Instancology as a Foundational Framework for Quantum Mechanics

0) One-paragraph abstract

We propose a 2×2 instancological ontology (AA, RA, AR, RR) that cleanly separates timeless wholeness from time-bound parts, mapping the quantum wavefunction to the Micro World (AA/RA) and measurement/outcomes to the Macro World (AR/RR). Collapse becomes an issuance (rebirth) event: an AR→RR transition under wholeness control. This yields crisp accounts of nonlocality, contextuality, and decoherence, suggests where the Born rule lives, and motivates testable constraints on decoherence rates and correlation structures.

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1) Introduction & motivation

The two gaps in QM: ontological clarity and interpretational unity.

Why previous interpretations stall: they mix layers (law/object/observer) in one plane.

Instancology’s promise: a minimal ontology that respects wholeness vs. parts and absolute vs. relative.

Thesis. QM formalism describes RA-level lawful structure of a Micro-World instance; outcomes live in RR via AR→RR issuance events governed by AA/RA.

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2) Primer on Instancology (for physicists)

2.1 The 2×2 core

AA (Absolute-Absolute): issuing source; timeless; non-empirical.

RA (Relatively-Absolute): invariant laws, logic, math (structures).

AR (Absolutely-Relative): concrete-yet-contexted states ready to issue.

RR (Relatively-Relative): situated, macroscopic, measured outcomes.

2.2 Micro vs. Macro: Micro is timeless/whole; Macro is time-sequenced/parts.

2.3 Necessity (wholeness) vs. Contingency (parts).

2.4 Rebirth Principle (重生): issuance of a fresh state-instance.

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3) Mapping QM objects into the 2×2

3.1 Wavefunction ψ

Lives as a Micro-World object: (AA-anchored, RA-structured); unitary evolution expresses RA necessity.

3.2 Hilbert space & operators

RA: the lawful geometry (inner product, spectrum, commutators).

3.3 Quantum states before measurement

AR: context-latched, issuance-ready instantiations of ψ relative to an experimental arrangement.

3.4 Outcomes / records / classical apparatus

RR: macroscopic, time-embedded results; decohered, selectable, copyable.

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4) Measurement as issuance (AR→RR)

4.1 Replace “collapse” with issuance: a wholeness-governed selection from AR into RR.

4.2 CPTP maps as the math of issuance: instrument maps  encode AR→RR channels.

4.3 Decoherence reinterpreted: RA constraints + environment coupling create RR-compatible branches; issuance is the selection of one RR record.

4.4 Wigner’s Friend clarified: friend’s RR is local issuance; external observer’s AR remains unissued until interaction—no contradiction across layers.

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5) Nonlocality, contextuality, and necessity

5.1 Bell nonlocality: violations express wholeness constraints (necessity) at Micro level; parts’ contingencies cannot screen them off.

5.2 Kochen–Specker contextuality: “no joint assignment” = RR cannot pre-encode necessity; context lives in AR.

5.3 Entanglement: a measure of “wholeness binding” strength; predicts structure of allowed correlations without signaling.

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6) Time and the Micro/Macro split

6.1 Unitary evolution is timeless law (RA); “time” is a Macro bookkeeping for RR sequences.

6.2 Links to Page–Wootters/relational time: clocks are RR devices; Micro doesn’t “flow.”

6.3 Why interference disappears in RR: issuance aligns with RR’s directed temporal ordering.

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7) Towards the Born rule

7.1 Symmetry-necessity route: amplitudes encode RA-level symmetries; probabilities emerge as RR frequencies of issuance under wholeness constraints.

7.2 Candidate derivation sketch: Gleason-type + issuance minimality (no extra RR structure) → .

7.3 Testable edge cases: contexts where issuance constraints slightly bias decoherence paths (see §10).

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8) Relation to major interpretations

8.1 Copenhagen: keeps the AR/RR split but lacks AA/RA grounding; issuance clarifies “cut.”

8.2 Many-Worlds: treats all AR branches as equally RR-real; Instancology keeps them AR-real until issuance.

8.3 Bohmian: pilot law fits RA necessity; particle configuration is RR; issuance explains “effective collapse.”

8.4 QBism/ψ-epistemic: personalist update rules live in RR; Instancology keeps ψ ontic in Micro (AA/RA).

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9) Formal core (axioms)

A1 (Layer Axiom): Every physical description decomposes into (AA, RA, AR, RR) roles.

