Æther XIV: Event-Projected Time and Dissipative Emergence of Temporal Order in the TSTU Program

Abstract:

The present paper (Paper XIV) proposes a precise and radical thesis: observable physical time is not a background dimension, but the dissipative integral following discrete topological ruptures of the TSTU scalar field. This thesis is formalized by the central equation:

t_phys = (1 / Lambda^2) * Integral[ phi_dot^2 * d_tau ]

where Lambda^2 = V(phi_min) represents the energy scale of the relaxed configuration. The strict distinction between the formal parameter (tau) and observable physical time (t_phys) resolves the apparent circularity of the TSTU program.

Key results developed in this work:

1. Origin of the Arrow of Time: A derivation of temporal asymmetry from the isotropic geometry of post-event dissipation, without requiring a pre-existing thermal state.

2. Multiscale Unification: Four distinct phenomena (atomic ticks, radioactive decay, gravitational collapse, and quantum measurement) are unified under a single topological mechanism.

3. Cosmological Consistency: Exact alignment with the quantified predictions of Paper VI (mu ≈ 1.018, E_G deficit in voids), where the field is reinterpreted as a dissipative projector generating time.

4. Numerical Validation: Through high-resolution Klein-Gordon simulations (Leapfrog integration), we establish a robust temporal rarefaction ratio of 1.343 between the cosmic void (unscreened) and dense matter (screened) regimes.

5. Dynamic Signature: Numerical evidence shows that TSTU dynamics differ from a classical damped oscillator by an order of magnitude, indicating that time generation is governed by spatial radiation of scalar modes rather than local friction.

This paper establishes the numerical proof of concept for the TSTU temporal mechanism. While the current results provide a stable lower bound for time rarefaction, they define the technical agenda for Paper XV, which will focus on absolute SI calibration and high-order non-linear integration.

Supplementary Material: This deposit includes the full suite of Python validation scripts (v5c, v5d, etc.) ensuring the reproducibility of the reported ratios and stability tests.