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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.17632454 |
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Table of Contents:
- <p><strong>Boundary-Condition Quantum Mechanics III: A Stochastic Growth Model for Causal Event Chains and the Emergence of Inertia</strong></p> <p>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 <em>q-wave</em>: an informational propensity field that guides the stochastic growth of a particle’s event chain.</p> <p>Building on BCQM II (event ontology and emergent spacetime) and the separate Analytical Proofs note, this work:</p> <ul> <li>defines a concrete, Lorentz-respecting mathematical form for the retarded q-wave \psi^+ on a future boundary;</li> <li>specifies a hop-bounded, retarded graph-growth rule (Algorithm 1) that realises a particle’s worldline as a sequence of stochastic “ticks”;</li> <li>ties the lattice regulator and environment window to a finite coherence horizon W_{\mathrm{coh}}, and shows how to take a clean continuum limit;</li> <li>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}};</li> <li>shows that the effective inertial parameter scales as m_{\mathrm{eff}} \propto W_{\mathrm{coh}}^{-2}, supported by simulation and an operator-theoretic sketch.</li> </ul> <p>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 <strong>not</strong> represent backwards-in-time dynamics and cannot be used for signalling; all realised events are ordered along the usual chronological time.</p> <p>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:</p> <ul> <li><strong>Code:</strong> <a href="https://github.com/PMF57/BCQM_III">https://github.com/PMF57/BCQM_III</a></li> <li><strong>Archived code and figure-generation scripts: </strong>10.5281/zenodo.17632820This paper is part of an ongoing series on BCQM:</li> </ul> <ul> <li><strong>BCQM I – Foundations and collapse horizon:</strong> 10.5281/zenodo.17191306</li> <li><strong>Analytical Proofs for BCQM:</strong> 10.5281/zenodo.17242311</li> <li><strong>BCQM II – From quantum events to spacetime:</strong> 10.5281/zenodo.17398294</li> <li><strong>BCQM Primitives – hop-bounded selection rule:</strong> 10.5281/zenodo.17495038</li> </ul> <p>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.</p>