moving at speed v, the photon energy is E, but this energy comes from a source which releases the energy that is 'seen' in that frame plus a further amount of (v/c)²/2 times this energy, owing to motion through the cosmic frame. The energy quantum that is 'seen' in the Earth frame of the Hall resistance experiment is φi (c.f. equation 4), but the actual energy released is hυ augmented by the factor (v/c)²/2.

In terms of evaluating the flux quantum, it is necessary to imagine that the photon energy hv requires supplementing by the additional term so that the condition of the local field co-moving through the cosmic or preferred frame is suitably primed to cater for this action.

Consider what this does to the determination of the flux quantum or the value of the quantized Hall resistance R. It will increase by the very small factor (v/c)²/2, meaning that α^-1 will be greater in the moving Earth frame than it is for photons generated in the static free-space preferred frame. In other words, the discrepancy between the theoretical free-space value and the measured value will tell us how fast the Earth is moving through the preferred frame.

The ratio of 137.036012(11) to 137.0359148 is 1+(v/c)²/2, telling us that v is 357+/-21 km/s, or rather that it had this particular value at the time of measurement.

Had we argued from relativistic considerations that the motion v cannot be sensed by experiments confined within the Earth laboratory, then v should be zero and the discrepancy between the theoretical and measured values of α remains. By arguing that there is a cosmic motion effect we have obtained a value close to the 390+/-60 km/s obtained from the measurement of cosmic background radiation [14].

It is then clear from this that the author's photon theory might be tested by precision measurements of the fine-structure constant that are accurate enough to trace the Earth's annual motion around the sun. This would be represented by the effects of the 30 km/s speed of the Earth in its solar orbit, which should correspond to the fluctuations in the fine-structure constant measurement in an annual cycle.

Before discussing this further, it is of interest to discuss supporting evidence that is independent of the argument just used.

ELECTRON g-FACTOR MEASUREMENTS

Resonant interactions are of basic importance to the author's photon analysis. An interaction involving the fine-structure constant is found in resonant cavity models of the electron. Such models have been used by Jennison [15] to explain the property of inertia and by the author [16] to explain the anomalous component of the electron magnetic moment in the g-factor expression.

The general property involved is that there is a spherical field cavity containing resonant oscillations centred on the electron. These are at the Compton electron frequency and imply a field cavity radius of half the Compton electron wavelength.

The question of interest here is whether this spherical field cavity is distorted if the electron is moving through the preferred frame. Now, if the cavity were formed by a rigid body, we could think of it as a system of mirrors having attributes of the mirror configuration used by Michelson and Morley in their famous experiment. They could not detect any motion through the preferred frame. However, the fact that the mirrors are spaced apart by distances measured in tens of thousands of wavelengths means that standing waves are formed. These could act as a forcing constraint to cause the energy field to affect the wave velocity differently in opposite directions, in spite of the motion through the preferred frame. The Michelson-Morley test is not, therefore conclusive in disproving that such motion is detectable.

When one considers longitudinal oscillations of the electric field over a round trip distance equal to one wavelength there is no basis for standing waves in the conventional sense. Also the field cavity radius is not rigidly determined. It can vary in dependence upon the resonant conditions. Indeed, we may expect it to vary with orientation relative to the direction of motion of the cavity centre with respect to the cosmic background or the preferred frame of reference. This may seem to be speculation, but, just supposing that the resonance exists, then we know that the radius of the cavity in a given direction will be related to the radial wave velocity.

If the radial wave velocity is c+v in the direction opposite to that in which the electron is moving at speed v through the preferred frame and c-v in its direction of motion, then the radius is such that the round trip period is independent of v. The period is that characteristic of the Compton electron frequency. For resonance regardless of the direction of the wave velocity, the bounding field cavity will be of ellipsoidal form, having its major axis in the direction of motion of the electron. Indeed, this major axis will be determined by the Compton wavelength of the electron and be independent of v. The electron can be regarded as lying at a focus of the elliptical form, when the field perturbation becins to radiate from it outwardly at speed c in the preferred frame. The electron is then deemed to be moving at a steady speed v towards the other focus, reaching it with the perturbation that is reflected back to this new focus after deflection at the field cavity boundary. Then the cycle repeats with the electron in its new forward position and a new field cavity is fcrmed in a correspondingly-advanced position in the next cycle of oscillation at the Compton frequency.

The semi-minor axis is smaller than the semi-major axis by the small factor (v/c)²/2. When averaged over all directions, bearing in mind that the semi-major axis is independent of v, the average cavity radius is reduced by the small factor (v/c)²/3.