A2 (Law Priority): RA constrains AR; AR cannot violate RA.

A3 (Issuance): RR facts arise only via issuance maps from AR under RA constraints.

A4 (Wholeness Constraint): Correlations in AR may violate classical separability; RR cannot signal faster-than-light.

A5 (Minimality): No RR-level hidden variables that overrule RA symmetries.

Math anchors:

States:  (RA structure), contexts: POVMs  (AR); issuance: instrument maps  with  CPTP (AR→RR); outcomes  (RR).

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10) Predictions & falsifiable consequences

P1 Wholeness-weighted decoherence: In multipartite systems with structurally “strong” entanglement (graph/connectivity measures), decoherence rates exhibit context-dependent plateaus not captured by standard local bath models.

Test: superconducting qubits with tunable couplers; compare non-Markovian revivals vs. bath-matched simulations.

P2 Issuance bias under symmetry breaking: Slight asymmetries in RA constraints (e.g., engineered Hamiltonian anisotropies) produce measurable skews in outcome frequencies before full decoherence completion.

Test: photonic interferometers with controlled loss/phase disorder; pre-decoherence sampling.

P3 Context-gated nonlocal revivals: Post-selection on AR-context can restore interference in “which-path” experiments beyond standard quantum eraser envelopes.

Test: delayed-choice erasers with adaptive POVMs; look for enhanced fringe visibility bounds.

P4 No superluminal signaling (strong form): Any protocol claiming signaling via entanglement across issuance boundaries must fail; provides crisp falsifier.

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11) Experimental programs

11.1 Superconducting circuits: multi-qubit entanglement graphs; tomography of issuance maps via gate-set tomography + fast mid-circuit measurement.

11.2 Photonics: high-dimensional entanglement; adaptive POVMs implementing AR context changes on the fly.

11.3 Optomechanics: mesoscopic “cat” states; measure issuance thresholds vs. mass/temperature.

11.4 Atomic arrays/Rydberg: tunable interaction graphs to probe wholeness-weighted decoherence.

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12) Interface with QFT and gravity

**12.1 QFT fields as RA structures; Fock states as AR instantiations.

12.2 Particle detection (RR) = issuance at detectors.

12.3 Semiclassical gravity: RR stress-energy arises after issuance; suggests where “objective collapse” proposals should (not) appear.

12.4 Timeless Micro suggests compatibility with constraint-quantization and path-integral formulations.

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13) Objections & replies

O1 “Isn’t issuance just collapse?”

Reply: It is collapse with a layered ontology that removes the paradox of where/when by definition of AR→RR.

O2 “Hidden variables?”

Reply: No RR hidden variables; micro-wholeness lives in AR/RA and respects no-signaling.

O3 “Empirical distinction?”

Reply: Yes—§10 predictions target pre-decoherence statistics and non-Markovian structure.

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14) Roadmap & deliverables

Formal theorems: (i) No-signaling from issuance; (ii) Born rule from issuance minimality + Gleason; (iii) Context composition laws for instruments.

Open problems: uniqueness of issuance maps; quantitative wholeness measure; link to quantum Darwinism.

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15) Glossary (for cross-discipline readers)

Issuance (Rebirth): AR→RR mapping yielding a recorded outcome.

Wholeness constraint: Nonseparable structure governing multipartite AR states.

Micro/Macro: Timeless RA/AR vs. time-ordered RR.

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16) Appendix sketches

A.1 Instrument formalism worked example (Mach–Zehnder with which-path & eraser).

A.2 Toy model of wholeness-weighted decoherence (spin-bath with graph-coupled system).

A.3 Born-rule derivation outline (Gleason + issuance minimality).