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Email: Walter Babin

The Synthesis of Quantum Electrodynamics, Special Relativity and Classical Mechanics

Presented July 9, 2002 at the International Scientist's Club, Congress 2002,
University of St. Petersburg, Russia

Copyright © Walter Babin

Box 433, Rodney, Ontario, Canada, N0L 2C0
Telephone: (519) 785-0413

A re-assessment of the pivotal experiments of the last century leads to a broad generalization which incorporates the seemingly divergent tendencies of classical mechanics, relativity and the new quantum mechanics into one comprehensive physical theory. Apart from the ability to simplify, many of the well-known contradictions in current theory are resolved by its application. A resolution of problems involving the propagation of light and interaction with matter is presented along with new insights into the structure of atoms and their constituent particles.

Introduction

The past century has witnessed the sublimation of a pragmatic and deterministic philosophy of physics into the almost religious fervor of relativism and probabilism. Quantum mechanics, whose very name infers discreteness, localization and simplicity found itself expressed through an obscure methodology and mathematical formalism of almost impenetrable complexity1. No sooner had the duality of particle and wave been experimentally confirmed than the "new" quantum mechanics emerged which attempted to supplant the former with the latter. The probabilistic tendency continues despite a proliferation of universal constants which argue the opposite. Among these are:

  [c] - The speed of light
  [e] - The charge on the electron
  [h] - Planck's constant of angular momentum
  [Rk] - The Rydberg constant
  [a ] - The "fine line" constant (1/137.036)
  [vo] - The velocity ratio of constants, e2/h and ca
  [mo] -The rest masses of the electron and proton

The purpose of this paper is to effect a generalization in physics and thereby resolve many of its outstanding problems and contradictions. The generalization will confirm that all contemporary theories devolve to, or are an extension of the classical determinism of previous centuries. Of particular significance is the identification of the dual states of mechanics and electrostatics as opposing forces. A sound theoretical basis is established for relativistic dynamics and it is shown that both the electron and proton are aspects of the same fundamental particle.

Sub-atomic particles are assumed and ESU measurements are used throughout unless otherwise indicated.

Addendum Apr. 21, 2005:
An objection has been raised to the following interpretation of the propagation of light in that it does not explain stellar aberration. This is easily resolved since it requires only that a wave front be discontinuous; an attribute postulated by Huygens over 300 years ago and resurrected by A. Einstein in the form of light corpuscles (photons). In order to capture the image11, a telescope of length [l] moving with a velocity [v] must be angled a distance [d], so that [d = lv/c].

---------------

1. The Nature of Light

The Michelson-Morley experiment and those subsequent to it confirm that the speed of light is constant in the observer's frame of reference. The following conclusions must logically be drawn from this result:

  1. Light propagates independently in all inertial frames of reference.
  2. It exhibits compound velocities as measured by observers in relative motion.
  3. The existence of a medium specific to each reference frame is required.
  4. The speed is a characteristic of the medium only and is also independent of frequency2
  5. Its constancy defines the common attributes of the medium through which it moves.
  6. It is a disturbance of the medium. A localized "object" cannot simultaneously occupy multiple locations.
  7. The energy varies directly with relative motion between frames.
  8. There is no contiguity between frames of reference.

Corroborative evidence for compound velocities may be found in the Lorentz transformation equations3 and are the sole reason for the invariance of Maxwell's equations for the propagation of light with respect to them. The significant difference between the classical view and the above is that absolute reference frames are an attribute of the particle and not of a universal substructure. This interpretation is consistent with the concept of the equivalence of all inertial frames of reference whereas a universal aether is not. It follows that absolute measurements within all reference frames are validated while allowing relative interactions between them.

The photon concept proposed by Einstein and its application in the photoelectric and Compton effects does not conflict with the above assessment. Photons have a parallel in Huygens wavelets4 used to explain the sharp demarcation of light waves at boundaries. Both argue strongly for the view that radiation is due solely to the quantum excitation of orbital electrons and collisions rather than the continuous spectrum of uniform oscillations whose wavelength varies with impulse and relative speed. The regularities of spectroscopy are a confirmation of this and also suggest if only by inference, that photon magnitudes remain constant.

