BCQM keeps all the successful predictions of standard quantum mechanics while reframing how outcomes arise. It treats quantum experiments as boundary-condition problems and introduces the operational “horizon”  W that bounds when coherence can persist. The goal is clarity, testability, and a clean bridge from quantum events to inertial motion and spacetime structure.

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In one paragraph

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In BCQM, the q-wave is the probability structure only—not a physical substance. It guides possibilities, while the particle carries conserved quantities and appears at an outcome. Outcomes are selected stochastically, weighted by the q-wave’s amplitudes (Born-rule emerges from t  t  ). The operational  finite W-horizon that limits how long coherence can persist, until an irreversible record is made. With these ingredients, BCQM preserves no-signalling and standard quantum statistics, but makes where the randomness enters—and when coherence is possible—transparent and testable.

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Why this matters

 

• Measurement without mystique: BCQM pinpoints the stage at which randomness is realised and how records make outcomes irreversible.

• Built-in tests: A finite W implies concrete laboratory signatures (e.g., a temperature-independent floor to dephasing, sharp recoverability thresholds in eraser/echo-type setups).

• From events to spacetime: By modelling physical processes as growth of stochastic event chains bounded by the W horizon, BCQM outlines a route to emergent inertia and, longer-term, to gravity and spacetime structure.​

 

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Key ideas at a glance

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• Q-wave (probability structure): Encodes possibilities and their weights. It does not carry energy or momentum.

• Particle (physical carrier): Carries conserved quantities; it is what is detected.

• Stochastic outcome selection: Exactly one channel is realised, randomly, with Born-rule weighting.

• W-horizon (coherence horizon): A finite, operational bound on how long coherence can persist—even at very low temperature.

• Compatibility: Designed to respect no-signalling and to reproduce standard quantum predictions in their tested domains.

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What’s available here

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This site is the home for my Boundary-Condition Quantum Mechanics (BCQM) project. From here you can access:

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• BCQM I – Foundations and collapse horizon

The core interpretation: q-waves as propensity fields, a finite coherence horizon W   ,  and collapse as absorption of the q-wave.

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• Analytical Notes / Proofs

The operator-theoretic backbone for BCQM I–III: probability law, no-signalling checks, and the t  t  pairing that underpins the Born rule.

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• BCQM II – From quantum events to spacetime

Events and their links form a stochastic causal graph; smooth spacetime and light-cone structure appear as coarse-grained limits.

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• BCQM III – Stochastic event chains and emergent inertia

A concrete graph-growth algorithm (Algorithm 1) plus simulations. Classical inertial motion emerges statistically, with an effective mass scaling m     proportional to  W     .

The full simulation and figure-generation code is openly available and archived with a DOI.

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• BCQM IV – Inertial noise and entangled clusters

Uses the BCQM III event-chain engine to define an intrinsic “inertial noise” spectrum associated with a finite coherence horizon W     , and introduces entangled clusters as configuration-space primitives. Shows how inertial mass and noise are linked in the BCQM picture, sketches a universality class for inertial-noise spectra, and sets up the questions that the numerical companion paper IV_b tackles.

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• BCQM IV_b – Baseline inertial-noise spectra from a control model

​A numerical companion to BCQM IV. Develops a simple, W   -  blind control kernel (“bcqm_toy_3”) and a basic cluster toy to test the inertial-noise pipeline. Demonstrates that the single-thread control model has no spurious W    -scaling (β ≈ 0), that independent-probe clusters give the expected centre-of-mass noise suppression proportional to  N      , and maps the dimensionless spectra into SI units for illustrative experimental benchmarks.

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• BCQM IV_c – Diffusive inertia and the limits of binary hop kernels

Explores a single primitive event thread with a “soft–rudder” binary hop kernel and shows that, for natural coherence–horizon–dependent slip laws, the inertial–noise amplitude scales as A(W_coh) proportional to W_coh^{-1/2}. This establishes a robust diffusive floor for isolated threads and motivates the move to multi–thread bundles in later BCQM papers.

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• BCQM IV_d – Lockstep bundles and the glue-axis “sweet spot”

Extends IV_c from single threads to multi-thread bundles and introduces the four glue axes (shared bias, phase-lock, domains, cadence disorder) as the minimal mechanism set for bundle stiffening. Shows how coherent “lockstep” can form hierarchies (dominant background bundles plus smaller coherent sub-bundles) and maps where centre-of-mass behaviour becomes markedly stiffer than the diffusive single-thread floor. Establishes the practical scan protocol and diagnostics that later feed directly into the emergent-spacetime interpretation in BCQM V.

