from potentials by the calculus process of differentiation, as exhibited in Eq. (\[a\]). Differentiation is carried out at a point in spacetime. It is *local*. If potentials are to be expressed from fields, that requires integration, consisting of information from a range of spacetime values; it is *nonlocal*. The fact that the Schrödinger equation requires the local information from potentials, and cannot be described by fields without inferring nonlocality in spacetime, is direct evidence that potentials are more fundamental than fields.

Ambiguity in the electromagnetic field tensors
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The basic field tensor of electrodynamics is defined as$$F^{\mu\nu}=\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu}. \label{aj1}$$ It is important to note that this expression is in terms of the derivatives of potentials rather than the potentials themselves. Thus it is not surprising that the Lorentz invariant found from the inner product of $F^{\mu\nu}$ with itself yields an expression in terms of fields:$$F^{\mu\nu}F_{\mu\nu}=2\left(  \mathbf{B}^{2}-\mathbf{E}^{2}\right)  .
\label{aj2}$$ A dual tensor can be defined as$$G^{\mu\nu}=\frac{1}{2}\epsilon^{\mu\nu\rho\lambda}F_{\rho\lambda}, \label{aj3}$$ where $\epsilon^{\mu\nu\rho\lambda}$ is the completely asymmetric fourth-rank tensor. (The conventions of Jackson [@jackson] are being employed.) The inner product of the basic and dual tensors gives a second Lorentz invariant:$$G^{\mu\nu}F_{\mu\nu}=-4\mathbf{B\cdot E}, \label{aj4}$$ also in terms of fields. The two Lorentz invariants$$\mathbf{E}^{2}-\mathbf{B}^{2},\quad\mathbf{E\cdot B} \label{aj5}$$ are said 