Breaks and Self-Reference: The Origin of Self-Reference in Quantum Mechanics

wangchao

David Hestenes

José Caetano de Mattos

Formally resolves the infinite regress of the von Neumann measurement chain under the Type III₁ algebraic boundary framework. Combines Quantum Reference Frame (QRF) transformations with the IRM theorem under Algebraic Quantum Mechanics. Proves the chain terminates at the first open system satisfying the Absolute Self-Origination (ASO) condition — a Self-Originating Observer whose internal reference algebra constitutes a Type III₁ von Neumann factor stabilised by a continuous active feedback loop. Resolves the Wigner's Friend paradox, preferred basis problem, and reality problem. Derives a doubly-falsifiable spectroscopic prediction: defective non-Hermitian Exceptional Point at critical coupling g_c=γ/2, producing t·exp(−γt) decay envelope testable in linear Paul traps.

Mark S Swanson

Han Qin

Full bilingual text and framework available at self-as-an-end.net The Born rule — that the probability of a measurement outcome is given by the modulus squared of the quantum state — is introduced as a postulate in standard quantum mechanics and confirmed by experiment to very high precision, yet the origin of its modulus-squared form has long been a central question in the foundations of quantum mechanics. The major approaches locate this origin in the mathematical uniqueness of Hilbert space (Gleason), the decision-theoretic norms of a rational agent (Deutsch–Wallace), the symmetry of system–environment entanglement (Zurek's envariance), subjective belief (QBism), or hidden variables (Bohmian mechanics). This paper gives an ontological origin for the modulus-squared readout within the Self-as-an-End (SAE) framework. The central claim: the modulus squared is the one-sided reading of a pre-closure state that lies below the causal slot, takes the uncertainty-wave form, and is simultaneously subject to time arrows on both sides — and is therefore without causality. In this region the time arrow and causality are distinct: the time arrow exists at every scale (the quantum evolves forward in our frame, the dynamical layer), whereas causality is the influence of a single-direction time arrow. Above the causal slot the state is subject only to single-direction influence, so causality holds and the outcome is definite; below the causal slot it is subject simultaneously to the our-frame and opposite-frame bidirectional time arrows (two faces of one dual-4DD structure, per Cosmo V), so no single direction can fix causation and there is no causality. A one-sided reading therefore cannot read off pre-written definite content, and presents as a probability distribution (degenerating to a definite P=1 readout for an eigenstate). At the amplitude layer this manifests as the conjugate pairing of dual orientations, ψ♯ψ = A² — the modulus squared. The paper works at three commitment levels: T1 (Gleason-type mathematical uniqueness, taken over externally), T2 (a strong structural derivation of the quadratic readout, the core contribution — not a full Gleason-equivalent theorem), and T3 (an ontological mechanism picture, offered as a candidate). It answers why the both-sided reading is multiplicative rather than additive: reciprocity prescribes that one side close with its dual in the native algebra of the object read — a scalar density closes additively (Λ₁+Λ₂=0), a complex phase carrier multiplicatively (ψ♯ψ=A²); the two substrates are isomorphic (both θ+θ♯=0), the microscopic one wearing one coat of exponential dualization. On this basis it places Born randomness (no pre-written content; weights from dual-orientation pairing), demarcates SAE from Gleason, Many-Worlds (via a causality firewall), QBism, and Bohmian mechanics, and interfaces with P4's cross-ladder readout, P5's Tsirelson bound, and no-signaling marginals. Whether the Born rule is modified in the strong-field regime is marked as an open problem. 