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The Born Rule as a Natural Transformation of Functors 玻恩定则作为函子的自然变换
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-20 DOI: 10.1007/s10701-026-00918-w
Boyu Yang, James Fullwood
{"title":"The Born Rule as a Natural Transformation of Functors","authors":"Boyu Yang,&nbsp;James Fullwood","doi":"10.1007/s10701-026-00918-w","DOIUrl":"10.1007/s10701-026-00918-w","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a <i>natural transformation of functors</i>. In particular, we show that given a fixed quantum system <i>A</i>, there exists an explicit bijection from the set of density operators on the associated Hilbert space <span>(mathcal {H}_A)</span> to the set of natural transformations between the canonical measurement and probability functors associated with the system <i>A</i>, which formalize the way in which quantum effects (i.e., POVM elements) and their associated probabilities are additive with respect to a coarse-graining of measurements.</p>\u0000 </div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Extendible Spacetime Without Closed Timelike Curves Whose Every Extension Contains Closed Timelike Curves 一个没有封闭类时曲线的可扩展时空，其每一个扩展都包含封闭类时曲线
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-18 DOI: 10.1007/s10701-026-00914-0
H. Andréka, J. Madarász, J. Manchak, I. Németi, G. Székely
{"title":"An Extendible Spacetime Without Closed Timelike Curves Whose Every Extension Contains Closed Timelike Curves","authors":"H. Andréka,&nbsp;J. Madarász,&nbsp;J. Manchak,&nbsp;I. Németi,&nbsp;G. Székely","doi":"10.1007/s10701-026-00914-0","DOIUrl":"10.1007/s10701-026-00914-0","url":null,"abstract":"<div><p>By removing a fractal from time-rolled Minkowski spacetime, we construct an extendible spacetime without closed timelike curves whose every extension contains closed timelike curves. This settles a question posed by Geroch.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relational Information Towards a New Kind of Information in Quantum Mechanics 走向量子力学中一种新的信息——关系信息
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-07 DOI: 10.1007/s10701-026-00916-y
Niccolo Covoni, Marco Sanchioni
{"title":"Relational Information Towards a New Kind of Information in Quantum Mechanics","authors":"Niccolo Covoni,&nbsp;Marco Sanchioni","doi":"10.1007/s10701-026-00916-y","DOIUrl":"10.1007/s10701-026-00916-y","url":null,"abstract":"<div><p>This paper argues that von Neumann entropy plays two conceptually distinct roles in quantum theory. When applied to global mixed states, it expresses the quantum analogue of the informational entropy. But when applied to reduced states of entangled systems, it measures objective physical correlations. We propose that this second usage realizes a new informational <i>kind</i>, which we call <i>relational information</i>. Unlike information in communication theory, it reflects structural interdependence between systems, not probability about a certain outcome. We further suggest that this informational <i>kind</i> has ontological significance: relational information is a physically instantiated feature of entangled systems, and not merely an agent-relative concept.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Avoiding Sparseness in a Flash Ontology 避免Flash本体中的稀疏性
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-03 DOI: 10.1007/s10701-025-00908-4
Joe Coles
{"title":"Avoiding Sparseness in a Flash Ontology","authors":"Joe Coles","doi":"10.1007/s10701-025-00908-4","DOIUrl":"10.1007/s10701-025-00908-4","url":null,"abstract":"<div>\u0000 \u0000 <p>Collapse theories provide one of the main approaches to the quantum measurement problem. Roderich Tumulka’s collapse theory (GRWf) has attracted interest because it offers a relativistic collapse theory. GRWf utilises an ontology of flashes to accommodate EPR-Bell type non-local influences within a relativistic theory, an idea suggested by John Bell. Tim Maudlin raises a concern with Tumulka’s flash ontology, arguing that it is too sparse to convincingly account for certain microscopic phenomena. This paper proposes a modification to GRWf that addresses the problem of sparseness, whilst retaining a relativistic treatment of quantum non-locality. The proposal, referred to as the space-time normalisation interpretation (STN), combines the GRWf flash ontology with a statistical interpretation of the wavefunction. The statistical structure of the interpretation is presented as a Hawkes process, consisting of flashes and an intensity function governing their occurrence. For a single-particle system, the square modulus of a renormalised wavefunction serves as the intensity function of the Hawkes process.</p>\u0000 </div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Role of an Intrinsic Action Uncertainty in Classical Dynamics 论经典动力学中内在作用不确定性的作用