Photons are discrete and the collisions of the Compton effect suggest a spherical symmetry with respect to them. The same conclusion may be drawn from the spectral series of the hydrogen atom. The Rydberg formula is:

k = Rk(1/nf2-1/ni2) (1)

where Rk = v/(4πλ c), k = reciprocal wavelength, nf and ni = quantum integers of initial and final orbits.

Acceleration and deceleration produce an increase in potential and subsequent emission of radiation. This transfer involves a squared time and spherical surface in the denominator due to induction.

B = -[r(E2 - E1)]/2c(t2 - t1) ≡ v2e/2c2r2 ≡ e/2c2t2

where B = magnetic field , E = electric, r and t = radius and time.The general form equates with the above given the same dimensions. (Times are equalized and fundamental units are assumed.)

The kinetic energy of a photon is expressed as a frequency times Planck’s constant (2π movor). By introducing [kc] as the radiation frequency [f], a valid energy expression of one-half the squared velocity is derived due to the [4π ] term in the denominator of Rk.

hf = hkc = ½mxcvo (2)

where mx = photon "mass-equivalent", ie., the absence of mass.

This provides an entirely satisfactory result since the emission precisely equals the difference in mechanical energies when the quantum numbers are included. The problem of de Broglie’s lagging matter wave and its probabilistic interpretation5 is resolved. Note also that the angular momentum of the photon will couple with the experimentally derived intrinsic magnetic moment of the electron.

By restricting our inquiry to sub-atomic particles, we may identify the medium as the electromagnetic field thereby avoiding conjecture. While it has been the practice to think of an underlying continuum devoid of physical attributes, the field concept incorporates the familiar physical quantities associated with charge and matter. There is a progression in the quantized states of the hydrogen atom to the point of zero energy. The progression is evident in wavelengths. Beginning with the "classical electron radius", the Compton wavelength, the first Bohr orbit of the hydrogen atom and the Rydberg Constant increase progressively by a factor of [1/a ], the fine line constant.

The propagation of light is no doubt dependent on this ratio. In a qualitative sense, the function appears to be a rapid transfer between kinetic and potential energies signified by the light and sub-light speeds in (2). This combination of speeds occurs throughout and is particularly evident in the formulas of relativity. There is a simultaneous generation of magnetic and electric fields which cannot be attributed to anything but the medium, or as will be identified later, a dual medium and the continual regeneration of electromagnetic force.

Compound velocities relative to the observer’s frame constitute a de facto basis for the Sagnac effect. The calculation is generally based on a rotation, but precisely the same result ensues for a linear translation when a relative speed is substituted for the rate of rotation.

There are strong indications that the photon aspect of light (its physical momentum) is an exclusively magnetic phenomenon detached from matter as it incorporates all of the following:

  1. The charge of the emitting fundamental particle is constant. The magnetic field varies.
  2. The photon bears no net charge, which infers a dipole arrangement.
  3. A Compton collision exhibits only dynamic and magnetic variables. Charge is constant.
  4. A spin of one is comprehensible only in a dipole arrangement, if at all.
  5. In a classical wave train, the direction of the magnetic force is parallel to the motion.
  6. The Compton effect is a coupling of the wavelength of the intrinsic magnetic moment with the photon.

To these may be added the essential fact that a photon is the release of potential energy. Its discrete character is no doubt due to the spherical aspect identified above.

 

2. Kinematics

FIG 1.

A statistical distribution of photons are emitted from a moving source at time t = 0. Frames S and S' coincide at O. At t = 1, the wave front has traveled to radius ct = a in S and O' is at point vt. Accordingly, the light wave has advanced to radius a' in S'. Since light speed is constant in each frame of reference, the result is the physical presence of two separate wave fronts. No distortion is evident other than the displacement of the material object relative to the wave front in the observer's field. Each observer must therefore use compound velocities to calculate the positions of wave fronts relative to the material object in the opposing frame of reference. The requirements of Galilean relativity are satisfied since measurements in S and S' are in all respects equal.

