A Six-Birds' Eye View of Quantum Theory: Defining Objects by What We Can Distinguish, Not What We Imagine
Year: 2026
Type: preprint
Abstract: Summary Quantum theory uses a single object, the quantum state, for two different jobs: describing how a system evolves and keeping track of what has been recorded about it. This paper keeps the two jobs apart. Using the packaging language of Six Birds Theory (SBT), a closure-based emergence calculus, physical evolution is modelled by one map and record formation by another: a packaging map that keeps only the distinctions a chosen record interface can hold. Packaging twice changes nothing, and the states that packaging leaves unchanged are the objects of the descriptive layer. Key results Pinching as packaging (Lean 4): pinching in a record basis is idempotent, trace preserving and completely positive; full dephasing fixes exactly the diagonal states, while pinching only an apparatus register fixes block-diagonal states, so coherence can survive in unmeasured registers. Layers and dynamics (Lean 4): the Leibniz quotient behind a descriptive layer, the exact condition under which substrate dynamics passes to that layer, and the identification of the quotient by equal packaged values with the fixed points of an idempotent packaging map. Packaging versus dynamics: packaging commutes with evolution diagonal in the record basis and generally fails to commute with generic Hamiltonian evolution; for two qubit record bases the route mismatch is computed in closed form. Double slit and quantum eraser: with equal path envelopes, fringe visibility equals the magnitude of the overlap between the which-path records; an eraser recovers complementary fringes only in subensembles conditioned on a marker outcome. Measurement and the cat: in a system–apparatus–environment model the global state stays pure while the record-level description is a classical mixture over pointer values. Contextuality: order dependence of dephasing channels is separated from contextuality, and the Peres–Mermin obstruction to a context-independent, product-preserving value assignment is mechanized. Classical analogue: a metastable Markov chain shows staged objecthood, and why near-idempotence alone does not certify persistent coarse objects. The framework does not derive the Born rule, select a single outcome, or resolve Bell's theorem; it gives a precise and checkable way to say which distinctions belong to which descriptive layer. Mechanized proofs and reproducibility All mechanized statements build in Lean 4 against mathlib, with an axiom audit confirming that they use only Lean's standard foundations. All numerical results and figures are generated deterministically by the accompanying Python package: python -m sbtq.run_all --seed 0 --out artifacts python -m pytest -q cd lean/Sbtq && lake build
Author: Tsiokos, Ioannis
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128615949
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