On the Derivation of Relativistic Dynamics and the Foundations of Quantum Theory from a Correspondence Principle and the Hypothesis of an Absolute Minimum Action

Modern physics rests, by historical convention, on an architecture of independent postulates: the constancy of the speed of light, the covariance of physical laws under transformations between inertial frames, the quantization of energy, wave–particle duality. Each of these was introduced historically in response to a specific empirical anomaly, and the resulting structure today appears more as a stratification of brilliant intuitions than as an axiomatic edifice. The present work shows that this entire architecture can be deduced from just two postulates: (i) the correspondence principle, namely the requirement that any new theory must reduce, in an appropriate limit, to Newtonian mechanics; (ii) the physical meaninglessness of an arbitrarily small action, that is, the existence of a threshold Ω such that no physically realized action can be smaller than it. From these two assumptions alone there emerge — guided by heuristic and aesthetic principles, and not as further postulates — the existence of a limiting velocity κ, the geometric structure of Minkowski spacetime, the mass–energy relation, the uniqueness of the relativistic Lagrangian, the Planck–Einstein relation E = Ων and the de Broglie relation p = Ω/λ, and the wave-like nature of matter. Comparison with experimental data finally yields the identifications κ ≡ c and Ω ≡ h. The physical universe, in its dual relativistic and quantum guise, thus appears as the necessary manifestation of just two constraints imposed on classical mechanics.