A THEORETICAL ANALYSIS OF THE ELECTRODYNAMICS OF SUB-ATOMIC PARTICLE INTERACTIONS
Walter Babin
Archon Scientific Research Corporation
Box 433, Rodney, Ontario, Canada, N0L 2C0
E-mail: wbabin@sympatico.ca Telephone: (519) 785-0413
Abstract:
The logical contradictions evident in the kinematics of Special Relativity have been independently identified by a number of individuals since the original publication of the paper. Despite this, the theory remains operative through a perceived correspondence with experiments that pre-date, or were subsequent to its publication. However, a rigorous analysis of the experiments leads to a new theory based on classical electrodynamic principles independent of the precepts of SRT.Introduction:
A. Einstein’s Special Relativity incorporated the contraction of space and the dilation of time as basic arguments towards the maintenance of universal constancy for the speed of light. Consideration of the classical conservation laws led to equivalent modifications in the concept of mass. Experimental corroboration; notably that of Kaufmann, 1901, Bucherer in 1908 [1] and Compton in 1923 [2] lent credence to the theory despite opposition and criticism from the outset. [3]
An independent analysis of relativistic kinematics was made in a previous paper [4] where it was proven that arguments supporting contraction and dilation of space and time were tautological. The analysis will not be repeated here, other than to demonstrate that presumed modifications between equivalent frames of reference must be reciprocal and therefore undetectable in strict accordance with the first postulate.
In the following, a comparison is made of equal measured lengths, (x and x’), in two frames of reference, (S and S’) in uniform relative motion. The length x’ would be “viewed” by an observer in S as contracted by the factor, b = (1 - v2/c2)1/2 as required by Special Relativity. Conversely, x would be contracted by the same factor to an observer in S’. Either observer may consider his frame to be fixed or in motion. We then have the relationships:
x’ =xb and x = x’b
x’/x = x/x’ \ x’ =x (1)
Precisely the same argument may be applied to both time and mass.
Since no adjustments in lengths or times can be admitted, it is obvious that clocks separated by a distance may be synchronized either by mechanical means or, if we affirm the constancy of the speed of light, [5] by the transmission of light signals. Regardless of the geometry of space-time, it is evident that if clocks situated at distant coordinates are related by a consistent formula, then synchronism is possible.
Lorentz Transformation Equations
We may presume the above arguments were considered by many, and presume further that they were disregarded because of the perceived agreement of relativity theory with experiment. Furthermore, it was well known that Maxwell’s equations for the propagation of electromagnetic waves were not invariant under a Galilean transformation, but remained so under a Lorentz transformation. [6]
There is no doubt that this invariance was viewed an impressive contribution towards confirmation of the theory in general. However, it cannot be attributed to relativistic space-time modifications for the above reasons. Furthermore, an asymmetry between the two reference frames is required. Since the Lorentz transformations were introduced to maintain the constancy of the speed of light, the asymmetry can only apply to time. By eliminating b in accordance with the preceding assessment, the transformation equations reduce to:
x = x’- vt’ x’ = x + vt
t = t’ + vx/c2 t’ = t - vx/c2 (2)
Since x = ct, and x’ = ct’, the equations for time become:
t = t’(c - v)/c t’ = t(c + v)/c (3)
The ratios of the equations of (3) cannot be attributed to the dilation of time or asynchronous clocks. By inverting them, we see that the Lorentz time transformations become the classical Doppler equations for the frequency of light and the space transformations of (2) become those of wavelengths.
¦ ’ = ¦ (1 +/-v/c)
l ’ = l (1 +/- v/c) (4)
This explains the invariance of the equations. If relativistic modifications of wavelength and frequency are indeed an experimental fact, they must necessarily be attributed to the cause of propagation or contained in the nature of light itself.
It is contended from the foregoing that the kinematics of Special Relativity cannot logically provide a theoretical basis for electromagnetic interactions or for dynamics in general. Clearly, a new theory is required. The principle goal of the following is to provide a general theory for sub-atomic particle interactions, and an analysis of the characteristics of light and matter. This will be largely qualitative through necessity, as the subject is extremely broad. Also, many aspects have not been sufficiently explored through experiment.
The Compton Effect
The A. Compton experiments were widely hailed as corroborative evidence for Special Relativity. The following re-evaluation suggests that an entirely different conclusion may be reached.