What this means is that, owing to the cosmic motion at speed v, the field energy of the electron that is located outside the resonant cavity is increased in proportion to this factor (V/C)2/3. Now, it is this external energy component that is excluded from the effect of electron spin and that causes the electron g-factor to be anomalous, as shown by the author elsewhere [16]. It follows that the empirical value of the fine-structure constant, as derived by assuming that v = 0 by the author's method, using the experimental value of the g-factor, will be in error by the fractional amount (v/c)²/3. Then, since the empirical value found for α^-1 was 137.0359894, as shown in reference [17] on the assumption that v = 0, that is that there is no v-dependence, we really need to correct this value by reducing it by the (v/c)2/3 factor. Now, ideally, according to the author's photon theory, the free-space (v=O) value of α^-1 is 137.0359148. Therefore, if this theory is valid, the empirical data tell us the speed v at which the laboratory was moving through the preferred frame at the time of the measurement. This allows us to determine v/c as 0.001278, which tells us that v was 383 km/s.

This value is in such close accord with estimates of the cosmic speed of the solar system relative to the isotropic radiation background that it does suggest that the theory is valid. We have arrived at the interesting proposition that the precision measurement of the electron g-factor should ultimately reveal a variation in an annual cycle as the km/s motion of the Earth around the sun is compounded with the sun's motion to give a value of v that varies. The effect of this annual variation would be quite small, resulting in a mean deviation in the electron g-factor of the order of 50 parts in a trillion, but, curiously, this happens to be commensurate with the reported uncertainty in the measurement, supposing that it is a true constant.

THE VARIATION OF THE FINE-STRUCTURE CONSTANT

It is generally supposed that the fine-structure constant does not vary with time. The reason for this is the argument that the comparison of the time kept by an atomic clock and by a resonant oscillation sustained in a superconducting cavity shows no variation [18]. The argument supposes that the atomic clock involves a in a different dimensional combination from that applicable to the superconducting cavity. Then the constant ratio of their time rates infers that a cannot change, even by the very small amount that we would expect from the earlier discussion.

The weakness of this argument is the assumption that Planck's constant h and the speed parameter c in the formula α=2πe²/hc are true constants. In fact, it is pure assumption to suppose that h as used to determine the basic quantum of angular momentum of the atomic electron is identically the same as the h which defines the relationship between a frequency and an energy quantum. So far as c is concerned, our whole discussion concerns its possible variation, either owing to our choice of reference frames or because light speed is affected by passage through energy fields, whether within matter or due to resonant interactions, as in standing wave situations. Indeed, the speed of light is known to vary under the influence of a gravitational field in the vacuum medium.

Accepting the assumption in reference [18] that the dimensions of the superconducting cavity cannot physically depend upon motion at speed v, which is the author's opinion also, we must accept that the speed c depends upon v. The reason for this is that we know that the atomic clock suffers a loss of time rate owing to translational motion. The experiment shows, in effect, that two clocks keep the same relative time. Therefore, even though they operate in different ways, the period of the oscillations in the superconducting cavity must also be affected by motion at speed v.

To underline this critism of the accepted argument on which a is deemed to be invariant, note that it depends upon the supposition that the physical separation of atoms in the substance forming the superconducting cavity is fixed in relation to the Bohr radius of the atomic electron. This radius is determined by the value of h as it applies to the quantum of angular momentum. Logically, if this is a universal quantum set by the undisturbed vacuum field, it would mean that h as used in this context is a true constant. Equally, the fundamental unit of charge e should be time-invariant. The frequency of oscillations in the superconducting cavity will, accordingly, be proportional to the speed of electromagnetic waves in the cavity, which is likely to be a function of v. In contrast, the time-keeping of the atomic clock considered in reference [18] concerns a hyperfine transition in a Caesium atom. Supposing that the gyromagnetic ratio of the proton and the proton- electron mass ratio are both constants, which is consistent with the author's theoretical evaluation of these quantities [19], [20] it may then be shown that the frequency of the clock is proportional to the square of the fine-structure constant α, as derived from the angular momentum meaning of h, and inversely proportional to h in its connotation as an energy-to-frequency conversion factor.

It follows that the experiment reported in reference [18], which shows that the clock rates keep the same time independent of v, for the atomic clock and the superconducting cavity oscillator, merely tells us that, if a based on the angular momentum connotation is a true constant, then a based on a combination of a v-dependent h and a v-dependent c is also constant. This does not preclude v-dependence of effective values of a formulated by using a v-dependent h and a non-v-dependent c, and vice-versa.

