Aharonov Bohm Effect Interaction Energy Interpretation => E_m = -∇Φ - DA/Dt?
The <PERSON> paper "An experimental proposal to test the physical effect of the vector potential" proposes an experiment to decide between two interpretations of the Aharonov-Bohm effect:
“the interpretation of electromagnetic potentials”
or
“the interpretation of interaction energy”
The <PERSON> paper "What the electromagnetic vector potential describes", takes the interaction energy interpretation and shows the motional scalar potential of the curl-free vector potential:
$$\vec{v} · \vec{A}$$
has the derived electromotive ($\vec{E}_m$) field:
$$\vec{E}_m = - ∇(\vec{v} · \vec{A})$$
With force $\vec{F}$ measurable by a test charge q moving with velocity $\vec{v}$:
$$\vec{F} = q ( - ∇(\vec{v} · \vec{A}) ) $$
The Lorentz force:
$$q ( -∇Φ - \frac{\partial \vec A}{\partial t} + \vec{v} × (∇ × \vec{A}) )$$
does not contain this term in its electromotive field. Adding it:
$$q ( -∇Φ - \frac{\partial \vec A}{\partial t} + \vec{v} × (∇ × \vec{A}) - ∇(\vec{v} · \vec{A}))$$
is, by the vector identity of the total derivative:
$$q ( -∇Φ - \frac{D \vec A}{D t} )$$
Hence, the <PERSON> paper proposes an experiment that can determine whether
$$\vec{E}_m = -∇Φ - \frac{D \vec A}{D t}$$
is true.
This conclusion appears to result from main stream physics but flies in the face of the <PERSON> force accepted since the time of <PERSON> thence <PERSON>'s 1905 paper "On the Electrodynamics of Moving Bodies".
Apocryphal, non-mainstream apologetics for the $ - ∇(\vec{v} · \vec{A})$ term maintain it has escaped classical notice because it integrates to 0 around any circuit, and should appear only in open electrodynamics as occur in plasmas and antennas.
It is hard to believe there is a contradiction this long-standing between the recognized classical Lorentz force:
$$\vec{F} = q ( -∇Φ - \frac{\partial \vec A}{\partial t} + \vec{v} × (∇ × \vec{A}) )$$ and quantum physics implied by the interaction energy interpretation of the Aharonov-Bohm effect: $$\vec{F} = q (-∇Φ - \frac{D \vec A}{D t}) = q ( -∇Φ - \frac{\partial \vec A}{\partial t} + \vec{v} × (∇ × \vec{A}) - ∇(\vec{v} · \vec{A}))$$ Why is the conclusion reached above, $\vec{E}_m = -∇Φ - \frac{D \vec A}{D t}$ incorrect? 649