Gomuwa, Adahas (2026) Temporal Roles and the Limits of Global Time: Causal Order, Accumulated Change, and Thermodynamic Direction. [Preprint]
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Abstract
Physical theories employ temporal notions in several distinguishable roles. Time orders events, measures elapsed duration or accumulated process, and is associated with an apparent direction from past to future. These roles are often represented by a single scalar parameter, but their unity is not automatic. This paper offers a structural clarification of the conditions under which such unification is possible.
The central claim is modest. Causal order, accumulated change, and thermodynamic direction are individually meaningful structures, but they do not by themselves entail a single global scalar time parameter representing all three. In particular, if an accumulated transition quantity is to be represented as the difference of a scalar state function, then it must satisfy an exactness condition: the accumulated quantity between two states must be independent of the path or process connecting them. Many physically important quantities fail this condition. Proper time, action, heat, work, entropy production, dissipated work, and thermodynamic length are naturally associated with curves, processes, or protocols rather than with endpoint states alone.
The paper does not argue that global time functions are impossible, nor that time is unreal. Newtonian mechanics, many relativistic models, globally hyperbolic spacetimes, and numerous effective theories make legitimate use of temporal parameters. The point is instead diagnostic: whenever temporal order, duration, and direction are represented by one scalar, additional structure is being used. Such structure may include a metric, foliation, preferred parametrization, boundary condition, equilibrium assumption, or integrability condition. The unity of temporal roles is therefore a substantive feature of particular theoretical frameworks, not a consequence of causal order, physical change, and thermodynamic asymmetry alone.
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