Causal Reconstruction: Elementary Succession and the Planck Energy This article addresses a foundational gap left by the first six papers of the reconstruction programme: the causal structure was previously assumed through a Lorentzian background, rather than derived from the reconstruction framework itself. Purpose The paper proposes that causality should not be defined by a pre-existing spacetime metric, but by the cost of reconstructive transitions between states. In this view, two states are elementarily causally successive when the minimal reconstructive action connecting them equals one action quantum and the transition is oriented by entropy production. Main Definition Two reconstruction states R₁ and R₂ are in elementary causal succession when: the minimal reconstructive cost between them equals the action quantum a₀; the relative entropy strictly increases from R₁ to R₂. The cost condition provides the elementary transition, while the entropy condition supplies the causal arrow. Main Results Cost alone is not causality. The reconstructive cost is symmetric under path reversal and therefore defines a geometric distance, not an oriented causal relation. The arrow comes from entropy production. The Fisher information appearing in the reconstructive cost is also the entropy production rate through the de Bruijn identity. This supplies an intrinsic orientation to causal succession. Strict causal order. The transitive closure of elementary succession defines a strict partial order, because relative entropy acts as a strictly increasing order-potential. Three reconstruction quanta. From c, G, and the UV cutoff Tmin, the paper defines an action quantum a₀, a minimal time τmin, and a reconstructive energy Erec, satisfying exactly: a₀ = Erec · τmin. Planck energy interpretation. When Tmin is calibrated to the Planck length, Erec coincides with the Planck energy and a₀ coincides with ℏ. Emergent time. Physical time is interpreted as a causal counting variable: a chain of N elementary transitions corresponds to a duration Δτ = Nτmin. Quantised histories. Causal histories have actions that are integer multiples of the elementary action quantum a₀. Modular Normalisation The paper further connects the elementary action quantum to modular closure. A complete modular cycle carries action h = 2πa₀, while the elementary action per modular angle is a₀ = ℏ. This fixes the normalisation and excludes the alternative identification a₀ = h. Relation to the Programme This paper treats the atomic, locally closed regime of causal succession, corresponding to one elementary step. Article 19 later generalises this structure to finite segmental closures, including tunnelling, superposition, decoherence, and measurement. Conclusion This paper replaces the previously assumed Lorentzian causal structure with a reconstructive causal order derived from transition cost and entropy production. It proposes that physical time emerges from the counting of elementary causal successions, while the Planck energy becomes the energy cost of one elementary reconstruction step.
Jean-François Rigollet (Tue,) studied this question.