Dynamical Origin of Decay Rates and Internal Time in a Metric Affine Coherent Substrate

We extend a metric-affine coherent framework to the dynamical regime and investigate the origin of decay processes within a unified geometric setting.

In this approach, particle states are interpreted as coherent configurations of an underlying substrate, characterized by an intrinsic dynamical frequency. This internal frequency defines both the mass scale and the characteristic timescale governing transitions between configurations.

Decay processes are described as transitions across an effective potential landscape and are captured by a universal structure combining internal dynamics, barrier suppression, configuration compatibility, and phase-space contributions. This leads to a unified decay law in which rates are controlled by the same dynamical quantity that determines masses.

As a first nontrivial test, we construct an explicit benchmark for muon decay and show that the framework reproduces the correct order of magnitude and scaling behavior. The extension to tau and beta decay further supports the internal consistency of the approach.

The present formulation is effective in nature and does not rely on a full microscopic derivation. Nevertheless, it provides a coherent and constrained description of decay processes, suggesting that mass generation and particle instability may originate from a common dynamical structure.