§ 8. Quantum Electrodynamics
In "Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction" (1950), Feynman's quantum electrodynamics is based on Maxwell's theory.
"This separation is especially useful in quantum electrodynamics which represents the interaction of matter with the electromagnetic field. The electromagnetic field is an especially simple system and its behavior can be analyzed completely." (Feynman, Intro).
Maxwell's expanding electromagnetic fields cannot maintain the particle structure of a QED electromagnetic photon since as a photon propagates, electromagnetic fields expand which would eliminate the particle structure of a QED photon. Plus, photons conflict with the continuity of Maxwell's electromagnetic fields since as an light beam propagates, the spaces between photons would increase eliminating the continuity of Maxwell's electromagnetic fields. Also, Maxwell's theory is based on Faraday's induction law yet induction does not discharge visible light; consequently, QED is an analogy. In addition, Feynman's photon energy equation E = hγ is represented with the units of the kinetic energy (g . m2 / s2) since h = 6.55 x 10-27 erg . s and erg = g . m2 / s2 yet a photon is massless.
Feynman's QED photons cannot be used to represent diffraction since the destruction of photons violates energy conservation. Moreover, the magnitude of the square of a position probability (Ψ2) is a positive value or zero and cannot form a negative value required in the formation of wave interference. The formation of the dark fringes of the diffraction pattern is represented with the complex probability amplitudes from all possible paths to that point cancel each other out. Each path contributes an amplitude with a phase, and at certain points these phases are such that when you add the amplitudes as complex numbers, the sum is zero. Since the probability of detecting a photon is the squared magnitude of this sum, a zero sum gives zero probability, which appears as a dark fringe. The dark fringe is not caused by negative probabilities or destroyed photons, but by the complete destructive interference of the complex amplitudes but probability waves represent an unknown where arbitrary quantities cannot be used to represent the structure of effect of light. A position probability forms a single peak of the standard deviation yet a quantum mechanics probability wave is composed of multiple peaks which proves a probability wave is an unknown quantity.
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