A Complex-Number Model of Matter-Spacetime Attributes and the Manifest-Latent Duality

This paper explores whether material properties and the spacetimebackground share a common geometric ontology, aiming to construct a unified descrip?tive framework that encompasses relativistic kinematics and the foundational relations ofquantum mechanics. [Methods] Taking“spacetime and matter share a common origin”
and“the attributes of physical entities possess a complex structure”as basic postulates,and proceeding from the complex geometric representation of Minkowski spacetime, this paper elevates complex numbers from computational tools to an ontological structure, 9 thereby establishing a matter-spacetime complex geometric model. In this model, the real part corresponds to particle nature and the imaginary part to wave nature, with the two being correlated through a phase-angle parameter. [Results] From this single geometric structure, the model naturally yields: (1) the mass-velocity relation, mass-energy equation, time dilation and length contraction, and the Doppler shift of special relativity; (2) the de Broglie relations of quantum mechanics and a geometric interpretation of waveparticle duality; (3) a unified geometric resolution of the Abraham-Minkowski dilemma concerning photon momentum in a medium; and (4) a derivation of gravitational redshift via the equivalence principle. Massive particles and photons are encompassed within the same complex geometric language. [Limitations] At present, this constitutes only a kinematic framework and has yet to incorporate dynamical mechanisms or the curved spacetime of general relativity. [Conclusions] The indispensability of complex numbers in the physical world is rooted in an intrinsic“manifest-latent”complex structure of reality itself. The complex geometric framework proposed herein provides a new ontological foundation for the unified description of relativity and quantum mechanics. Keywords Manifest-latent duality; Complex-number ontology; Wave-particle duality; Matter-spacetime common origin; Complex geometry