DOI: 10.5281/zenodo.17359232
title: TDCF Temporal Direction-Consumption Framework (TDCF): A Foundational Chronodynamic Theory of Time Decay and Multi-Domain Collapse

description: \begin{abstract} The Temporal Direction-Consumption Framework (TDCF) models time as

a dynamical, consumable scalar eld whose local rate of progression decays due to an

intrinsic generation-dissipation balance. We present a rigorous axiomatic foundation,

derive the Temporal Direction-Consumption Equation (TDCE) from a variational principle,

extend to coupled Multi-Temporal Collapse Dynamics (MTCD), embed the elds into

relativistic geometry with an explicit energy-momentum tensor, dene the Chrono-

Consumption Relation (CCR) for relativistic regimes, and formulate a thermodynamic and

quantization program. We prove local well-posedness, supply linear stability and causality

conditions, and give a fully specied empirical prediction pipeline (Temporal

Desynchronization Law, TDL) suitable for Bayesian calibration against modern

cosmological and timing data. The manuscript removes heuristic gaps present in earlier

drafts and provides a self-contained foundation for TDCF as a rst-class basic physical

theory. To address potential conicts with the standard model and enhance testability, we

include preliminary numerical simulations demonstrating decay behavior and bounds

from experiments like muon lifetime measurements \cite{muonlifetime}. TDCF is

formalized across nine layers: axiomatic, mathematical, geometric, quantum,

thermodynamic, empirical, computational, philosophical, and epistemological, oering a

unied framework for entropy, cosmic expansion, and quantum coherence. We add

comparisons to Shape Dynamics \cite{Barbour2011}, preliminary data ts to

DESI/SNIa/PTA, detailed TDCE stability proof, and MTCD simulations for N=100 and N=3.

Inspired by Kozyrev’s causal mechanics \cite{Ludwig2020}, we incorporate time density;

1 / 19address the problem of time in quantum gravity \cite{Anderson2010}; develop chronon

eld theory \cite{Caldirola1997}; and align with the dynamic theory of time

\cite{Emery2020}. We expand empirical methodology with cosmographic methods for

redshift drift \cite{Heinesen2020}, include 5 case studies, actual experiments on time

asymmetry, derive chronon QFT Lagrangian, integrate Loop Quantum Gravity

\cite{Rovelli1998}, enhance LaTeX formatting, and expand simulation plots with gures.

\end{abstract}

\tableofcontents \bigskip

1. Introduction

Classical physics treats time as a background parameter. Empirical phenomena (time

dilation, irreversibility) and conceptual problems in quantum gravity motivate a theory

where local time is a dynamical eld \cite{Eddington1928, Brans1961, Page1983}. TDCF

posits such a eld and derives its dynamics from a variational principle plus physically

motivated dissipative corrections. This manuscript formalizes TDCF to the level required

for physical scrutiny: explicit axioms, units, derivations, mathematical properties,

geometric coupling to gravity, thermodynamic interpretation, quantum extension, and a

complete observational pipeline. Compared to alternative proposals like varying

constants, decaying dark matter, Penrose’s CCC \cite{PenroseCCC}, or big rip cosmologies

\cite{Caldwell2003}, TDCF uniquely predicts domain-correlated desynchronization and

velocity-dependent energy decay, testable with current data.

TDCF is formulated in nine layers to cover its various aspects: we begin with core postulates

(axiomatic layer), then develop mathematical evolution equations (mathematical layer)

for the temporal eld. We next embed TDCF in spacetime geometry (geometric layer) and

quantize it (quantum layer). We examine thermodynamic implications, particularly

regarding entropy and the arrow of time (thermodynamic layer). We then discuss

observable consequences (empirical layer) and outline how to simulate the theory

(computational layer). Finally, we consider philosophical implications (philosophical layer)

and issues of measurement and knowledge (epistemological layer).

The framework is structured in layers for clarity, incorporating rigorous proofs,

experimental constraints, and simulations to mitigate speculation. Spatial gradients are

neglected assuming slow variation, justied for cosmological scales where domain sizes are

large compared to light-travel times.

To incorporate Kozyrev’s causal mechanics \cite{Ludwig2020}, we extend the theory with

time density (\rho

_

t), inuencing dissipation and providing a physical basis for time’s

asymmetry.