Reply to da rocha and rodrigues' comments on the orientation congruent algebra and twisted forms in electrodynamics

摘要

The recent claim by da Rocha and Rodrigues that the nonassociative orientation congruent algebra (OC algebra) and native Clifford algebra are incompatible with the Clifford bundle approach is false. The new native Clifford bundle approach, in fact, subsumes the ordinary Clifford bundle one. Associativity is an unnecessarily too strong a requirement for physical applications. Consequently, we obtain a new principle of nonassociative irrelevance for physically meaningful formulas. In addition, the adoption of formalisms that respect the native representation of twisted (or odd) objects and physical quantities is required for the advancement of mathematics, physics, and engineering because they allow equations to be written in sign-invariant form. This perspective simplifies the analysis of, resolves questions about, and ends needless controversies over the signs, orientations, and parities of physical quantities.