A Mathematical Extension That Reveals Deeper Structure of Light Beyond Quantum Electrodynamics

Abstract

Quantum Electrodynamics (QED) currently provides the most accurate description of electromagnetic interactions, yet it treats photon energy quantization exclusively through frequency. Motivated by conceptual limitations in the photon hypothesis, the Einsmax Theory of Light Quanta and Massless Particles introduces a complementary quantization framework in which amplitude plays a primary mathematical role. In this paper, a unified theoretical and mathematical formulation is presented that fully preserves Maxwellian wave propagation, the Planck–Einstein relation, and relativistic momentum conservation. Discrete amplitude quantum levels at fixed frequency are derived and shown to provide deeper explanatory power for interference, black-body radiation, and image formation in darkness. This work establishes amplitude as an active quantum variable, offering a mathematically grounded extension to the foundations of optical physics.