The scattered radiation of a wave particle interaction was considered by Compton to be the quantum result of an elastic collision between an electron and a photon. A more accurate description would be to view it as a partially elastic coupling or a transfer of energy between fields since the wavelength of the scattered radiation is found experimentally to be:
l ’ = l + h(1 – cos f )/mec (5)
Where h = Planck’s constant and me is the rest mass of the electron.
The latter term is precisely the magnitude of the wavelength of the electron’s magnetic moment. Since [h] has the dimensions of the angular velocity of an electron in the first Bohr orbit, the masses cancel. However we will continue with the original derivation, since no changes should be introduced unless warranted by the experimental evidence.
The energy, E’ of the scattered radiation may be derived from the Compton relationship:
1/E’ = 1/h¦ + (1-cos f )/mec2 (6)
Where ¦ is the initial frequency of the wave. The energy value of the scattered radiation may be used in the relativistic energy equation along with the initial energy value E, of the photon. The energy relationship is:
E + mec2 = E’ + mefc2 (7)
Since the total energy, (mefc2 ) equals the sum of the kinetic energy (K) and rest energy of the electron, we have:
mefc2 = mec2 + K (8)
and
E + mec2 = E’ + mec2 + K,
or
E – E’ = K (9)
Which simply states the photon energy loss equals the kinetic energy of the electron.
mef c2 = mec2 + ½ mefvk2 (10)
The similarity between equation (10) and that of the energy density of a moving charge at unit distance should be noted. By re-arranging terms and division by the total energy we find the ratio of the rest and “kinetic” masses to be:
me /mef = 1 – vk2/2c2 (11)
This is neither the mass ratio, nor the velocity required by relativity. Furthermore, it precludes the null result of b when the velocity reaches the speed of light. By substituting the mass and the energy of the scattered radiation in the momentum equation, we have:
E/c + 0 = -E’/c + mef vc (12)
The presence of conflicting speeds may be resolved by considering that an accelerated electric field produces a magnetic field, or more accurately, that there is an instantaneous manifestation of both. The ratio of the masses expressed as the two velocities is:
me/mef = (1 – vk2/2c2)2 = 1 – vc2/c2
\ vc2/c2 = vk2/c2 - vk4/4c4 (13)
The third term of equation (13) may be attributed to induced electrical and magnetic fields in opposition to the growth of the initial fields. The transferred energy of the coupling is retained since the “mass” increase is not modified. If we view the process as a field interaction, it provides a satisfactory explanation for the reduced momentum. If the interaction is viewed as an electron-photon collision, a change in the intrinsic angular momentum of the electron is a likely candidate for the shortfall. In any case, it is obvious that the reduction is not due to emitted radiation as required by classical electromagnetic theory since the mass increase is retained and energy conservation can be satisfied totally within the interaction.
The wavelength of the scattered radiation is seen to be the sum of the initial wave and that of the magnetic moment of the electron. Therefore, it is reasonable to assume that the wavelength of the magnetic moment is affected in return. However, where the wave is additive in the case of the photon, the situation with the electron is considerably more complicated.
An evaluation of equation (11) strongly supports the existence of an internal or intrinsic standing wave configuration with component velocities at (c + v) and (c – v). The de Broglie wave provides further support for this assessment, since it incorporates the increased mass of equation (11) and the base particle attributes of (h). In fact it is reasonable to assume that it is the de Broglie wave since it differs only by a few percentage points at experimental limits.
Regardless of whether the Compton interaction is viewed as a collision between particles or a field coupling, it is amply evident that the total particle-wave aspect of the electron is involved and that total energy is conserved. The increase in “mass” may be considered to apply either to the electron or the electromagnetic field. The probable answer would be that the symmetry evident between electrical and magnetic properties also exists in a dual form of matter and is a property of electromagnetic radiation as well. This is effectively confirmed by the existence of pair production, which generates electromagnetic fields and particles.
Further evidence is available in consideration of the cross-field configuration of mass spectrometry [8] where the inertial effects and selective process may be viewed as the result of a magnetic field density in opposition to the external field, as well as an increase in the electron’s mass. The standing wave configuration would find additional support if electrons were included in the process despite opposite spin orientation. Velocities up to the maximum of twice the speed if light are also indicated, and the orbital/intrinsic standing wave hypothesis provides a theoretical basis for the Sagnac effect.
