Electron - Positron Annihilation and Absorption Models
An experimentally verified mathematical model that precisely describes the attraction and motion between an electron and positron does not yet exist. Although there have been no direct experimental measurements of the particle velocity when the distance between the two particles approaches zero, the basic inverse square model used for point charges is thought to be inadequate because it would predict speeds in excess of c, the speed of light. Modifications to this basic model have been made by theorizing a variable velocity dependent relativistic mass or a velocity dependent force. Using these models, that assume the electron and positron both attain a velocity of approximately c during their annihilation collision, results in a very compelling model of a photon as an electron and positron in a two body orbital union traveling through space. However, photon models based on this assumption show that the photon translational velocity must have some dependence on the photon wavelength. Further exploration of the basic inverse square model of electron - positron attraction shows it predicts the first order two body photon model without this wavelength dependent dispersion. Furthermore, study of the electron-positron interaction with a hydrogen like atom shows that the popular notion of a photon having an angular momentum on the order of ħ and an energy of ħw can be derived from first principles.
Randy T. Dorn, "Electron - Positron Annihilation and Absorption Models", Presented at SPIE , The Nature of Light: What are Photons? VI, (August 11, 2015 San Diego, CA)
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The Two Body Photon
The physical observations that light exerts pressure on objects and light is bent by gravity can be considered as evidence that photons do indeed have mass. The requirement for mass to be convertible to radiant energy which is net electrically neutral yet has alternating positive and negative potentials and an alternating magnetic field leads to the consideration of a photon as an electron and positron joined in a two body orbital union traveling through space. This simple mechanical model comes directly from conservation of matter and observations of electron-positron annihilation and electron-positron pair production. Since electrons and positrons are generally considered to be fundamental particles, we should believe the electron and positron to be conserved throughout the process of photon creation and destruction. Most interpretations of the mathematics of special relativity would lead one to believe that mass cannot travel at the speed of light because the mass or momentum would be infinite at that velocity. However, under the influence of an inverse square force, speed of light particles are actually predicted using accepted mathematical models. Furthermore, the equations of motion of charged particle interactions can be rearranged and interpreted so that the force varies with velocity instead of the mass. This change in perspective makes the concept of speed of light particles entirely plausible and allows a renewed appreciation for the concepts and definitions of classical mechanics.
Randy T. Dorn, "The Two Body Photon", Proc. SPIE 8832, The Nature of Light: What are Photons? V, 88320K (October 1, 2013); doi:10.1117/12.2023683;
Copyright 2013 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
The High Velocity Version of Classical Mechanics
A good understanding of the actual mechanism for the attraction between an electron and positron is necessary for the effective study of electron – positron phenomenon such as annihilation and pair production. This “action at a distance” force has mathematical descriptions, but the underlying phenomenon is really not well understood. Our intuitive understanding of how force is delivered through the action of an impulse comes from our everyday experience and is described by Newton’s Laws. If we extend this classical mechanical line of reasoning to these more mysterious forces, it leads to the derivation of a high velocity version of F = ma. The basis of this model is Newton's notion that gravity could be attributed to multiple impacts of invisible bodies. In this model it is assumed that such an acceleration field is made up of tiny bodies that travel at the speed of light and that these bodies deliver energy to accelerated particles by elastic collisions. The result is a mathematical model comparable to relativistic equations. This similarity leads to the conclusion that it is reasonable to rearrange and interpret the relativistic equations as a velocity dependent force. There is no reason to change the classical definition of mass, momentum and energy for the physics that has heretofore been described by relativity.
Randy T. Dorn, "The High Velocity Version of Classical Mechanics", Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 812107 (September 28, 2011); doi:10.1117/12.892928;
Copyright 2011 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.