玻恩规则——测量结果的概率由量子态的模平方给出——在标准量子力学中作为公设引入,由实验以极高精度确认,但其模平方形式的来源长期是量子力学基础的核心议题。主流进路分别把这一来源放在 Hilbert 空间的数学唯一性(Gleason)、理性主体的决策规范(Deutsch–Wallace)、系统-环境纠缠的对称性(Zurek 的 envariance)、主观信念(QBism)或隐变量(Bohmian)之上。 本文在 SAE(Self-as-an-End)框架内,为模平方这一读出形式给出一个本体来源。核心论点是:模平方是因果槽以下、测不准波形态、同时受双侧时间箭头影响、因而无因果律的闭合前态的单侧读数。在此区域,时间箭头与因果律是两件不同的事:时间箭头在任何尺度都存在(量子在本侧沿时间箭头正常向前演化,动力学层),而因果律的本体内容是单向时间箭头的影响。因果槽以上只受本侧单向影响,故有因果律、呈现确定;因果槽以下同时受 our frame 与 opposite frame 双向时间箭头影响(二者同为同一 dual-4DD 结构的两面,Cosmo V 既立),无单一方向可定因果,故无因果律。正因量子同时受双侧影响、无因果律可定向,单侧读出读不到预先写就的确定局部内容,而呈现为概率分布(若已是某测量的本征态,则退化为 P=1 的确定读出)。在振幅层,这表现为对偶取向的共轭配对 ψ♯ψ = A²,即模平方。 本文区分三层强度:T1(Gleason 类数学唯一性,外部承接)、T2(二次型读出的强结构推导,核心交付——非 Gleason 等价完整定理)、T3(本体机制图像,作为候选)。本文回答了为何双侧读出取乘性而非加性:互易规定一侧须与其对偶在被读对象的原生代数中闭合——标量密度加性闭合(Λ₁+Λ₂=0),复相位载体乘性闭合(ψ♯ψ=A²);两层底座同型(皆 θ+θ♯=0),微观层只多一层指数对偶化。据此本文给出玻恩随机性的定位(无预写内容,权重由对偶取向配对给出),划定 SAE 与 Gleason、Many-Worlds(以因果律防火墙)、QBism、Bohmian 的关系,并接合 P4 跨阶梯读出、P5 Tsirelson 上界与无信号边缘分布。强场下玻恩规则是否有修正,标记为开放问题。 Related identifiers (Related/alternate identifiers) All "is referenced by / references" relations to established SAE works. Use relation type references (this paper references them); for the QM-series siblings, isPartOf the series is also appropriate where Zenodo supports it. Relation Identifier (DOI) Resource references 10.5281/zenodo.20277037 QM P2 references 10.5281/zenodo.20340595 QM P3 references 10.5281/zenodo.20369138 QM P4 (Tunneling) references 10.5281/zenodo.20455398 QM P5 references 10.5281/zenodo.19361950 Physics Foundation (cross-layer closure) references 10.5281/zenodo.19341043 Four Forces Prequel references 10.5281/zenodo.19464447 Four Forces Finale references 10.5281/zenodo.19245267 Cosmo I (cosmological constant) references 10.5281/zenodo.19329771 Cosmo V (dual-frame Ġ/G) references 10.5281/zenodo.19836185 Relativity P1 (time dilation) references 10.5281/zenodo.19910546 Relativity P2 (motion/gravity unification) references 10.5281/zenodo.19740020 Information Theory P1 (4DD ontology) references 10.5281/zenodo.19880112 Information Theory P4 (black-hole information) references 10.5281/zenodo.19510868 Mass Series Convergence (E/c³) (External standard references — Born 1926, Gleason 1957, Busch 2003, Deutsch 1999, Wallace 2012, Zurek 2005, Fuchs–Mermin–Schack 2014, Bohm 1952, Dürr–Goldstein–Zanghì 1992, Tsirelson 1980, Popescu–Rohrlich 1994 — are listed in the paper's reference section; they need not all be entered as Zenodo related identifiers, though DOIs may be added if desired.)

Eiji Konishi

We propose a mechanism for system-induced spontaneous time reparametrization symmetry breaking in canonical gravity. We consider a model of extended canonical gravity, based on Sen's spinorial expression of the spatial-diffeomorphism-gauge independent part of the shift vector, with one additional long-range self-interacting massive spin-$1/2$ particle whose spin is coupled to Sen's spinor in the Hamiltonian. This additional particle plays the role of creating the system-induced time reparametrization invariant potential. We use this potential to break time reparametrization symmetry spontaneously. We identify the symmetry breaking with the origin of the quantum energy measurement processes in the ensemble interpretation of quantum mechanics. Our theory uses a novel interpretation of quantum mechanics with respect to quantum mechanical position uncertainties of particles. The spatial-diffeomorphism-gauge independent part of the shift vector is attributed to this novel interpretation of quantum mechanics.