A Real-Valued Formulation of Electromagnetic Waves and Photon Mechanics

Abstract:In legacy quantum mechanics and classical electrodynamics, modeling wave propagation necessitates the use of complex-valued fields. Traditional frameworks rely on Euler's formula and the imaginary unit (i = √-1) as structural mechanisms to sustain continuous oscillation, avoiding value-sinks caused by legacy sign-inversion rules (- × - = +). This paper extends the foundational axioms established in "The Natural Order of Maths"—specifically the Identity View of Mirror Magnitude—to the behavior of light and photons. By realigning the number line so that negative magnitudes increase symmetrically toward negative infinity, we demonstrate that the electromagnetic wave equation, photon momentum scaling, and boundary geometric transitions operate identically on a stable, single-dimensional, purely real vector space. This framework removes the necessity for a complex mathematical plane, presenting a clean, logical physics where light moves, scales, and reflects entirely within a single, continuous, real-valued reality.