Each wave front is retarded with respect to its opposite which demonstrates that there is a displacement between frames, or more properly fields, that is distinct from particle interaction. The reciprocal aspect guarantees that distances between wave fronts as well as between material objects are equal for each observer. The kinetic energy of the object varies directly with relative motion, as does the energy of the wave. The fundamental systems are invariant. Assuming successive emissions of radiation, the frequency will depend on the cosine of the viewing angle and will constitute a first-order Doppler effect.

There is a linear displacement of the material object relative to the observer's wave front on the X axis of (c-v) and (c+v). Assuming a spherical "field" surface circumscribing an electron with a radius on the order of a Compton wavelength, the displacement relative to the particle would be equivalent to that shown. Any actual change in wavelength proportional to uniform motion is inconsistent with Galilean relativity. Arguments stating that changes in lengths between reference frames are reciprocal and therefore undetectable are redundant. Differences in lengths and times have been disproved in a previous work6.

A geometric interpretation of the figure, [(c-v)(c+v)]1/2 shows that the relativistic factor, [b = (1-v2/c2)1/2] of the dilations and contractions in special relativity can only apply to perpendiculars drawn from the object to the wave front. This may define the diameter and circumference of a de Broglie wave as measured in the observer’s frame, which may be the effective dimensions involved in any interaction. While there is a displacement relative to the observers’ frame, no distortion or indication of reduced dimensions are evident in either coordinate system, although this is probable with impact. If a coordinate system were connected to the moving frame, the angular momentum (based on the angle of reference) would be reduced by [b ] as would a magnetic field.

3. Dynamics

Special relativity found confirmation in the early experiments (Bucherer7) with mass spectrometry and the bending of electron trajectories in a magnetic field. The standard formula8 is,

eveB/c = mov2/r: The term on the left equals e2vevb/c2r2 and movevb(v2)/c2r (3)

where e = charge, B = magnetic field, (fundamental units), ve and vb are the electron and magnetic field source velocities (Bohr equivalence, mov2r = e2). Note that the magnetic field is identified as a conservative (potential) force.

The initial equality in (3) is not dimensionally correct or is at least simplistic, since there is a magnitude [v2/c2] that is not accommodated. The dimensions are that of an induced electric current and not of the principle force. However, the experimental result is known and is attributed to an incremental increase in the mass of the electron, whereas it is clearly a field configuration. The dimensions of the de Broglie "matter" wave must be that of the combined wavelengths of primary and induced fields with opposite orientation (Sagnac Effect). This however, should now be viewed as a displacement between fields as indicated in the kinematics. The proper formulation for the experiment is found in equation (15), below.

Regardless of the magnitudes involved in the foregoing, an electron orbiting in a magnetic field signifies a definite balance, primarily between the angular momentum vector and the opposing magnetic moment and not their absence as proposed by quantum mechanics. The potential source is understood to be magnetic and the mechanical angular momentum vector of the electron is guaranteed to be the same magnitude by the Bohr equivalence.

Symmetry requires an opposing radial force since both field and particle are in motion. Since the Coulomb and mechanical forces cannot represent a combined attraction or a combined repulsion, the problem is resolved. As a condition of orbit, the momentum of the central source and of the orbiting electron must be equal. If an infinite source or no source is assumed, [vb] is zero and equilibrium is nullified. The Coulomb interaction currently has the trivial dimensions,

½e2/r – e2/r = -e2/2r (4)

The combined energy (particle and field source; circular orbit) equation according to classical mechanics and the conservation of energy is,

- (½V2memp)/(me + mp) + (Imemp/r) = Imemp/2r (5)

where me and mp are electron and proton masses, r = radius, V = combined speeds, and I = the proportional constant.

There is a direct correspondence between Coulomb and mechanical configurations. Current theory identifies mass as the inertia of the field, and also a component of the kinetic energy of the Coulomb attraction. The inertia of mass can only be attributed to the electric field. This effectively posits the existence of dual states of particle-field/anti-particle-field equivalence whose existence becomes evident only through the application of external force. With respect to the ground state of a hydrogen atom, equilibrium (free-fall) is the fundamental attribute. This resolves the question of action-at-a-distance, the absence of radiation, and the need for an initial momentum for orbit. However, no indication of quantum effects is yet evident.

