The Geometric Nature of Fundamental Constants: From Lorentz's Ether to Δ-Axiomatics

This work shows that the appearance of the same numerical invariants — √2, 1/2, ε⁻¹/² — in special relativity, classical electrodynamics and quantum mechanics is not accidental. These quantities are the geometric parameters of a universal discrete triangular structure of spacetime, the elementary cell of which is a right triangle with unit legs (Δ₁×₁). An analysis of Lorentz transformations, the 4/3 electromagnetic mass problem and a number of other physical situations leads to the conclusion that “mysterious” constants act as bridges between the continuous analytic formalism and the true discrete geometry of reality. Within Δ-axiomatics, Lorentz’s ether is interpreted as a basal Δ-lattice, and the constant 1/2 acquires the status of the minimal area of a phase cell, linking relativistic effects to the uncertainty principle. Invoking musical, crystallographic and combinatorial analogies deepens the understanding of why theories “get stuck” on these numbers and opens a way to overcome the impasse.