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On the Non-Essential Nature of Phase and Probability Interpretation in Wave Equations --- A Conceptual Reexamination Based on the Continuity of Light ---

Akihito Sugawara

Published Jan 10, 2026• 0 citations
Publisher

Abstract

This paper reexamines the concept of phase in the description of light and electromagnetic waves, focusing on its physical meaning and role in theoretical formulations. Although phase is commonly treated as a physically meaningful quantity, particularly in explaining interference phenomena such as the double-slit experiment, this work argues that phase should instead be understood as a mathematical variable introduced for convenience in solving and expressing wave equations, rather than as a physical entity. Electromagnetic waves are fully described by the wave equation, and phase naturally appears as part of its mathematical solution. This paper clarifies that phase velocity can exceed the speed of light without violating causality, precisely because phase does not correspond to the propagation of energy or information. Misinterpreting phase as a physical motion leads to conceptual confusion about the nature of light. Furthermore, the paper explores an intuitive perspective in which light is regarded as a continuous information structure, and examines how this intuition aligns with formal mathematical descriptions. It is shown that interference and related wave phenomena can be explained without assigning physical reality to phase itself, relying solely on the properties of the wave equation. By separating mathematical description from physical ontology, this work aims to refine the conceptual understanding of light and to highlight how terminology and formalism influence our interpretation of physical phenomena.

DOI
10.5281/zenodo.18202921

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The frequency f (or ν) is inversely proportional to this distance: the closer two light quanta are, the higher the frequency f; the greater the distance, the lower the frequency f. It can be expressed through the classical wave velocity formula: c=fλ. Within the visible spectrum, λ≈0.5×10⁻⁶ metres (500 nanometres). Remarkably, this distance corresponds precisely to the typical dimensions of bacteria (approximately 0.5–5 micrometres). The evolutionary tree of life takes bacteria as its root, while the wavelength of visible light—the fundamental scale for human vision and quantum information interaction—aligns exactly with this root-level dimension. As the product of billions of years of bacterial evolution, our human perception, communication, and even consciousness may possess an intrinsic connection to this "bacterial-scale" queue distance of light quanta. 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