Einstein explained Planck’s law by hypothesizing that a radiation field consists of photons, whose energy is in proportion to the frequency of the radiation and whose quantity is in proportion to the electromagnetic intensity. In this paper, classical electrodynamics has been quantized in this fashion by starting with the Fourier transform frequency spectrum and using the non-relativistic Doppler shift formulae. Because this paper presents a quantum theory, it has been necessary to introduce the electromagnetic duality. It has been considered that insofar as an electron is a quantum of electric charge, the positron is a quantum of magnetic charge. Then the anti-matter solution of Dirac’s and Feynman’s QED becomes a magnetic monopole. Instead of just four equations of electromagnetism, we are forced to consider eight equations, and explain the consequences of this. We then conclude that photons consist of fermions, (electrons, positrons) travelling on pilot electromagnetic waves. Although photons are therefore electrically or magnetically charged, they do not interact with electromagnetic fields, as the Lorentz force is negated insofar as the electric and magnetic amplitudes are orthogonal to each other and to the propagation vector. Insofar as there are two kinds of Doppler shift, relativistic and non-relativistic, we show how the relativistic formulae relate to our frequency spectrum. Chemical and biological consequences of the theory are examined, specifically in regard to the Diels-Alder [4+ 2] cyclo-addition reaction, (Chemistry), and the cowpea phosphatase functionality, (Biology). 4-vectors are discussed, and two new 4-vectors introduced, and it is shown that an electromagnetic flux tube, as observed in solar flares and in terrestrial electromagnetic circuits, is a consequence of the existence of the space-time 4-vector. Finally, the weak and strong nuclear forces are introduced as thermodynamic consequences of the electromagnetic duality presented in this paper, the transfer of enthalpy and entropy. In this respect, we have the unification of particle physics and thermodynamics. A final point of note is that insofar as photons consist of electric and magnetic quanta propagating on “pilot” electromagnetic waves, the speed of propagation can be ascertained from two of the Maxwell and Maxwell-dual equations, the electric divergence equation and the magnetic divergence equation. This is because, obviously, if we know the radius of an electron or positron, and we know the spin of these fermions from quantum mechanics, then we know the propagation velocity, c = 1 / (ε0μ0)½, where 1/ε0 is the proportionality constant for the electric divergence and μ0 is the proportionality constant for the magnetic divergence. In the non-dual classical electromagnetism of Maxwell, all four of the non-dual equations are required to ascertain the speed of the electromagnetic propagation.