An electric charge has no screw sense--a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues

TL;DR

The paper critiques the twistfree formulation of electrodynamics proposed by da Rocha & Rodrigues, emphasizing the importance of vector distinctions rooted in electric charge properties and clarifying misconceptions about deriving the Lorentz force from Maxwell's equations.

Contribution

It refutes the claims of da Rocha & Rodrigues, clarifying the necessity of vector distinctions and correcting their misinterpretation regarding the derivation of the Lorentz force.

Findings

Vector distinctions are essential due to electric charge properties.

The proposed derivation of Lorentz force from Maxwell's equations is flawed.

The RR approach offers no new insights into electrodynamics.

Abstract

Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.