To facilitate this argument, the v-dependence can be expressed in terms of a factor β, which approximates 1-(v/c)²/2 for small v/c. Then, if the angular momentum quantum value of Planck's constant is h_o, we can write h as h_o/β, where h has a value applicable to the equation E=hυ in a system moving at speed v through the preferred frame. Also, we can think in terms of a constant value of light speed c, in the preferred frame and a speed c equal to βc_o in a system moving at speed v through the preferred frame. The superconductivity cavity oscillator operates at a frequency proportional to c or βc_o. The atomic clock operates at a frequeny inversely proportional to h or h_o/β. The ratio of their frequencies is independent of β but the atomic clock rate is still a function of β. The fine-structure constant formulated from hc is also independent of β and is the same as that formulated from h_oco, but the question at issue is what is measured in the test based on equation (7).

The derivation of equation (7) involves an α relationship containing a v-dependent value of h, because h comes in via the E=hυ term of equation (4), and a non-v-dependent value of c, because c comes in really as c_o via the quantized motion of the charge e and not from the standing wave system that holds, for example, in the superconducting cavity oscillator. The flux quantum of equation (7) is really hc_o/e and this tells us that the Hall resistance measurement of R is really a measure of (1/β) times h_oc_o/e². This latter expression, in its reciprocal and adjusted form as 2πe²/h_oc_o or 2πe²/hc can be said to be the true fine-structure constant. It follows, as we have seen from the earlier analysis, that the fine-structure constant is underestimated by the measurements of the quantized Hall resistance, by a small factor that depends upon motion through cosmic space at the speed v. Also, the experimentally-based argument that the fine-structure constant is invariant proves to be valid. It is just that the experiment used to measure the fine-structure constant, whether the quantized Hall resistance measurement or via the Josephson route, happens to measure a hybrid version of the fine-structure constant that depends upon motion through space.

THE VARIATION OF LIGHT SPEED

By introducing the expression c=βc_o we have raised a very fundamental issue. The author sees this as the alternative to time dilation, which is the enigmatic feature in Einstein's theory. The speed c_o is the isotropic light speed of free waves in vacuo as referenced on the preferred frame. The speed c is a speed that is characteristic of motion of components of a standing wave system, whether set up in the superconducting cavity oscillator, a laser, or the Michelson-Morley apparatus.

A wave moving one way through an oppositely-directed wave of the same frequency and intensity will set up standing wave oscillations. The standing wave energy is transported w-ith the apparatus and, unless we are prepared to accept that there is some phase-modulation which affects the symmetry of the interference, speeds of the two waves through the preferred frame have to adjust to become equal in the frame of the apparatus [21]. This is why the Michelson-Morley experiment gave a null indication. It did not preclude the existence of a true light speed c referenced on the preferred frame. The speed of a light wave is known to be affected on passage through the field energy of a refractive substance and it must, therefore, be affected by passage through a counterpart field of equal intensity set up by its own reflected wave.

The author believes that something characteristic of a space metric is caused to be transported by matter in which there are standing wave oscillations. This is the basis of the author's photon theory, which requires a lattice-structured space metric. A state of resonance characterizes this metric, causing the standing wave light speed c to be isotropic as judged by an observer moving with the metric. This goes a long way towards a compliance with some of the principles of Einstein's methods. However, Einstein would preclude the possibility of detecting motion of that metric or lattice with respect to a preferred frame. This is not the position taken in this paper.

Considering standing waves set up by a reflected beam perpendicular to motion through space at speed v, the energy in the standing waves is not carried relative to the preferred frame. The nodes which bound the energy packets have zero velocity relative to that preferred frame. Hence, we can suppose that the wave components can travel at the speed c_o, effectively being free waves. Then by the construction with which we are familiar from the theory of the Michelson-Morley experiment we can show that:
(c_o)² = C² + v² ............... (9) This gives us equality between c_o and c/β, thereby supporting the argument used in the previous section.

In order to prove experimentally that there is a preferred frame the above theory can be applied in the following way. The objective is to cause two light waves of identical frequency but different intensity to travel through one another in opposite directions along an axis in which a component of v is to be measured. To the extent that these waves cancel they will set up the standing wave system causing the wave components to move at speed c in the frame of the apparatus. However, to the extent that one wave is stronger than the other, the residual wave component will travel as a free wave at speed co referenced on the preferred frame. All that then needs to be done is to apply rather obvious interference methods to verify that c and c0do differ as a function of orientation of the apparatus. This experiment was proposed in reference [21]. A brilliant implementation has recently been reported by Silvertooth.