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-03 DOI: 10.1007/s10701-026-00911-3
Krishna Ramprasad
{"title":"On the Role of an Intrinsic Action Uncertainty in Classical Dynamics","authors":"Krishna Ramprasad","doi":"10.1007/s10701-026-00911-3","DOIUrl":"10.1007/s10701-026-00911-3","url":null,"abstract":"<div><p>We introduce a minimal, mathematically controlled modification of the classical action principle that embeds a small, divergence-free field <span>(f_mu (x))</span> into the Euler–Lagrange equations primarily through modifications in electrodynamics. This modification preserves locality, causality, and charge conservation while generating controlled, small deviations from standard classical trajectories, providing a unified, quantitative framework for mild classical indeterminism. The field <span>(f_mu)</span> is Lorentz-covariant and characterized by a physically motivated spectral density, ensuring consistency across particle, scalar, and gauge systems. To leading order, we derive corrected forces, compute ensemble-averaged trajectory shifts, and identify spectral signatures accessible to high-precision experiments such as Penning traps and cathode beams. With ultraviolet-regularized spectra, the predicted deviations lie within current experimental sensitivity, establishing a direct bridge between foundational theory and empirical testability.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithmic Idealism: What Should You Believe to Experience Next? 算法理想主义：接下来你应该相信什么？
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-02-03 DOI: 10.1007/s10701-026-00913-1
Markus P Müller
{"title":"Algorithmic Idealism: What Should You Believe to Experience Next?","authors":"Markus P Müller","doi":"10.1007/s10701-026-00913-1","DOIUrl":"10.1007/s10701-026-00913-1","url":null,"abstract":"<div><p>I argue for an approach to the Foundations of Physics that puts the question in the title center stage, rather than asking “what is the case in the world?”. This approach, algorithmic idealism, attempts to give a mathematically rigorous <i>in-principle</i>-answer to this question both in the usual empirical regime of physics and in some more exotic regimes within cosmology, philosophy, and science fiction (but soon perhaps real) technology. I begin by arguing that quantum theory, in its actual practice and in some interpretations, should be understood as telling an agent what they should expect to observe next (rather than what is the case), and that the difficulty of answering this former question from the usual “external” perspective is at the heart of persistent enigmas such as the Boltzmann brain problem, extended Wigner’s friend scenarios, Parfit’s teletransportation paradox, or our understanding of the simulation hypothesis. Algorithmic idealism is a conceptual framework, based on two postulates that admit several possible mathematical formalizations, cast in the language of algorithmic information theory. Here I give a non-technical description of this view and show how it dissolves the aforementioned enigmas: for example, it claims that you should never bet on being a Boltzmann brain regardless of how many there are, that shutting down computer simulations does not generally terminate its inhabitants, and it predicts the apparent embedding into an objective external world as an approximate description.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-026-00913-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Free Electron Paths from Dirac’s Wave Equation Elucidating Zitterbewegung and Spin 狄拉克波动方程中解释自旋和自旋的自由电子路径
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2026-01-07 DOI: 10.1007/s10701-025-00905-7
James L. Beck
{"title":"Free Electron Paths from Dirac’s Wave Equation Elucidating Zitterbewegung and Spin","authors":"James L. Beck","doi":"10.1007/s10701-025-00905-7","DOIUrl":"10.1007/s10701-025-00905-7","url":null,"abstract":"<div><p>The worldline of a free electron is revealed by applying Dirac’s velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two parts: the electron’s global motion of its inertia (or spin) center and an inherent local periodic motion about this point that produces the electron’s spin and has the zitterbewegung frequency found by Schrödinger in his operator analysis of Dirac’s wave equation. This zitter motion corresponds to the so-called polarization and magnetization currents in Gordon’s decomposition of Dirac’s current. In an inertial “rest”-frame fixed at the inertia center, Dirac’s wave function for a free electron with its spin in a specified direction implies that the zitter motion is a perpetual circular motion about the inertia center in a plane orthogonal to this spin direction with a radius one half of the Compton radius and moving at the speed of light. The electron continuously accelerates about the spin center without any external force because the inertia is effective at the spin center, rather than at its charge center where the electron interacts with the electro-magnetic field. This analysis confirms the nature of zitterbewegung directly from Dirac’s wave equation, agreeing with the conclusions of Barut and Zanghi, Beck, Hestenes, Rivas and Salesi from their classical Dirac particle models of the electron. Furthermore, these five classical models are equivalent and express the same free electron dynamics as Dirac’s equation..</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Holographic Strange Metals for Philosophers and Physicists 哲学家和物理学家全息奇怪金属
