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Fundamental Klein-Gordon Equation from Stochastic Mechanics in Curved Spacetime 弯曲时空中随机力学中的基本Klein-Gordon方程
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-07-09 DOI: 10.1007/s10701-025-00873-y
Eric S. Escobar-Aguilar, Tonatiuh Matos, J. I. Jiménez-Aquino
{"title":"Fundamental Klein-Gordon Equation from Stochastic Mechanics in Curved Spacetime","authors":"Eric S. Escobar-Aguilar,&nbsp;Tonatiuh Matos,&nbsp;J. I. Jiménez-Aquino","doi":"10.1007/s10701-025-00873-y","DOIUrl":"10.1007/s10701-025-00873-y","url":null,"abstract":"<div><p>This work presents an alternative approach to obtain the quantum field equations in curved spacetime, considering that sufficiently small particles follow stochastic trajectories around geodesic. Our proposal is based on a stochastic differential equation in which the noise term experienced by the quantum particles is a consequence of the stochastic background in spacetime. This fact allows the particles to describe erratic movements and locally the universe exhibits characteristics akin to a lake with gentle ripples rather than a flat unyielding surface. Building upon this foundational understanding, we investigate the influence of this background on quantum-scale particles without considering the metric to be stochastic, rather we let test particles move randomly around the geodesic of macroscopic particles. Their behavior aligns with solutions to the Klein-Gordon (KG) equation specific to this curved spacetime. As the KG equation, in its non-relativistic limit within a flat spacetime, reduces to the Schrödinger equation, consequently, we propose a compelling connection: the Schrödinger equation may emerge directly from a spacetime lacking local smoothness.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-025-00873-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163881","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
Quantum Probability Geometrically Realized in Projective Space 投影空间中量子概率的几何实现
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-07-09 DOI: 10.1007/s10701-025-00876-9
Stephen Bruce Sontz
{"title":"Quantum Probability Geometrically Realized in Projective Space","authors":"Stephen Bruce Sontz","doi":"10.1007/s10701-025-00876-9","DOIUrl":"10.1007/s10701-025-00876-9","url":null,"abstract":"<div><p>The principal goal of this paper and its originality consist in passing all formulas for quantum probability to the projective space associated to the complex Hilbert space of a given quantum system, thereby providing a geometric foundation of quantum probability, which should be considered as a step towards an eventual axiomization. Quantum events have consecutive and conditional probabilities, which have been used in the author’s work to clarify ‘collapse of the state’ and to generalize the concept of entanglement by incorporating it into quantum probability theory. In this way much of standard textbook quantum theory can be understood in the setting of the geometry of a projective space and its subspaces. The ultimate, future goal is to formulate all of quantum theory as the probability theory of projective subspaces, or equivalently, of quantum events. For the sake of simplicity the ideas are developed here in the context of a type I factor, but comments will be given about how to adopt this approach to more general von Neumann algebras.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163882","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
Weak Ratios 疲软的比率
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-07-09 DOI: 10.1007/s10701-025-00871-0
Yakov Bloch
{"title":"Weak Ratios","authors":"Yakov Bloch","doi":"10.1007/s10701-025-00871-0","DOIUrl":"10.1007/s10701-025-00871-0","url":null,"abstract":"<div><p>Weak values characterize a quantum system in the period of time between preparation and measurement and may lie outside the eigenvalue spectrum of the measured operator. The probability of such “superweak\" values for random quantum states has been calculated and applied to Klein–Gordon and Dirac waves, where the maximal probability for superluminal propagation was shown to be 1/2. In a recent paper, a different definition for the velocity of a relativistic quantum particle was proposed in terms of a ratio of two weak values. In this paper, we find the probability distribution of such ratios. With the new definition, the superluminal probability of photons is found to be bounded between <span>(1-1/sqrt{2})</span> and <span>(1/sqrt{2})</span>, while for general eigenvalue distributions the superluminal probability can take any value between 0 and 1.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-025-00871-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163877","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
From Global Time to Local Physics 从全球时间到本地物理
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-07-03 DOI: 10.1007/s10701-025-00869-8
Syed Moeez Hassan, Viqar Husain, Babar Qureshi
{"title":"From Global Time to Local Physics","authors":"Syed Moeez Hassan,&nbsp;Viqar Husain,&nbsp;Babar Qureshi","doi":"10.1007/s10701-025-00869-8","DOIUrl":"10.1007/s10701-025-00869-8","url":null,"abstract":"<div><p>Global time is a gauge or relational choice of time variable in canonical gravity. Local time is the time used in a flat patch of spacetime. We compare the dynamics of a scalar field with respect to choices of global time and Minkowski patch time in an expanding cosmology. Our main results are that evolutions starting from the same initial conditions are similar on the time scales of terrestrial experiments, and that global time leads to a mechanism for evolving coupling constants.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161365","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
Infeasibility of Graviton Detection as Cosmic Censorship 引力子探测作为宇宙审查的不可行性
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-07-03 DOI: 10.1007/s10701-025-00872-z
Andrea Palessandro
