Foundations of a Two-Time Relativistic Framework: Lorentz Symmetry, Proper Time, and Matter Structure

Abstract

Despite the success of quantum theory, its axiomatic foundations remain conceptually opaque, relying on postulates that resist geometric or physical intuition. In this work, we present a geometric framework that unifies quantum and relativistic principles through a two-dimensional concept of time, combining chronological evolution with intrinsic phase periodicity. Building on the time phase uncertainty exclusion interference triad introduced in earlier work [1],[2]. We reformulate the Lorentz transformation to incorporate geometric constraints and derive a correction relevant for particles on collision trajectories. This yields a refined interpretation of relativistic effects such as length contraction, invariants, and proper time. Particle motion is described using extended 5-vectors, enabling the formulation of a generalized velocity and a new Lagrangian from which relativistic energy and momentum naturally emerge. The framework further suggests a geometric origin for the structure of matter and electric charge, grounded in time phase topology. These results will not only reproduce known features of special relativity and quantum mechanics but also point toward a unified, axiomatic reformulation of quantum field theory rooted in geometric first principles.