The causal signal restriction of the model

Adopt as a physical assumption of this framework the following restriction on signal transmission, called the causal signal restriction of the model.

(i) Causal restriction. Let $p$ and $q$ be the emission and reception events of an idealized transmission that carries a signal, where a signal is understood as information, or a physical marker by which a prepared operation at the emission event is correlated with an observation at the reception event, within the model. Mathematically, the admitted endpoint pairs form a relation $\mathcal{T}\subseteq A\times A$, with $(p,q)\in \mathcal{T}$ meaning that the model admits a transmission from $p$ to $q$. The adopted restriction is $\mathcal{T}\subseteq \{(p,q):q\in J^{+}(p)\}$. Membership in this latter set is a necessary condition; it does not assert that a transmission exists for every such pair. Thus the model admits such a transmission only if $q$ lies in the causal future $J^{+}(p)$ of $p$ (Causal reachability, causal futures and pasts, causal diamonds, and reachability by future causal paths in affine Minkowski space), that is, only if the displacement $q-p$ is zero or future causal (Timelike, null, spacelike and causal vectors of a Lorentz vector space, Time orientation, future and past timelike/null/causal vectors, and the closed cones); equivalently, no signal connects an event with an event outside its closed future light cone.

(ii) Ideal light. The ideal vacuum light signals of Adopted ideal-clock and ideal-vacuum-light interpretation are the null boundary case of the restriction: for distinct emission and reception events their displacement is future null, so in the chart of every inertial frame with $x^0=ct$ (Inertial frames and inertial charts of the affine Minkowski model, SI units and coordinate conventions of the special-relativity framework) they attain $\mathrm{\mid }{x}_s(q)-x_s(p)\mathrm{\mid }=x^0(q)-x^0(p)$.

(iii) Status. This is an adopted assumption about the idealized model; it is not a theorem of the affine geometry of Oriented time-oriented affine Minkowski space (the spacetime primitives), it is not derived here from the other postulates or from any experiment, and it is not an empirical claim about nature. In particular the framework does not assert that no physical process whatsoever exceeds $c$, and the question whether any specified physical process is a signal of this model, and with what reliability and reach, is left to a separate experimental interface.

(iv) Explicit non-restriction. The assumption does not forbid kinematic patterns in which spacelike-separated events are produced by independent prearranged mechanisms without any signal or energy transfer between them (for example a prearranged row of devices triggered in a fixed sequence), and it imposes no bound on correlations between spacelike-separated events.

(v) Scope. The assumption concerns idealized point-like transmission events in the flat classical model and carries no statistical, apparatus, source or detector content; no choice principle is used.

The restriction is adopted, not proved. The cited treatments motivate the reading that the model's causal structure is what a signal can respect — the cone as a statement of possible cause and effect and the absence of signals outside it (Adopted ideal-clock and ideal-vacuum-light interpretation, whose light-ray clause supplies the boundary case), and the reversal of the temporal order of the endpoints of a superluminal transmission in a moving inertial frame, which is what makes the restriction significant rather than vacuous. Crowell Section 4.7.1 presents its arguments for the restriction as a defense in depth and explicitly calls the causality argument the weakest; the source's own textual status is recorded here rather than converted into a derivation. Crowell Section 2.1.3 also records a modest causality postulate P1, the existence of events whose displacement is timelike in every frame; that is a different, existence-style statement, it is not re-minted or adopted here, and no identification with the restriction of clause (i) is made. Tolman Sections 51-52 give a one-way order-reversal computation in older notation, used on this page only as a motivation for the conditional relay analysis; no measurement is reported.