A Field-Based Model of the Photon: Lorentz-Covariant Quantization

The macroscopic Maxwell equations, which quantum mechanics uses to define radiation fields, are shown to be in violation of the special principle of relativity. This is resolved by applying Maxwell's equations microscopically to each of the n constituent wave trains of a macroscopic wave. It is then shown that spontaneous emission may be accounted for by subjecting a bound electron to the combined influence of the n superimposed wave trains. If emission is induced by a coherent wave, then frequency-doubling phenomena are predicted. Several examples are cited, showing the pervasiveness of frequency doubling in nature. The evidence suggests further that quantum statistics is due to microscopic field fluctuations rather than photon counting. A manifestly covariant description of an electron transition is obtained in the form of a Lagrangian density, which is then quantized by applying appropriate limits of integration. A simple shift in these limits yields an independent field in free space, or photon, which is bounded by parallel surfaces separated by a distance equal to the wavelength and period. The implications of this photon model upon interference phenomena and the inverse square law are briefly discussed. A test of the inverse square law is proposed.