The Nature of Light
Excitation of an electron creates instantaneous and proportional fluctuations in electrical and magnetic amplitudes. Since all aspects are dimensionally equivalent, propagation cannot be attributed to an electromagnetic ratio at the source or at any point along the line of propagation. The virtual particle aspect of the photon immediately suggests a contribution from the particle’s mass characteristics. A ballistic explanation for convection is suggested and with it, an associated space and time continuum (wavelength and frequency).
The periodic nature may be due to a pulsation or fluctuation of the posited duality in matter. Since we know that a sufficiently energetic wave will produce an electron-positron pair, we can be reasonably confident of this explanation unless it is shown that pair production is attributable to the target nucleus. Also, the application of equation (11) to a photon provides immediate support for the dual hypothesis.
An entirely equivalent evaluation may successfully be applied to the wave characteristics of light. The carrier in this case would be the particle’s electromagnetic fields or “lines of force” superimposing themselves on the fields of all inertial frames of reference. (Note that a null field merely denotes an equilibrium position that would be disturbed by the intrusion.) From the standpoint of symmetry, both explanations would apply.
We see that the energy of a photon is directly proportional to its frequency from the relationship E = h¦ . The variable aspect of the energy density immediately suggests an explanation for the constancy of its speed. As the frequency is reduced or increased, the particle or wave aspects become less localized or more so and the inertial effects vary accordingly. The mutual dependence on the velocity of the source or observer clearly identifies the energy as potential. The mass characteristics are only evident with impact (braking).
The Nature of Matter
It is evident from the foregoing that we have not identified any specific relationship between fields and matter. Inertial effects of mass apply to electromagnetic interactions. We may argue that the reverse also applies. This would support the view that any material entity has a four-fold symmetry and that a complete description requires all aspects be considered.
The radial and tangential characteristic of electromagnetism suggests dual conservative and non-conservative forces, each resisting any change in the position of equilibrium between itself and the emergence of an antithetical arrangement of anti-matter; an eight-fold symmetry. The intrinsic spin of a sub-atomic particle is an indication that the equilibrium is not complete if in a stationary position, or that the particle is in motion. The existence of anti-matter would explain the standing wave configuration since fields and matter would have opposite orientations.
A Generalization of the Compton Effect
The Compton equations involve interactions between particles and electromagnetic waves and as such must either implicitly or explicitly encompass Rayleigh scattering, photoelectric effect, and pair production. Also, particle-particle interactions should not be excluded.
If we gradually reduce the energy of the photon, or increase the mass of the target as in a tightly bound atomic configuration, we see that the result of the collision is a Rayleigh scattering. Also the ratio vk/vc becomes progressively smaller until we reach the classical limits of virtual equality.
The photoelectric effect posits the total absorption of the wave/photon. This is indicative of a superpositioning of the wave on the orbit of the outer electrons since total absorption is not indicated in the Compton effect. The addition of waves would also account for the excitation of an electron from one orbit to another where the wavelength is equal to or a multiple of the de Broglie wave.
A necessary condition of pair production is the entirely logical requirement that the internal speed equals the external velocity or that the potential energy equals the kinetic energy. This simultaneously posits the existence of two masses and fields. This is the configuration of an electromagnetic wave. Sufficient energy must be available for the process to materialize. Obviously a charge dependency is also indicated for the separation to take effect. Otherwise a Rayleigh scattering would result.
Arbitrarily increasing the energy of the photon in a Compton formulation indicates that an energy balance cannot be achieved for a free electron or proton. This has been amply proven in particle accelerator experiments and can be considered one of the reasons for their stability.
Replacing the collision process with the Coulomb attraction between particles provides an important analogy that will not be pursued in this paper. This subject, and others, is addressed in a second paper not currently available for publication. At this point, we will only observe that a sufficiently energetic electron will exhibit the potential energy-mass of a muon at an approximate radius of 2.8 fermi from a proton.
Summary
The above theory, although for the most part qualitative, is entirely consistent with the known data and should provide a strong framework for future development in physics. Also, the arguments should be sufficient to cast doubt on a number of claims in the generalized quantum hypotheses of probabilism and indeterminacy as well as conflict with classical physics. The probabilistic quantum argument that “if it works consistently, it is true” has an equivalent deterministic one that states “if it is true, it works consistently”.
April 6, 2000
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