Neutral Time, Emergent Clock Dynamics, and the A⁵ Law: A Unified Operational Framework for Relativity, Quantum Mechanics, and Thermodynamics

This preprint presents an operational framework for connecting General Relativity, Quantum Mechanics, and Thermodynamics through the hypothesis of a neutral informational background underlying observed physical dynamics. The central idea is the introduction of a pre-temporal neutral time τττ, a background ordering parameter that has no intrinsic thermodynamic arrow and does not correspond directly to ordinary laboratory time. Within this framework, observed time ttt is not assumed as fundamental, but emerges through an interaction-activated clock map, where physical interactions, decoherence, dissipation, and irreversible information flow activate the measurable temporal direction. The manuscript proposes that the arrow of time is not produced by the mere existence of information, but by the causal dynamics of information. In this sense, temporal order becomes an operational consequence of physical interaction, rather than a primitive postulate. The framework separates the neutral background component from interaction-induced fluctuations and uses this distinction to organize gravitational, quantum, and thermodynamic sectors within a common formal structure. A key result of the work is the formulation of a falsifiable A⁵ operational signature, appearing as a fixed residual-decoherence scaling law in a validated clock-linear regime. In terms of calibrated drive amplitude AAA, the predicted excess decoherence follows an A⁵ scaling law; equivalently, when expressed through calibrated power P∝A2P A²P∝A2, the corresponding prediction is a P²·⁵ scaling law. This exponent-based prediction is not presented as an amplitude-matching claim, but as a laboratory-testable discriminator designed to survive ON/OFF subtraction, calibration checks, log–log fitting, and competitor-model rejection. The experimental strategy is built around laboratory-ready protocols, including differential ON/OFF controls, clock-linear window validation, weighted log–log regression, AIC/BIC model comparison, null diagnostics, and possible cross-platform replication. Candidate systems include superconducting quantum platforms, NV centers, and related open-quantum systems where decoherence, information flow, and residual noise channels can be measured with controlled precision. The framework also introduces an operational open-quantum sector based on Lindblad dynamics, allowing entropy production and the recorded temporal arrow to be treated through measurable state evolution. The use of unital open dynamics, excess decoherence rates, and information-driven interaction scalars provides a concrete route for testing whether temporal direction can be linked to controlled informational dynamics rather than treated as a purely external assumption. This work does not claim to provide a final theory of everything. Instead, it proposes a testable operational research pathway: a structured framework in which the emergence of time, decoherence, entropy production, and physical interaction can be examined through precise experimental signatures. Its main contribution is the construction of a falsifiable bridge between fundamental theoretical physics and controlled laboratory observation, with the A⁵ law serving as the central operational signature.