We build on the classification in [1] of event sequences in the influence network as respecting collinearity or not, so as to determine in future work what phenomena arise in each case. Collinearity enables each observer to uniquely associate each particle event of influencing with one of the observer's own events, even in the case of events of influencing the other observer. We further classify events as to whether they are spacetime events that obey in the fine-grained case the coarse-grained conditions of [2], finding that Newton's First and Second Laws of motion are obeyed at spacetime events. A proof of Newton's Third Law under particular circumstances is also presented.
We build on the classification in [1] of event sequences in the influence network as respecting collinearity or not, so as to determine in future work what phenomena arise in each case. Collinearity enables each observer to uniquely associate each particle event of influencing with one of the observer's own events, even in the case of events of influencing the other observer. We further classify events as to whether they are spacetime events that obey in the fine-grained case the coarse-grained conditions of [2], finding that Newton's First and Second Laws of motion are obeyed at spacetime events. A proof of Newton's Third Law under particular circumstances is also presented.
We build on the classification in [1] of event sequences in the influence network as respecting collinearity or not, so as to determine in future work what phenomena arise in each case. Collinearity enables each observer to uniquely associate each particle event of influencing with one of the observer’s own events, even in the case of events of influencing the other observer. We further classify events as to whether they are spacetime events that obey in the fine-grained case the coarse-grained conditions of [2], finding that Newton’s First and Second Laws of motion are obeyed at spacetime events. A proof of Newton’s Third Law under particular circumstances is also presented.
In recent works, Knuth and Bahreyni have demonstrated that the concepts of space and time are emergent in a coarse-grained model of direct particle-particle influence.In addition, Knuth demonstrated that observer-made inferences regarding the free particle, which is defined as a particle that influences others, but is not itself influenced, result in a situation identical to the Feynman checkerboard model of the Dirac equation.This suggests that the same theoretical framework that gives rise to an emergent spacetime is consistent with quantum mechanics.In this paper, we begin to explore the effect of influence on the emergent properties of a particle.This initial study suggests that when a particle is influenced, it is interpreted as accelerating in a manner consistent with special relativity implying that, at least in this situation, influence can be conceived of as a force.
Questions about quantum measurement are often collected under the umbrella term “the measurement problem,” which conflates record-bearing structure, fine-event actuality, and statistical weighting into a single explanatory task. This paper separates those roles through a reduction–reconstruction strategy with two structural results. First, Born weighting is suspended and the physically defined record architecture is maximally coarse-grained to the distinction between non‑record‑bearing and record‑bearing sectors. After an ideal measurement interaction, the final state may lie entirely in the record-bearing sector, establishing sharp coarse record-sector support without selecting any fine-grained event. Restoring physically meaningful record resolution preserves that coarse truth while enlarging the represented question space: whenever the same postmeasurement state has support in more than one distinguishable fine sector, no occupied fine sector contains the global state. The single-event question therefore appears not through failure of coarse dynamics, but through successful coarse dynamics followed by finer physical resolution. Second, the paper asks what could genuinely supply the missing fine-event specification. Relative to a theory‑relative completed standard-description map D̄, a deterministic actuality map X̄ is already determined by the completed description exactly when X̄ = G ∘ D̄ for some G. Non‑injectivity of D̄ alone is insufficient for actuality underdetermination; the decisive obstruction is variation of X̄ within a fiber. Failure of factorization signals the need for residual run‑level information beyond the completed standard description, whereas factorization eliminates that informational need without implying that the candidate law G is part of standard quantum theory. Stochastic completions may instead add an independently specified law of event occurrence. Probability is then restored as an empirical reconstruction constraint: admissible completions must recover the Born distribution, preserve cross‑resolution consistency, and, where applicable, reproduce protocol‑level registered‑history laws. The result is a structural separation among record‑sector support, fine‑event actuality, Born weighting, and registration, without selecting a preferred interpretation or proposing an actuality mechanism. This is version 1.0 of the manuscript.
Boundary-Condition Quantum Mechanics III: A Stochastic Growth Model for Causal Event Chains and the Emergence of Inertia This paper develops the third stage of the Boundary-Condition Quantum Mechanics (BCQM) programme, in which spacetime is modelled as an emergent causal graph of irreversible quantum events. The central object is the q-wave: an informational propensity field that guides the stochastic growth of a particle’s event chain. Building on BCQM II (event ontology and emergent spacetime) and the separate Analytical Proofs note, this work: defines a concrete, Lorentz-respecting mathematical form for the retarded q-wave \psi^+ on a future boundary; specifies a hop-bounded, retarded graph-growth rule (Algorithm 1) that realises a particle’s worldline as a sequence of stochastic “ticks”; ties the lattice regulator and environment window to a finite coherence horizon W_{\mathrm{coh}}, and shows how to take a clean continuum limit; demonstrates numerically that the classical principle of inertia is an emergent statistical consequence of phase coherence: the coarse-grained trajectory follows the path of stationary action, with jitter set by W_{\mathrm{coh}}; shows that the effective inertial parameter scales as m_{\mathrm{eff}} \propto W_{\mathrm{coh}}^{-2}, supported by simulation and an operator-theoretic sketch. Particular care is taken to clarify the role of the “advanced” contribution: in this paper, “advanced” refers only to the advanced Green’s-function branch used to maintain time-symmetric amplitude bookkeeping. The advanced factor enters as the conjugate co-contribution in the t^+/t^- pairing at an event and is absorbed into the normalisation at the probability step. It does not represent backwards-in-time dynamics and cannot be used for signalling; all realised events are ordered along the usual chronological time. The record includes simulation details and parameter tables (Appendix A–C), normalisation and advanced-branch conventions (Appendix D–E), and a brief complexity estimate. A reference implementation of the stochastic event-chain simulations used for Figs. 1–4 is available in the public GitHub repository: Code: https://github.com/PMF57/BCQM_III Archived code and figure-generation scripts: 10.5281/zenodo.17632820This paper is part of an ongoing series on BCQM: BCQM I – Foundations and collapse horizon: 10.5281/zenodo.17191306 Analytical Proofs for BCQM: 10.5281/zenodo.17242311 BCQM II – From quantum events to spacetime: 10.5281/zenodo.17398294 BCQM Primitives – hop-bounded selection rule: 10.5281/zenodo.17495038 BCQM III provides the “engine” linking the event-based ontology to classical inertial motion. The follow-on work (BCQM IV) uses the same framework to analyse the inertial noise spectrum and its prospective experimental signatures. v2 - note (updated BCQM III) 2025-11-18: This version clarifies the scope and assumptions of the paper. In particular, it makes explicit that the phase structure \Delta S \approx p_\mu \Delta x^\mu is used at the emergent spacetime level as an effective description, and that deriving this structure (and the underlying Lorentzian geometry) from the primitive BCQM event-graph rules is deferred to future work (BCQM IV–V). No results, simulations, or numerical conclusions have been changed; the update is purely conceptual and expository.
We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| fulfills a sum rule generalizing that of classical probability theory. We interpret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve *conditonal* preclusion (which apparently requires a notion of coarse-graining for its formulation) and the need to "locate spacetime regions in advance" without the aid of a fixed background metric (which can be achieved in the context of conditional preclusion via a construction which makes sense both in continuum gravity and in the discrete setting of causal set theory).