Electromagnetic and Quantum Mechanical Waves

Horst E. Wilhelm

A formulation of the quantum mechanics of charged particles in time‐dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.

Ping Sheng

Nobuo Nagai, Hirofumi Sanada, Takashi Yahagi

The electromagnetic waves derived from the Maxwell equations are characterized by being lossless. It is known that such lossless electromagnetic waves are obtained in the electromagnetic fields of coaxial cables and the electromagnetic fields generated using coils and capacitors. Because the physical behavior and effects of electromagnetic waves differ depending on frequency, the electromagnetic waves propagating through the electromagnetic fields of coaxial cables and the electromagnetic fields generated using coils and capacitors are limited to very high frequency (VHF) and ultrahigh frequency (UHF). Electromagnetic waves of other frequencies are left as problems for future research. Also, as stated in Section 8 of this article, a "lossless circuit" is also derived from the equations of motion for molecules (Newtonian mechanics). Namely, because the oscillations of a periodic system consisting of N molecules are expressed in the representation equivalent to the circuit representation of lossless electromagnetic waves, it has been demonstrated that a lossless circuit also arises from the motion of molecules with mass derived from Newtonian mechanics. This is the key physical phenomenon that links quantum mechanics to mathematics. We will leave this point as an important problem for future research.

F. J. Duarte

Electromagnetism and quantum mechanics share a few crucial characteristics. First of all, both electromagnetism and quantum mechanics, separately and in unison, provide the foundations for the informational civilization we now live in. Take electromagnetism away and civilization collapses. Take quantum mechanics away and civilization crumbles. The second essential feature that both these physical phenomena share is that they function via waves and fields. Thirdly, as Freeman Dyson so insightfully indicated, both electromagnetism and quantum mechanics are configured in a two layer structure. Intangible waves and fields plus a two layer structure of understanding introduce their fourth commonality: a propensity to be misunderstood. Here, we describe how electromagnetism and quantum mechanics find a common meeting ground in the field of optics.

George Frederick James Temple