Equal forces in direct opposition are equivalent to no force. Only perturbations and secondary effects would be measurable by experiment. Any deviation from equilibrium would entail a change of state subject to the second law of mechanics. A displacement at the point of perturbation would be evident at every juncture as an increase in potential. The subsequent release of energy (radiation) would be analogous to that of tension in a spring. The disturbance will propagate throughout the system at light speed as per section 1.

4. A Qualitative Description of Dual States

The duality identifies inertia (that which is inert) as a property of the constants, mass and charge. Collectively, the theory identifies fields and matter coincident with anti-fields and anti-matter (charge) comprising an antithetical whole for each particle. Note that anti-matter denotes the absence of matter and not the presence of an equivalent particle with reverse charge. The problem of the balance of matter and antimatter is completely resolved by this interpretation.

Kinetic energy varies directly with relative motion, as does magnetism in the reverse sense of the above. Potential is the direct result of acceleration and is retained until deceleration, then released at light speed as radiation. This identifies magnetic and kinetic effects as opposing pairs. It also identifies potential as a property of the object. Fig. 1 represents a two dimensional analogy of this. In an orbital system, the cube of the space (volume) is divided by the square (surface) of the time. Equally, charge [e2] is a cube as can be deduced by any metric conversion, this identifies magnetism as the time correlate. The force of a magnetic dipole varies by the cube of the distance. Clearly, the formulation must be the same for both the electrostatic and mechanical configurations, although the magnitudes may vary.

Potential may transfer or convert incrementally to matter on impact. The latter requires the presence of a sufficient, mass/charge to effect a permanent transfer. Any interaction below the unit threshold is subject to decay. The co-existent dual states provide an ontological basis for the conservation laws and specifically exclude the possibility of any unilateral force such as gravity. Of further significance is that three-dimensional configurations must rotate through a fourth dimension for coincidence.

5. Special Relativity

Kinetic energy in relativity theory is defined as,

(m - mo)c2 = ½mvk2 = K (6)

mo /m = 1 – (vk2/2c2) = b1 (7)

As indicated in section 3, the presumed relativistic "mass" increase must be attributed to the incremental induced field - an increase in potential. If this is the case, mass is unaffected and should drop out of the relativistic momentum-energy equivalence equations9,

(Pc)2 +(moc2)2 = (K+moc2)2 (8)

and the equality,

b = (1-vm2/c2)1/2 = b 1 = (1-vk2/2c2) (9)

where vm and vk are the velocities of the momentum and kinetic energy equations.

m2vm2c2 + mo2c4 = m2vk4/4 + mmovk2c2 + mo2c4 (10)

m2vm2c2 - m2vk4/4 = mmovk2c2 (11)

mvm2 - mvk4/4c2 = movk2 (12)

movm2 - movk4/4c2 = movk2 - movk4/2c2 (13)

movm2 = movk2 - movk4/4c2 (14)

vm2 = vk2 - vk 4/4c2 (15)

Equation (15) is the proper configuration for the mass spectrometry of (3) as well as any gain or loss in potential due to accelerations or deceleration. It involves a primary field, an induced field and their issue. The [b ] and [b 1] formulations provide the same end result, but obscure the actual field configuration. In particular [vm] is a resultant velocity and cannot in any way contribute to the internal modifications. A further reduction shows,

(vk – (vk2/2c))(vk + (vk2/2c)) = vm2 (16)

which displays a combined aligned and anti-aligned configuration.

Equation (15) must apply to all velocities, including that of light. Expressing [vm2] as [c2] requires that [vk2 = 2c2].

The light and sub-light speeds identify (8) as a total dual-state formulation. The scalar product in the root of the kinetic energy expression as compared to the vector of the momentum signifies rotation. It is difficult not to identify the moment vector as the 4th coordinate; specifically, rotation as the three dimensional manifestation of it since there is no representation for spin in Cartesian coordinates. One might consider an alignment of axes in the 4th dimension manifested much like a shadow projection in three.

