Unprovability of First Maxwell's Equation in Light of EPR's Completeness Condition -- A Computational Approach from Logico-linguistic Perspective

Abstract

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This modification is in tandem with the completeness condition for a physical theory, that was stated by Einstein, Podolsky and Rosen in their seminal work. Working with such a modification, I show that the first Maxwell's equation, symbolically identifiable as ``$\vec{\nabla}\cdot\vec{E}=\rho/\epsilon_0$'' from the standard literature, is {\it unprovable}. This renders Poynting's theorem to be {\it unprovable} as well. Therefore, the explanation of `light' as `propagation of electromagnetic energy' comes into question on theoretical grounds.