DoT: The Duality of Time Postulate

The most productive tests compare a specified generative model with a specified conventional or phenomenological alternative. Merely agreeing with a standard formula used to build the model is not a distinguishing test.

Dispersion. Equation (5.4) is exact for the two-component update. In a low-frequency expansion, let $a=k\ell$ and $b=\theta$. Then

The correction is model dependent. It becomes a physical prediction only when $\ell$, $\Delta t$, and the identification of the mode are fixed independently. A zero mass parameter has exactly linear branches locally within the principal momentum range of this particular walk, so a generic photon-dispersion claim would be unwarranted.

Memory. Add a weak driving force $f(t)$ to the first line of Eq. (6.1). For zero initial data, its Laplace-domain response is

The two-pole response can be compared with a one-pole Markov approximation. A meaningful test determines parameters from one preparation and predicts a different drive or time window. Agreement demonstrates the usefulness of that reduced model; distinguishing a unique temporal ontology requires an additional restriction that competing hidden-variable realizations cannot reproduce.

Clock universality. A proposed microscopic clock law should predict whether distinct matter clocks accumulate the same proper time after accounting for known interactions. A composition-dependent residual would be a departure from universal coupling. A universal result must be proved across sectors, rather than imposed separately for each clock.

Coherence and records. A nonunitary completion law should specify when interference changes, how outcomes are distributed, and whether energy is conserved. The parameters must also satisfy existing experiments. If completion is only an operational quotient, standard quantum predictions may remain exactly unchanged; that is an interpretation, not a new detectable effect by itself.