Photons with Scalar Fields Should Exist
Abstract
The author believes that scalar photons should exist. Scalar photons are photons corresponding to scalar fields φ. This type of photon is different from the photons we usually understand, as they correspond to the vector potential A.This paper explores the theory of mutual energy flow within the framework of the Helmholtz equation, proposing a novel interpretation of particle-like energy transfer through the interaction of retarded and advanced waves. Traditional electromagnetic and quantum theories describe energy flow via self-energy flow (e.g., Poynting vector or probability current density), which fails to localize energy transfer. In contrast, mutual energy flow arises from the synchronized interaction between a retarded wave emitted by a source and an advanced wave emitted by a sink, forming a localized energy channel. We demonstrate that the Helmholtz equation must be modified - by introducing source-sink dynamics, defining a corrected magnetic field, and halving the mutual energy flow intensity - to derive a consistent energy conservation law. The resulting mutual energy flow density exhibits particle-like behavior: it is generated at the source, propagates directionally, and annihilates at the sink, with zero leakage outside this path. Crucially, self-energy flow is shown to represent reactive power, incapable of energy transfer, while mutual energy flow alone accounts for active energy propagation. This approach bridges electromagnetic theory and quantum mechanics, aligning with action- reaction principles and transactional interpretations. The findings suggest that particles can be modeled as mutual energy flows, resolving wave-particle duality by unifying retarded and advanced waves into a single physical entity. This work challenges classical field theories and offers a pathway to revise Maxwell’s and Schrödinger’s equations for particle-like localization.