A 4D Geometric Foundation for Relativistic Quantum Mechanics via Crystallographic Twinning Compatibility

This is the authors' abstract. We don't add key points for this paper.

We present a strictly local and deterministic geometric foundation for relativistic quantum mechanics by mapping the phenomenological theory of martensitic crystallography onto a four-dimensional pseudo-Riemannian spacetime manifold. By generalizing the classical 3D Hadamard compatibility condition to a 4D covariant tensor field framework, we demonstrate that the fundamental equations of quantum mechanics emerge naturally from the geometric constraints of a continuous lattice undergoing structural phase transformations. Defining a complex field structure from the local volume fraction density of twinned variants and the kinematic phase front normal, the principle of stationary action yields the exact, unapproximated Klein-Gordon and Dirac equations. By doing so, we provide a concrete, solid-state mechanical realization to the historical hydrodynamic formulations of Madelung and the double-solution models of de Broglie. Under this paradigm, abstract probability amplitudes are reinterpreted as real, structural domain distributions, and the Bohm quantum potential is identified as the localized interfacial surface energy density of sub-microscopic twin boundaries. Finally, we resolve the historical problem of wave-function collapse without invoking anthropocentric or non-local interventions; utilizing a framework of macroscopic structural decoherence, we prove that the perception of a single, definitive measurement outcome is an unavoidable consequence of the thermodynamic orthogonality and strict kinematic constraints governing macroscopically bound solid-state detectors embedded within a globally twinned 4D block universe.