The energy transfer from one state to the other (from kinetic to potential and the reverse) can only be effected in this manner and is made probable in the 4th order dimensions of [vk]. Note that acceleration may be expressed as follows:

mr/t2 = Qr4/t4 = Qv4 (17)

where [Q] may be the gravitational [G] or the electromechanical [I] proportional constant identified above.

Any torque would result in constant spin states in an orbital equilibrium. The orbital (and linear with respect to a point of observation) magnetic moment of an electron is anti-parallel to its angular momentum. This fact, along with spin orientations, fine-line splitting and field coupling suggests with respect to fundamental particles at least, rotational and linear displacements are coincident and according to equation (8), co-equal.

A rigorous analysis of these statements will be covered in a subsequent paper. The significance of the above is:

  1. Equations (13 and 16) contain the components for aligned and anti-aligned spin states.
  2. The combined first and second order magnitudes of (16) provide the theoretical basis for quantized moments, L =[l(l + 1)]1/2 h , [l= 0,1,2] (l2l)1/2 h [l = 1,2,3…] and uL. The configuration is parabolic which supports the concept of transfer of energy between kinetic and potential dual states as the speed of escape.
  3. The reverse sense of the components of (16) indicates a Sagnac effect for orbits and spin rather than the standing wave argument of the Schroedinger equations.
  4. Equation (15) contains the proper relationship for the fields in equation (3). Relativistic effects are entirely the result of induced fields as per equation (15). The relativistic Doppler equations are also the result of this configuration.
  5. Mass is conserved and classical determinism applies.

6. The Compton Effect

This is viewed as an elastic collision between a photon and a free electron. However, the appearance of the magnetic field at the electron identifies a partially elastic or totally inelastic field coupling at the Compton wavelength, and the subsequent emission of radiation. If the "mass" of the electron is increased as in tightly bound orbital states, or the photon’s energy is decreased, the recoil approaches a Rayleigh scattering. The dependency on frequency in the photoelectric effect is consistent with the quantized states of the Bohr orbits. Collisions of photons and free particles fall between. This suggests the Compton effect may apply to the total spectrum of sub-atomic particle and field interactions including Coulomb forces. The preceding section substantiates this view.

A classical one-dimensional elastic collision between an electron and a mass-equivalent photon [h/l c = mx = mo] would result in a Newtonian velocity [vn] of,

2mxc/(mo + mx) = vn = c (18)

A similar configuration in a Compton collision gives, [cvm = vk2]. If the mass ratio is modified and/or a two-dimensional collision is introduced,

2mxcvmCos f /(mx + mo ) = vnvm = vk2 (19)

where f is the recoil angle of the electron. Substituting (19) into (16),

(vm/vn = (1 – vk2/4c2) (20)

Equation (20) conforms with Dirac's relativistic treatment of the energy levels of the hydrogen atom and more importantly, provides an ontological basis for fine structure splitting of spectral lines based on the dual states of Section [4] .

The velocity [vn] is implicit in (8) through (16). It would appear that classical mechanics has not been supplanted, but obscured. The parabolic configuration is again confirmed in (19). Furthermore, the velocity associated with total energy is explicitly defined in the square of the angular velocity [vk2]. Since this is equal to the combined linear velocities, an immediate explanation for its scalar attribute is also identified.

The Compton formula10 may be expressed in terms of mass,

l’ = l + h (1 - cos f ) /mocº l ’/hc = l /hc + (1/ moc2) – (cos f / moc2) º 1/mx’ = (1/mx) + (1/ mo) – (cos f /mo ) (21)

where l , l ’ are the initial and recoil wavelengths, f is the photon angle of recoil and mx , mx’ are "mass" equivalents

By setting the photon scattering to 90 degrees, its "mass equivalence" is equal to the reduced mass [mxmo/(mx + mo)] of an electron-photon pairing.

