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Temporal Ratio Theory: A Conversion-Based Model of the Arrow of Time Matthew Dominik (Hollis Black) Dominik Research Institute, Cleveland, OH Abstract: This preprint presents Temporal Ratio Theory, a mathematical framework in which the arrow of time emerges from an asymmetric conversion operator acting at the present boundary. The theory models the future as an expanding exponential field of unresolved potential and the past as a contracting field of concluded structure. The present functions as a finite-width collapse zone where future potentials are converted into past outcomes through a sign-reversing operator. The model yields a clear testable prediction: a measurable discontinuity must exist between field magnitudes approaching the present from positive and negative temporal domains. This discontinuity constitutes the physical signature of temporal asymmetry within this framework. 1. Introduction Temporal Ratio Theory aims to reformulate the arrow of time not as a property of time itself, but as a property of the conversion process that links future potential to past structure. Classical physics treats time as fundamentally symmetric, while thermodynamics and quantum measurement introduce irreversibility. This theory unifies these perspectives by locating asymmetry in the present boundary rather than in the temporal axis. 2. Temporal Domains Time is modeled as T = (-∞, ∞). The positive domain corresponds to future potentials, the negative domain corresponds to concluded past structures, and the present is a conversion boundary Zε of finite thickness. Future potentials are described by Φ_T(t) and past structures by Φ_A(t). 3. Conversion Operator The present transforms potentials into structure by a sign-reversing operator C such that C(t) = −f(t) for t > 0. This operator is asymmetric under time reversal, providing the mechanism for temporal directionality. The past is formally the image of the future under this operator: Φ_A(t) = C(Φ_T(t)). 4. Temporal Ratio and Field Evolution The core observable of the theory is the temporal ratio R(t) = |Φ_T(t)| / |Φ_A(t)|. Field evolution is defined as Φ_T(t) = Φ_T(0+) e^(k■ t) and Φ_A(t) = Φ_A(0−) e^(−k■ t). The resulting ratio evolves as R(t) = C■ e^((k■ + k■)t). This creates a compact dynamical system in which temporal asymmetry is quantified. 5. Testable Prediction The theory predicts a measurable discontinuity at the conversion boundary: lim(t→0■) Φ_T(t) ≠ lim(t→0■) Φ_A(t). This conversion differential must be non-zero if the arrow of time exists. Any experiment capable of
probing fields immediately adjacent to the collapse moment—such as quantum state resolution, entropy gradients at phase boundaries, or measurement-induced decoherence—should detect this asymmetry. 6. Significance Temporal Ratio Theory reframes temporal flow as the result of the imbalance between expanding potential and contracting structure. The present is treated as a phase transition surface, analogous to shock fronts or horizon boundaries in physics. The fact that the theory yields a falsifiable signature distinguishes it from purely philosophical treatments and allows integration with existing physical models. 7. Conclusion By shifting temporal asymmetry from the structure of time to the conversion operator, Temporal Ratio Theory provides a concise and potentially unifying explanation for the arrow of time. Future work may explore extensions into relativistic settings, quantum measurement models, or information-theoretic formulations.
