Before c, ℏ, G: The Scalar Phase Field and the Operational Origin of Physical Law

Abstract

This book is the result of a return. A return to the year 1860, before relativity took the shape we know today, before the “why” of physics overwhelmed the “how”. In those years, the notions of space and time were not yet taken for granted. One could still ask: “If no metric is given beforehand, how can distance be defined?” and “If no external clock exists, how can the passage of time be measured?” I decided to take these questions seriously. Not out of opposition to standard physics, but out of a simple disbelief: can physics be rebuilt from scratch without borrowing any pre-built stage — without spacetime, without a metric, without imported constants? This book is the answer. The mental laboratory. Instead of a physical laboratory, where every measurement is influenced by local conditions (distance from a galaxy, ambient phase density, etc.), I built a mental laboratory. In that laboratory no local effect can influence the fundamental laws. The only primitive entity was a scalar phase field defined on the circle S 1 . Nothing else was given: no distance, no duration, no mass, no charge, no constant. Everything emerged from counting the cycles of this field: • Gam (length unit) and tick (time unit) came from counting crests of a travelling wave. • The action quantum h came from one complete 2π phase closure. • The wave equation came from smoothness d(dϕ) = 0 and the existence of shape-preserving patterns. • Electric charge came from phase leakage at the outer anchor of the 1−11−11−1 knot. Mass came from the closure budget of the active ring. • Maxwell’s equations, the photon, and gravity all appeared as emergent layers of this same structure. On parameters. The model claims to contain no free parameter of its own. Only one fundamental length scale ℓ0 (the maximal compression limit of the phase field) is introduced. In the final chapter this scale is identified with the Planck length — not as a free parameter, but as a translation factor that converts the pure numbers of the mental laboratory into SI units. All other numbers (the fine-structure constant, the electron mass, the gravitational constant) come out as predictions from the knot architecture alone.

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