With a wavelength equal to the ground state of a hydrogen atom, the mass equivalence of the photon, or in this case the equivalent Coulomb field, would be moa . Solving the Compton equations, and adjusting the momentum of the electron by [cos f ] to maintain a perpendicular configuration provides the following,

h/mvm = h/mov (22)

The equivalence is due to conservation of momentum but the scattering and the initial distribution of momentum between "mass" and velocity also identifies a field coupling and a re-established balance between material and anti-material states (electromagnetic and mechanical). The inference is also that in any interaction, the energy loss (radiation) in coupling is that of potential (magnetic) and the magnitude is in all instances equal to the reduced "mass" rather than a relativistic conversion of rest mass to energy.

As the electron approaches the nucleus, the Compton effect shows that the induced electric field approaches the magnitude of the primary field. The "scattered" radiation approaches the reduced mass of the electron. Of specific interest is where the field strength is equivalent to the proton mass, which occurs at the classical electron radius. The result is that it precisely parallels the total energies of the atom of equation (5). The electron assumes the "mass" of a proton, [vm] equals the sum of the speeds of the electron and proton, the "scattered" radiation equals the reduced mass of the electron and its speed is that of the first Bohr hydrogen orbit. The reverse inversion from proton to electron is not entirely clear and requires further study.

However, it is clear that an inversion of space, time and mass takes place at this point. It is also clear that the proton and electron are both aspects of the same fundamental particle. The inversion also applies electrostatically, since the proton charge is positive. Furthermore, by logical extension it may be stated that if penetration is greater than that allowed for the release of the electron, it will result in the creation of a neutron. This cannot be considered stable particle unless it is under the constraints of an energetic nucleus, or decays to a proton with the ejection of the electron. The decay of the neutron into neutrinos, pions and muons accounts for their electrical neutrality. The sum of the mass ratios of the muon and pion to the electron are ½ the mass ratio of the proton divided by the anomalous "q" factor in the magnetic moment of the neutron. This confirms the "mass defect" of capture (or the energy required for release) is equal to the reduced mass.

The coincidence of the electrostatic and the mechanical indicate that the proton must occupy one focus of an orbital ellipse and the electric charge must occupy the other. The antithetical counterpart is a hyperbolic configuration and the transfer of energy from one to the other is identified in the parabolic configuration of equation (18). The intrinsic magnetic moment of the electron is greater than the proton by their mass ratio and would serve as the nucleus of the inverse configuration. The equilibrium in this configuration is no doubt the foundation for the regularity in orbits and of quantum states in general.

7. Summary

The possibility of "antigravity" is inherent in the identification of opposing electrostatic and mechanical states. These also point the way towards a unification of all forces into one encompassing theory.

The fact that the above results were implicit in the formulas for electromagnetism and relativity, attest to their validity. The problem occurs in the interpretation. It is astounding that simple oversights such as in equation (3) would lead to the complex, ad hoc and divergent theories of the previous century. The solutions to the fundamental problems were available at the outset. This emphasizes the need for a rigorous evaluation of any new theories and their relationship to those of the past.

8. Acknowledgements:

My sincere thanks to Mr. Jerome Gutoski for his confidence and his unfailing support.

9. References:

1. Nature certainly does not have its basic ideas described in such a clumsy and ugly way. There is probably some very neat solution which is still to be discovered. P. A. M. Dirac: Relativity and Quantum Mechanics: Austin, Texas Apr. 14, 1970.
2. The Speed of Light is Independent of Frequency: B. Schaefer, Physical Review Letters, June 21, 1999
3. A Theoretical Analysis of Sub-Atomic Particle Interactions: Walter Babin, http://wbabin.net/babin/dyna2.htm
4. K. R. Atkins: Physics, J Wiley & Sons 1966, p. 395
5. R. Eisberg, R. Resnic: Quantum Physics, J. Wiley & Sons, 1985, p. 69-76
6. An Analysis of the Theoretical Foundations of Special Relativity: Walter Babin, http://wbabin.net/babin/webdoc1.htm
7. Science Abstracts 11, 687, 1908.
8. Ibid note 5, p. 520
9. Ibid Note 5, Appendix A-17
10. A. Compton: Physical Review, 21, May 1923, p. 483
11 Max Born: Einstein's Theory of Relativity (1965) : Dover Publications Inc. p94-95