Spectral Relativity: Conceptual Foundations of Discrete Causal Time and Spacetime Emergence

Spectral Relativity proposes a foundational and conceptual framework in which time is treated as a discrete, ontological, and causal process, rather than as a continuous parameter or a geometric dimension. The work is explicitly pre-formal and aims to clarify the underlying conceptual structure from which a full mathematical formulation may later emerge. Physical evolution is described in terms of a growing causal structure, where each temporal update redistributes a conserved causal energy that regulates the local rate of causal growth. Spatial relations and geometry are not assumed a priori but arise effectively from patterns of causal connectivity. Within this framework, gravity appears as an emergent phenomenon associated with the inhibition of causal growth by matter, rather than as a fundamental force or curvature postulate. Horizons are reinterpreted as regions of vanishing causal update rate, and classical singularities are structurally avoided due to the discrete and generative nature of temporal evolution. In appropriate coarse-grained limits, the framework recovers the phenomenology of relativistic spacetime, with the invariant speed of light understood as a bound on the local rate of causal update. The framework further offers a conceptual explanation for quantum irreversibility and decoherence, arising from the evolution of non-unitarily equivalent Hilbert spaces across discrete temporal updates, without invoking environmental noise or fundamental non-unitarity. This article is intended as a conceptual foundation preceding mathematical formalization and serves as the first step in a broader research program aimed at understanding spacetime, gravitation, and quantum phenomena as emergent aspects of a deeper causal temporal ontology.