THE SILVERTOOTH EXPERIMENT

Silvertooth has recently claimed a break-through in the detection of our motion through cosmic space by optical interference tests in a confined laboratory [22], [23], [24] The tests indicated a typical cosmic speed of 378 km/s.

Silvertooth sets up the standing wave by using oppositely-directed rays from the same laser. He does not do this by direct retro-reflection at a mirror. Rather, the source beam is split and sent separately as two rays around a circuit of mirrors. The two ray paths are not symmetrical because one ray is reflected more times than the other. This helps to assure that the rays have different intensifies when they intercept at the detector.

The standing wave component sets up nodes that depend upon the speed c, whereas the residual wave component travels at speed c_o, which differs from c. As a result, the uniform amplitude of the standing wave is modulated by superimposed effect of the residual wave, which presents a wavelength differing from that of the standing wave components by the small factor v/c.

Silvertooth uses a special standing wave detector to scan along the beam and oscillates the mirrors to provide a measure of the wave amplitude. By tracking over the range of maximum change of signal a distance is measured which corresponds to (c/2v)λ, where λ is the wavelength of the laser beam used.

Silvertooth has found that v is directed along the axis that applies to our motion through space relative to the assumed-isotropic cosmic background radiation and he obtains values of v that are in accord with those measurements.

Note that this experiment does not measure the difference in the magnitudes of the two speeds c and c_o, meaning their second-order difference in terms of v/c. The experiment measures the first-order difference arising from the fact that they are referenced on different frames in relative motion at speed v. It is the precision measurement of the fine-structure constant that requires second-order adjustment.

Although Silvertooth has been preoccupied by experimental investigations aimed at achieving what Michelson and Morley set out to do over 100 years ago, success in this has repercussions for the parallel 1903 experimental work of Trouton and Noble [25]. They failed to detect our cosmic motion by an electrodynamic test based on the Lorentz force formula.

In this regard, the author [26], [27], [28], [29], [30] has, since 1960, been urging physicists to realize that the Lorentz force is deficient, in that it fails to include a term corresponding to the process of induction. The action between two separate discrete charges in motion is not that of a steady state magnetic field acting on a charge without transfer of energy. Allowance for induction effects adds a term which makes the Lorentz force have symmetrical form when written as a vector expression using scalar product notation. This additional term completely nullifies the Trouton-Noble experiment as a test for motion through the preferred frame.

The formal analysis which corrects for this deficiency results in a modification of the basic electrodynamic force law which, for action between like polarity charge in like (parallel) motion at the same speed, gives a mutual interaction force acting directly between the charges and varying only as the product of their strengths if their speeds are kept constant. The force -satisfies the inverse-square-of-distance form. Hence, the author, even in 1960, saw this as the link between electromagnetism and gravitation. It was from this that the author's photon theory led to a gravitational theory in which the constant of gravitation G could be derived in a dimensionless relationship with other constants, just as h had proved derivable in its fine-structure constant settings [10]. A basic feature of this theory was that gravitational effects involve a characteristic resonance at the frequency of the Compton electron.

The essential and underlying feature of the theory is the synchronously oscillating lattice comprising the ordered constituent of the vacuum medium. A recent paper discusses cosmic motion effects upon such a lattice [30].

THE MISSING ATOM

The object of this paper so far has concerned the support available for the author's photon theory to be found in precision measurements of the fine-structure constant. This support is important, from the author's viewpoint, because it reconciles a quantitative result deduced some 15 years ago with the latest measurements. It leads, however, to the need to accept that our motion through space at speeds approaching 400 km/s can be affecting the measurement of the fine-structure constant. This is tantamount to suggesting that our translational motion through space can be detected within the confines of the laboratory. This result is very far-reaching, because it runs counter to Einstein's theory and so will not be readily accepted. This is especially the case, because the basic photon theory involved relies on the formal analysis of the vacuum as a real and structured field medium, an approach which is very different from the mathematical formalism of fields in 4-space. It is for this reason that the author has taken a particular interest in the researches of Silvertooth and his experiment proving that we are moving at speeds of the order of 400 km/s through a preferred frame affecting the speed of light. To the author, this discovery in recent years has been quite exciting, because it had been thought that the experimental evidence supporting the author would be less direct. The problem of the Trouton-Noble experiment had, as already noted, been seen as the crucial factor in the author's earlier work.

