QM ↔ RT

Quantum mechanics / Registration Theory equivalence ledger

Established quantum mechanics is the constraint. This ledger asks whether Registration Theory can reconstruct the same physical content from a smaller ontological vocabulary, and records any mismatch that requires correction.

Governing rule: preserve the quantum result; revise the RT framing when they diverge.

The goal is ontological reduction and clarification, not replacement of successful quantum principles.

Entry 1ontological correspondence

Position–momentum uncertainty

Quantum mechanics

Position and momentum are canonically conjugate. Standard quantum mechanics gives [x,p] = iħ and therefore Δx Δp ≥ ħ/2.

Registration Theory ontology

Candidate RT bridge: space-facing registration supports propagation, extension, and spatial exchange, while time-facing registration supports retention, persistence, and localized re-identifiability. Momentum is therefore a candidate downstream observable of propagation/exchange-dominant registration, and position a candidate downstream observable of retention/localization-dominant registration.

Equivalence requirement

RT must eventually recover the exact canonical quantum structure, not merely a qualitative tradeoff: [x,p] = iħ or an equivalent structure implying Δx Δp ≥ ħ/2.

Current RT status

The corpus supports the space-face / time-face distinction, the candidate identification of exchanged spatial-motion amplitude with pc, and host-relative coarse-graining. RT does not yet derive the canonical commutator or the ħ/2 lower bound.

Mismatch / correction target

If an RT derivation gives a different canonical relation in the experimentally validated quantum regime, the RT bridge or its interpretation must be revised.

RT sources

The Canonical Foundations of Registration Theory A Candidate Relativistic Brokerage Law in Registration Theory The Emerging Mathematics of Registration Theory

Entry 2ontological correspondence

Measurement / outcome registration

Quantum mechanics

Laboratory quantum mechanics yields definite recorded outcomes at the effective measurement level, with outcome probabilities fixed by the quantum state and measurement context.

Registration Theory ontology

Candidate RT bridge: propagation-dominant coherent registration → consequence-bearing interaction → retained persistent registration. The interaction is treated as an energy-facing transformation that makes a distinction consequential to a host; the resulting record is time-facing in the RT sense because it persists and constrains later registration.

Equivalence requirement

RT must reproduce standard quantum measurement statistics and all experimentally validated interference and decoherence behavior. Its ontology cannot alter the successful quantum predictions.

Current RT status

RT has exact consequence, retention, bilateral-registration, and detector-architecture results in finite models, but it does not yet derive the complete quantum measurement map from primitive RT.

Mismatch / correction target

RT must keep decoherence, outcome selection, amplification, and thermodynamic record formation distinct unless a derivation shows that they reduce to one registration process.

RT sources

Closed-Event Consequence Completeness in Registration Theory Bilateral Participatory Registration in Canonical ACRF-4 Hosting versus Deriving the Born Rule in Registration Theory The Emerging Mathematics of Registration Theory

Entry 3interpretive correspondence

Decoherence and persistent record formation

Quantum mechanics

Environmental entanglement suppresses observable interference between components in an effective preferred basis and yields reduced-state decoherence for the subsystem.

Registration Theory ontology

RT interprets this through host-relative accessibility and persistence: interaction redistributes consequence into a larger registration environment; distinctions inaccessible to the host are removed by effective coarse-graining; a surviving stable equivalence class becomes a persistent record.

Equivalence requirement

RT must reproduce the same reduced-state phenomenology, interference suppression, and basis dependence obtained from standard quantum decoherence theory.

Current RT status

The coarse-graining and persistence framework exists, but RT has not yet derived the standard decoherence functional or reduced density-matrix dynamics from primitive registration dynamics.

Mismatch / correction target

RT must not identify decoherence by itself with unique outcome selection unless a later theorem establishes that additional step.

RT sources

Persistent Individuation and the Physical Preconditions of Mathematical Representation The Emerging Mathematics of Registration Theory

Next principles to audit

Superposition, interference, entanglement, indistinguishability, spin, phase, tunneling, complementarity, Born probabilities, contextuality, Bell correlations, and quantum statistics will be added one by one as their RT correspondence is examined.