 

• BCQM V – Emergent spacetime from lockstep bundles

A conceptual and numerical synthesis: the dominant lockstep bundles act as spacetime candidates (providing an operational “clock” and a stable background), while smaller coherent bundles behave as matter-like / clock-like structures embedded within that background. Uses glue-axis scans to show a two-step emergence pattern (connectivity first, coherent islands later) and motivates the “lockstep hierarchy” picture as an elegant single mechanism for both spacetime and matter-like organisation. 

 

• BCQM VI – Dynamic islands and ball-growth geometry in Path-A cross-linked bundles (Stage-1)

Moves beyond static snapshots by adding time-resolved (binned) diagnostics and a referee-grade ablation suite. Demonstrates that connectivity (“space on”) can percolate under Path-A cross-links even when clock coherence collapses (glue-off), confirming separability of space-connectivity and temporal coherence at Stage-1. Shows that “spacetime islands” are dynamic and threshold-sensitive (“space stays on while islands fluctuate”) and replaces unstable return-probability dimension fits on the short active slice with ball-growth as the robust geometry diagnostic (“channels + shortcuts” tightening with cross-link pressure). 

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• BCQM Primitives note​

A compact statement of the minimal ingredients: events, directed edges, complex amplitudes, and a hop-bounded realisation rule. This underlies the growth model used in BCQM III.

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Each item is hosted on Zenodo with a DOI and, where relevant, companion code on GitHub. This site simply gathers them in one place and gives a short guide to how they fit together.

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(Download the PDFs below.)​​

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Roadmap (what’s next)​

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BCQM VII – Stage-2 emergent spacetime: “cloth” geometry beyond the active slice

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Stage-1 (BCQM VI) shows that connectivity can be persistently “on” while coherent spacetime-islands fluctuate, and that ball-growth is the robust geometry diagnostic on the short active slice. Stage-2 will define a persistent background geometry object (“cloth”) built from long-run structure (e.g. epoch unions and stability/backbone filters) and test whether metric- and dimension-like behaviour becomes well-posed on that stable substrate. The emphasis is on reproducible diagnostics, ablations, and finite-size scaling, not on assuming a manifold.

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BCQM VIII – Emergent gravity: stochastic lensing and large-scale structure

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Once a stable cloth geometry is established, extend the event-graph picture to many interacting threads at scale. The aim is to see how effective gravitational behaviour and lensing could arise as statistical patterns in the web of quantum events, and what kind of spacetime “noise” that would imply observationally. This stage will focus on falsifiable signatures (e.g. lensing statistics, coherence-dependent structure growth, and noise spectra).

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Ongoing work​

 

• Refining primitives and growth rules and packaging them into reproducible code libraries (versioned releases with selftests and pipelines).

• Companion notes on process ontology and interpretation, clarifying how BCQM sits alongside standard quantum mechanics rather than replacing it.

• Incremental updates to published papers as the series develops (all versioned and tracked via DOIs).

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Broad direction

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Foundations → event graph → inertia → inertial noise → lockstep bundles → cross-links and dynamic islands → cloth geometry → emergent gravity.

As each stage is written up and released, it will be linked here.

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Quick FAQ

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Does BCQM change the predictions of quantum mechanics?

Not in ordinary regimes. It preserves observed quantum statistics while putting sharper, testable structure around when coherence can persist or be restored.

 

Is the q-wave “real”?

In BCQM the q-wave is probabilities only. The particle alone carries energy, momentum, and charge, and appears at the realised outcome.

 

How is this falsifiable?

A finite W (coherence horizon) implies measurable effects: a minimal, temperature-independent dephasing floor and threshold-like recoverability in interference-restoration experiments. If high-precision experiments rule out these signatures across relevant systems, BCQM would be constrained or falsified.

 

Is this Bohmian/pilot-wave?

No. BCQM does not posit a guiding physical wave that pushes particles. It treats quantum evolution as boundary-condition dynamics on possibilities, with outcomes selected stochastically under operational horizon W.​​

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How to use this site

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• Read the papers: Start with BCQM I, then BCQM II for the path from events to spacetime.

• Skim the proofs: Dip into the companion analytical notes for technical details.

• Follow progress: Check back for updates as Papers III–V are released.

 

 

​A note on style and scope

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BCQM aims to be clear, disciplined, and testable. It avoids unnecessary metaphysics and keeps close to experiment: horizon W is operational, defined by what can and cannot be done in the lab. The programme’s long-term aim is a coherent picture where quantum events, inertia, and gravity arise from the same underlying boundary-condition logic.

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