Observational motives underlying the choice of algebras in physics

We discuss observational motives for the adoption of specific algebras in physics. Then we perform an observational analysis of Dyson's exposition of Feynman's proof of Maxwell's equations. Based on the epistemology of observational realism, we argue that the non-commutation relations, adopted as principles in the proof, are algebraic representations of observational relativistic physics, contrarily to the opinion that relations of this kind are theoretical statements and abstractions. We also comment on the origins of the non-commutative algebra of quantum physics contrasting with the relativistic case.