Selection rules, causality, and unitarity in statistical and quantum physics

Henry Margenau

Samuel Fedida

We investigate a generalisation to Lüders’ rule à la Aharonov–Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture à la Tomonaga–Schwinger. We show that under this rule and under the additional assumptions of the integrability and unitarity of the Tomonaga–Schwinger dynamics and the foliation-independence of rays on acausal Cauchy hypersurfaces, selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated precompact regions. We highlight that this propagates to positive operator-valued measures, where the commutation is necessarily bosonic. In the instantaneous-measurement idealisation, this implies quantum no-signalling for non-selective measurements. We then examine Sorkin’s impossible measurements and show that immediate contradictions can be averted as long as collapse-inducing measurements are irreversible. These results reaffirm the consistency of the Tomonaga–Schwinger picture of relativistic quantum theory, for which unitarity, integrability and foliation-independence of the states exclude superluminal signalling despite the “instantaneity” of a side-cone measurement collapse rule. We finish by discussing the possibility of extending such results beyond the interaction picture. • Prove Aharonov–Albert side-cone updates are consistent with Einstein causality. • Instantaneous nonselective measurements imply no-superluminal signalling. • Sorkin’s impossible measurements are avoided assuming irreversible measurements.

Torben Wille

Abstract We derive the formalism of Quantum Mechanics from the axioms of Event-State Theory (EST). While Paper VI established General Relativity as the deterministic limit of computational optimization, this work addresses the stochastic limit where the computational temperature $\lambda$ is non-negligible. We demonstrate that the "Field of Potential" $\Omega$ functions as a phase space of possible next-frames, governed by a Boltzmann-like selection rule. By identifying matter not as point particles but as topological defects ("twists") in the causal graph, we show that the cost function acquires an oscillatory phase component to satisfy lattice continuity. This creates interference effects in the selection probability, reproducing the Feynman Path Integral and the Schrödinger equation. Thus, Quantum Mechanics is identified not as a fundamental framework, but as the statistical mechanics of causal exploration.

Henry Margenau

Wesley E. Brittin, Asım Orhan Barut

Trinity Labo

This paper proposes Causal Bandwidth Reconstruction as a finite-information framework for interpreting physical reality. The central claim is that an observer-like physical system does not access the complete instantaneous state of the universe, but reconstructs an effective reality from causally available information constrained by light-speed delay, channel bandwidth, source capacity, memory, and processing limits. The paper introduces a causal bandwidth bound combining propagation delay, effective information bandwidth, source information capacity, and observer integration capacity. It then defines observer-relative effective reality as a reconstruction map acting on information from the past light cone. Within this framework, classical physical laws are interpreted as stable compression rules: position, velocity, mass, temperature, pressure, rigidity, friction, optical objects, and field values are treated as low-dimensional variables that remain stable after inaccessible microscopic distinctions are removed. The revised version adds a conditional Born-rule stabilization argument. It does not claim to derive the Born rule from light speed alone. Instead, it shows that if stable quantum records form an orthogonal event algebra and the reconstruction map is positive, normalized, additive on orthogonal channels, unitarily invariant, noncontextual, and stable under finite-bandwidth coarse-graining, then Gleason-type reasoning selects the squared Hilbert amplitude as the unique stable record probability. In this interpretation, the Born rule is treated as the probability measure naturally selected by stable finite-bandwidth record reconstruction. The paper also adds testable directions. These include finite-bandwidth delayed-choice quantum eraser experiments, bandwidth-controlled decoherence and record-stabilization studies in macroscopic quantum systems, finite-time Wigner-type record synchronization, and numerical estimates using photon-counting detector bandwidths, sensory bandwidths, and integration capacities. A curved-spacetime extension is outlined by replacing the flat delay r/c with retarded causal time in a general metric and by interpreting horizons as extreme causal-bandwidth boundaries. This work is theoretical and interpretive. It does not replace standard quantum mechanics, relativity, thermodynamics, or statistical mechanics. Rather, it provides a unifying finite-information lens through which classical laws, thermodynamic coarse-graining, optical perception, field descriptions, quantum measurement, Born-rule stabilization, and observer-relative record formation can be understood as different regimes of causal information reconstruction. Interdisciplinary fields crossed by this work include theoretical physics, special relativity, quantum foundations, Born-rule studies, decoherence theory, quantum measurement theory, information theory, Shannon communication theory, statistical mechanics, thermodynamics, black-hole information theory, holographic principle research, philosophy of physics, information geometry, cognitive science of observation, artificial observer theory, AI systems, virtual embodiment studies, and complex-systems modeling.