In looking at the photon in a 3-space background and taking its very source to be the physical form of a spinning structure, the question now arises as to whether this structure intrudes upon the internal structure of atoms. This is not a new thought, but what is new is the idea that spinning photon structure can perturb an atomic electron at a frequency that is close enough to the Compton electron frequency to induce a resonant interaction with the gravity field in such a way that it is energetically unfavourable for the affected atom to exist with a normal lifetime in the stable Earth environment.

Accordingly, the author has explored this aspect of his theory to look for evidence of relevance, hopefully linking the photon with gravitational effects. This is an entirely different approach to verification of the author's photon theory.

The frequency at which an electron in the innermost shell of an atom would have to oscillate to be in resonance with the Compton electron frequency is exactly that which corresponds to an atom having a nuclear charge that is &alpha^-1 or 137.036 times that of the proton. An atom with an atomic number Z equal to 137 should, therefore, exhibit interesting properties related to positron emission and energy anomalies connected with gravitation.

Such atoms do not occur naturally, but can, in effect, be created transiently in high speed collisions between two atoms which have a combined Z value of 137. Research on this should give support for some of the views here expressed.

A relevant question then arises in the following way. Suppose that space has an electrical structure on a dimensional scale commensurate with the orbits of electrons in the K shell of the heavier atomic nuclei in the periodic table. This could perturb the electron motion. It will lead to harmonics in their basic modes of oscillation. Symmetry considerations indicate that it is the odd harmonics that will be produced. Accordingly, we then find that the nth harmonic, with n odd, would give a near resonance in an atom having a Z value given by 137/(n). This effect will be all the greater if the mean radius of the K shell happens to be close to the structural dimensions of the vacuum according to the author's photon theory. Hence, that theory can be tested if it leads to a prediction of an atomic nucleus that does have the necessary highly-anomalous properties.

The photon spin unit of the theory is a 3x3x3 cubic lattice defining sites which could be occupied by electric charges set in a neutralizing uniform sea of opposite charge. The optimum perturbation occurs when the spin axis drawnthroughthree charges is also the axis applicable to the orbital electron motion in the K shell. This means that the critical radius of the K shell is 2 times the lattice spacing d. As shown in reference [11], d is 72π times the classical electron radius.

From these very simple considerations, using Bohr theory as a guide, the value of Z given by this condition will be close to that satisfying equality between Z2 and (137)²/72π. This gives Z as close to 59, but we know that resonance selects the nearest value of Z as 137/(n), with n odd and as low as possible to make a resonance more likely. This has a unique solution with n=5, giving Z=61, which is the element promethium.

The crucial test for the theory then is whether promethium exhibits any special properties that might signal interaction with gravitation, as by exciting energy exchanges that somehow make the element unstable. Such evidence is before us in any data concerning the crustal abundance of elements. Promethium is so scarce that its natural abundance has not been measured. It is a rare earth that is so rare that gold is at least a million times more abundant and gold happens to be the element for which n=3 in the above argument. Promethium stands as the least abundant of all the elements in the periodic table that are not highly radio-active and, in particular, it is extremely scarce compared with its immediate neighbours in the periodic table. Yet the theory points to promethium as the unique element that should be special in the sense that photon interaction should excite resonance between its electrons and the natural frequency at which electrons and positrons are created.

This opens the way for research aimed at technological exploitation of the connection with the gravitational energy field, with spin-off that could verify this photon theory. Numerical aspects of the precision measurement of the fine-structure constant are not the sole means by which the photon theory can be verified.

A discussion of the abundance of promethium and a related phenomenon connected with technetium will be published separately [32], but it is suggested, as a conclusion to the work reported here, that resonance effects play a predominant role in determining the most fundamental physical constants. The ultimate truths concerning the photon will, it seems, provide the link between electromagnetism and gravitation via the structural properties of the vacuum medium.

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NOTE: The above paper is as published in the conference proceedings (see heading of the paper). It includes in the references three items that were not as yet published at the time the conference was held. The later publication data for these three items [8], [31] and [32] above are:
(8) Published by Plenum Press, New York in NATO ASI Series B: Physics Vol. 162 (ISBN 0-306-42670-6) 1987.
(31) Published in Hadronic Journal, 10 pp. 185-192 (1987)
(32) Published in Hadronic Journal, 10 pp. 167-172 (1987)