writing the Schrödinger equation directly in terms of electric and magnetic fields is discussed in Section IV. This is further evidence of the basic nature of potentials, and it also supports the notion of a hierarchy of physical phenomena. Quantum mechanics can be constructed from classical mechanics when expressed in terms of system functions like the Lagrangian or Hamiltonian, whereas a Newtonian form of classical mechanics has such an extension only by extrapolation to a desired result. System functions are related to energies, whereas Newtonian physics involves forces, and forces are directly connected with electric and magnetic fields, as shown by the Lorentz force expression.

The ambiguities inherent in the view that the $\mathbf{E}^{2}-\mathbf{B}^{2}$ and $\mathbf{E}\cdot\mathbf{B}$ Lorentz invariants reliably characterize the electrodynamic environment is another topic examined in Section IV. (The Lorentz invariants, as are all electromagnetic quantities throughout this paper, are stated in Gaussian units.) This concept has an important failure when both invariants are zero, since it associates propagating plane-wave fields with the completely different constant crossed fields. The commonly-held assumption that constant crossed fields are a zero-frequency limit of plane-wave fields (see, for example, Refs. [@nikrit66; @ritus85]), is shown to be untenable.

Another topic in Section IV 