Temporal Decoherence Theory Radial Coherential Dynamics v16.0 — Time from Coherence Decay

This preprint presents Temporal Decoherence Theory (TDT), the v16 extension of Radial Coherential Dynamics (RCD), offering a complete solution to the problem of time in physics. We propose that time does not exist as a fundamental dimension; instead, time is defined as the rate at which coherence decays in the universal coherence field C(x,t)C(x,t)C(x,t).

The central result is the emergent-time equation:

dt=−dCΓdt = -\frac{dC}{\Gamma}dt=−ΓdC

where Γ\GammaΓ is the decoherence rate.
This single relation unifies thermodynamics, causality, relativity, quantum mechanics, and cosmology under one coherent framework.

Key results include:

• The arrow of time emerges automatically from monotonic coherence decay.

• The Second Law of Thermodynamics is derived rather than postulated: entropy increases because dC<0dC < 0dC<0.

• Causality is coherence ordering: higher coherence states cause lower coherence states.

• Relativistic time dilation (gravitational and kinematic) arises from variations in the local coherence field.

• Schrödinger’s equation is derived from coherence evolution.

• The age and structure of the universe follow from cumulative decoherence since C=1C = 1C=1 at the Big Bang.

RCD v16 completes the conceptual unification of the theory: space, time, matter, gauge fields, quantum behavior, and gravity all emerge from the dynamics of a single coherence field.

This release establishes the foundation for RCD v17, which will present the full Lagrangian and complete mathematical unification.