https://osf.io/7cbsu/files/osfstorage/68c7ea06f7cafda5c11e44d1

Toward Operational Objectivity and Macro Additivity: Four Testable Predictions from Self-Referential Observers and Collapse Without Alignment

Abstract

We formulate four falsifiable predictions that operationalize two complementary frameworks: (i) self-referential observers—adaptive, memory-writing processes within standard quantum dynamics that yield internal collapse and cross-observer agreement under commuting readouts and shared records; and (ii) Collapse Without Alignment (CWA)—a macro-level principle explaining additive, phase-insensitive stability of observables under coarse-graining. The first two predictions quantify how redundant environmental records drive order-independent agreement (AB-fixedness) and suppress measurement-order effects; the third isolates a measurable penalty of self-referential latching; the fourth gives a phase-insensitive variance law for macroscopic aggregates. Each claim is paired with a feasible experiment (photons/ions/superconducting qubits). Together they provide a concise, testable “on-table” core for unifying discussions of objectivity and classical emergence within standard quantum theory.

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1. Set-up and definitions

We model measurements by instruments with effects $\{E_a\}$ and $\{F_b\}$. When these commute on the same pointer record, a joint observable $\{G_{ab}=E_aF_b\}$ exists, supplying an order-independent outcome structure. In the presence of redundant environment records (spectrum-broadcast-like structure), independent observers sampling disjoint fragments agree with probability approaching 1—AB-fixedness—without appealing to an absolute time order. These statements are formalized in Self-Referential Observers in Quantum Dynamics (SRO).
At the macro level, Collapse Without Alignment (CWA) posits that coarse-graining over large, misaligned micro-degrees of freedom yields additive, phase-insensitive observables with simple scaling laws.

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2. Predictions

P1 — Redundancy threshold for objectivity (AB-fixedness)

Claim. If a system’s pointer value $j$ is imprinted into $R$ disjoint environment fragments, the disagreement probability for two independent observers (who sample disjoint fragments) obeys an exponential bound

P_disagree ≤ exp(−2 κ · [R − R_*]_+), with κ ≔ −ln χ, 

where $\chi:=\max_{j\neq j'}\min_k \mathrm{Tr}\!\big(\sqrt{\rho^{(k)}_{j}}\sqrt{\rho^{(k)}_{j'}}\big)$ quantifies worst-case fragment overlap, and R_* ≔ ln(1/δ) / (2 κ) is the redundancy needed to push disagreement below $\delta$. This pins a numerical threshold to AB-fixedness predicted by SRO’s record-based objectivity.

Experiment. Cavity-QED or trapped-ion “scattering camera”: vary the number of scattered photons $R$ encoding the pointer; two detectors harvest disjoint photon sets and report $j$. The predicted knee at R_* and exponential falloff beyond it provide a sharp test.

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P2 — Order sensitivity bounded by non-commutation; suppressed by redundancy

Claim. Let $\Delta_{\mathrm{order}}:=\mathrm{TVD}(P_{A\to B},P_{B\to A})$ be the total-variation distance between outcome distributions for two sequential measurement orders. Then

$$\Delta_{\mathrm{order}} \;\le\; C \cdot \max_{a,b}\,\|[E_a,F_b]\|_\ast ,$$

for an instrument-dependent constant $C$ and a suitable operator norm. Moreover, if a redundant pointer record of size $R$ exists, then

$$\Delta_{\mathrm{order}} \;\lesssim\; C\,\max_{a,b}\|[E_a,F_b]\|_\ast \, e^{-\kappa R},$$

so order effects vanish exponentially with redundancy—quantifying SRO’s order-independence for commuting, recorded observables.

Experiment. Weak-measurement sequences on a single qubit with tunable basis angle (controls $[E,F]$); add a controllable photon bath to scale $R$. Measure $\Delta_{\mathrm{order}}$ vs. angle and $R$.

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P3 — Self-referential latching induces a measurable dephasing gap

Claim. Consider two nominally identical instruments acting on $S$. The latching instrument writes its outcome to an internal memory $M$ and conditions subsequent control (a “tick”), whereas the control instrument discards the readout. For a later incompatible probe after delay $\Delta t$,

$$\gamma_{\text{latch}}(\Delta t) \;\ge\; \gamma_{\text{nolatch}}(\Delta t) \;+\; \eta\, I(S\!:\!M)_{\text{tick}},$$

with device-dependent $\eta>0$ and mutual information $I(S\!:\!M)$ generated at the tick. The inequality operationalizes internal collapse (delta-certainty/latching) as a physically measurable backaction cost.

Experiment. Superconducting qubits: duplicate a readout chain; in one branch, the FPGA logs the bit and applies a conditioned Hamiltonian nudge; in the other, discard the bit. Compare Ramsey/echo visibility or process-matrix distances to estimate the gap vs. recorded information.

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P4 — CWA macro-additivity: phase-insensitive variance scaling

Claim. For a macroscopic observable $M=\sum_{i=1}^{N} X_i$ built from many pointer records with effective redundancy $R_{\mathrm{eff}}$,

$$\mathrm{Var}(M) \;=\; \frac{\sigma_0^2}{R_{\mathrm{eff}}} \;+\; o(1/R_{\mathrm{eff}}),$$

independent of microscopic phase relations among constituents; randomizing micro-phases changes $M$’s law only at $O(1/\sqrt{N R_{\mathrm{eff}}})$. This is a laboratory-checkable scaling law for CWA’s “macro coherence without micro alignment.”

Experiment. Photonic many-mode interferometer or cold-atom platform: hold single-body marginals fixed, scramble phases, tune redundancy by controlled copying to ancilla modes, and read the aggregate $M$. Verify $1/R_{\mathrm{eff}}$ variance scaling and phase insensitivity.

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3. Significance

P1–P2 convert SRO’s qualitative objectivity into quantitative laws (redundancy thresholds and order-suppression exponents) inside standard quantum mechanics. P3 isolates a distinctive signature of self-referential memory writes, linking “internal collapse” to an experimentally accessible dephasing penalty. P4 supplies a universal macro scaling that, if confirmed across platforms, would anchor CWA as a physics-grade law of classical stability. Together, these predictions delineate a compact, interoperable framework that different interpretational camps can test and adopt without leaving the standard formalism.

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Acknowledgments

Concepts of internal collapse/AB-fixedness and redundancy-based objectivity are developed in Self-Referential Observers in Quantum Dynamics; macro-additivity and phase-insensitive stability arise from Collapse Without Alignment from https://osf.io/7cbsu/files/osfstorage 

 

 

 © 2025 Danny Yeung. All rights reserved. 版权所有 不得转载

 

Disclaimer

This book is the product of a collaboration between the author and OpenAI's GPT-5 language model. While every effort has been made to ensure accuracy, clarity, and insight, the content is generated with the assistance of artificial intelligence and may contain factual, interpretive, or mathematical errors. Readers are encouraged to approach the ideas with critical thinking and to consult primary scientific literature where appropriate.

This work is speculative, interdisciplinary, and exploratory in nature. It bridges metaphysics, physics, and organizational theory to propose a novel conceptual framework—not a definitive scientific theory. As such, it invites dialogue, challenge, and refinement.

I am merely a midwife of knowledge.