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-12-29 DOI: 10.1007/s10701-025-00907-5
Enrico Cinti, Sebastian De Haro, Mark S. Golden, Umut Gürsoy, Henk T. C. Stoof
{"title":"Holographic Strange Metals for Philosophers and Physicists","authors":"Enrico Cinti,&nbsp;Sebastian De Haro,&nbsp;Mark S. Golden,&nbsp;Umut Gürsoy,&nbsp;Henk T. C. Stoof","doi":"10.1007/s10701-025-00907-5","DOIUrl":"10.1007/s10701-025-00907-5","url":null,"abstract":"<div><p>This paper introduces the physics and philosophy of strange metals, which are characterized by unusual electrical and thermal properties that deviate from conventional metallic behaviour. The anomalous strange-metal behaviour discussed here appears in the normal state of a copper-oxide high-temperature superconductor, and it cannot be described using standard condensed-matter physics. Currently, it can only be described through a holographic dual, viz. a four-dimensional black hole in anti-de Sitter spacetime. This paper first introduces the theory of, and specific experiments carried out on, strange metals. Then it discusses a number of philosophical questions that strange metals open up regarding the experimental evidence for holography and its realist interpretation. Strange metals invert the explanatory arrows, in that usual holographic arguments are seen as giving explanations of the bulk quantum-gravity theory from the boundary. By contrast, the aim here is, by using holography, to explain the experimentally discovered and anomalous properties of strange metals.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-025-00907-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Towards a Better Understanding of the Electron’s Magnetic Moment: A Reply to Sanchioni 迈向对电子磁矩的更好理解：对Sanchioni的回复
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-12-29 DOI: 10.1007/s10701-025-00909-3
Charles T. Sebens
{"title":"Towards a Better Understanding of the Electron’s Magnetic Moment: A Reply to Sanchioni","authors":"Charles T. Sebens","doi":"10.1007/s10701-025-00909-3","DOIUrl":"10.1007/s10701-025-00909-3","url":null,"abstract":"<div><p>In this short article, I seek to clarify some of the broader motivations and ambitions guiding my work on electron spin. I respond to Sanchioni (Found. Phys. <b>55</b>(67), 1–11 2025), who has criticized my recent study of the electron’s anomalous magnetic moment (Sebens Found. Phys. <b>55</b>(48), 1–28 2025). I argue against viewing quantum field theory instrumentally as merely “an architecture of consistent predictions” and in favor of explaining physical phenomena using descriptions of what is actually out there in nature. I defend the importance of asking how the move from the Dirac equation (with self-interaction) to quantum field theory takes you from a variable to fixed magnetic moment, emphasizing my agreement with Sanchioni that the Dirac equation yields only a flawed model of the electron. I explain that quantum field theory, as it stands, is incomplete, and discuss how we might be able to arrive at a better explanation of the electron’s anomalous magnetic moment.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From Joint to Single-System (psi)-Onticity Without Preparation Independence 从联合到单一(psi)——无准备的独立性
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-12-26 DOI: 10.1007/s10701-025-00910-w
Shan Gao
{"title":"From Joint to Single-System (psi)-Onticity Without Preparation Independence","authors":"Shan Gao","doi":"10.1007/s10701-025-00910-w","DOIUrl":"10.1007/s10701-025-00910-w","url":null,"abstract":"<div><p>The Pusey–Barrett–Rudolph (PBR) theorem establishes <span>(psi)</span>-onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of <span>(psi)</span>-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes <span>(psi)</span>-onticity for composite systems prepared in product states, the <span>(psi)</span>-onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving <span>(psi)</span>-epistemic models, and strengthens the conceptual foundations of <span>(psi)</span>-ontology.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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