Foundations for QED, Feynman operator calculus, Dyson conjectures, and Einstein’s dual theory

Abstract

Abstract This paper reviews research on the foundations of quantum electrodynamics (QED). We show that there are three definitions of the proper time that follow from Einstein’s theory. The first definition is used to prove that the universe has a unique clock (Newton-Horwitz-Fanchi time) available to all observers. This clock is used to briefly discuss the mathematical foundations for Feynman’s time ordered operator calculus. We use this calculus to solve the first and second conjectures of Dyson for QED: that the renormalized perturbation series is asymptotic and, that the ultra-violet divergence is caused by a violation of the time-energy uncertainly relationship. The second definition gives Minkowski’s version of Einstein’s theory and its problems are briefly reviewed. The third definition gives the dual Newton, dual Maxwell and dual quantum theories. The theory is dual in that, for a set of n particles, every observer has two unique sets of global variables (X, t) and (X, τ) to study the system, where X is the canonical center of mass. Using (X, t) time is relative with speed c, while in (X, τ), time is unique with relative speed b. The dual Maxwell theory contains a longitudinal (dissipative) term in the E field wave equation, which appears instantaneously with acceleration and we predict that radiation from a cyclotron will not produce photoelectrons. It is shown that this term gives an effective mass for the photon. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein’s theory and without the need for point particles or a self-energy divergency. This means that a second quantized version will not produce a self-energy or infrared divergency. These results along with the proof of Dyson’s second conjecture resolves all the problems with QED. The dual Dirac theory provides a new formula for the anomalous magnetic moment of a charged particle, which can give exact values for the electron, muon and proton g-factors.