{"title":"Infeasibility of Graviton Detection as Cosmic Censorship","authors":"Andrea Palessandro","doi":"10.1007/s10701-025-00872-z","DOIUrl":"10.1007/s10701-025-00872-z","url":null,"abstract":"<div><p>We construct an explicit model of inhomogeneous gravitational collapse leading to a naked singularity in which gravitational absorption is both efficient and observable. We propose that the infeasibility of (efficient) graviton detection is simply a consequence of Nature’s conspiracy to hide regions of strong curvature behind event horizons.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160607","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
Observable and Unobservable in Quantum Mechanics 量子力学中的可观测和不可观测
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-06-30 DOI: 10.1007/s10701-025-00868-9
Marcello Poletti
{"title":"Observable and Unobservable in Quantum Mechanics","authors":"Marcello Poletti","doi":"10.1007/s10701-025-00868-9","DOIUrl":"10.1007/s10701-025-00868-9","url":null,"abstract":"<div><p>This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of <i>onto-epistemic ignorance</i>: situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain that transmits information from a system A to a system B, rather than to any subjective lack of knowledge. It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra, formally equivalent to the fundamental postulates of quantum mechanics.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171657","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
Vacuum Branching, Dark Energy, Dark Matter 真空分支，暗能量，暗物质
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-06-30 DOI: 10.1007/s10701-025-00864-z
Don Weingarten
{"title":"Vacuum Branching, Dark Energy, Dark Matter","authors":"Don Weingarten","doi":"10.1007/s10701-025-00864-z","DOIUrl":"10.1007/s10701-025-00864-z","url":null,"abstract":"<div><p>Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. In an earlier version of the present work, we proposed a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. In the present article, we adapt the earlier version to quantum electrodynamics of electrons and protons on a lattice in Minkowski space. The earlier version, however, here is simplified by replacing a definition of complexity which takes the physical vacuum as 0 complexity starting point, with a definition which takes the bare vacuum as starting point. As a consequence of this replacement, the physical vacuum itself is expected to branch yielding branches with energy densities slightly larger than that of the unbranched vacuum. If the vacuum energy renormalization constant is chosen as usual to give 0 energy density to the unbranched vacuum, in an expanding universe vacuum branches will appear to have a combination of dark energy and dark matter densities. The hypothesis that vacuum branching is the origin of the observed dark energy and dark matter densities leads to an estimate of <span>(mathcal {O}(10^{-18} {m}^3))</span> for the parameter <i>b</i> which enters the complexity measure governing branch formation and sets the boundary between quantum and classical behavior.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171659","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
A Time Operator and the Time-Of-Arrival Problem in Quantum Field Theory 量子场论中的时间算子与到达时间问题
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-06-30 DOI: 10.1007/s10701-025-00866-x
Daniele Colosi, Robert Oeckl
{"title":"A Time Operator and the Time-Of-Arrival Problem in Quantum Field Theory","authors":"Daniele Colosi,&nbsp;Robert Oeckl","doi":"10.1007/s10701-025-00866-x","DOIUrl":"10.1007/s10701-025-00866-x","url":null,"abstract":"<div><p>The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we construct one-particle states of massive Klein-Gordon theory that are localized on the hypersurface in the temporal as well as two spatial directions. This addresses the longstanding problem of a “time operator\" in quantum theory. It is made possible by recent advances in quantization on timelike hypersurfaces and the introduction of evanescent particles. As a first application of time-localized states, we consider the time-of-arrival problem. Our results are in accordance with semiclassical expectations of causal propagation of massless and massive particles. As in the Newton-Wigner case, localization is not perfect, but apparent superluminal propagation is exponentially suppressed.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-025-00866-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171658","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
Reichenbach’s Forgotten Argument 莱辛巴赫被遗忘的论点
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-06-27 DOI: 10.1007/s10701-025-00870-1
Enrico Cinti, Alberto Corti, Vincenzo Fano, Marco Sanchioni
{"title":"Reichenbach’s Forgotten Argument","authors":"Enrico Cinti,&nbsp;Alberto Corti,&nbsp;Vincenzo Fano,&nbsp;Marco Sanchioni","doi":"10.1007/s10701-025-00870-1","DOIUrl":"10.1007/s10701-025-00870-1","url":null,"abstract":"<div><p>Reichenbach’s importance to the development of modern philosophy can hardly be overstated. However, many themes and arguments originally developed by Reichenbach are either overlooked or not properly credited to him. In this article, we discuss an important but often forgotten argument of Reichenbach against the Kantian notion of synthetic a priori. We first give a detailed historical reconstruction of the argument and discuss the mild conventionalism that Reichenbach developed following this argument. Then, we recast this argument in the modern language of General Relativity. We show that this argument is still relevant for a modern attempt at articulating the notion of synthetic a priori: Friedman’s relativised synthetic a priori.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170688","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 Hamilton-Jacobi to Bohm: Why the Wave Function Isn’t Just Another Action 从汉密尔顿-雅可比到玻姆：为什么波函数不只是另一种作用
IF 1 3区 物理与天体物理
Foundations of Physics Pub Date : 2025-06-21 DOI: 10.1007/s10701-025-00865-y
Arnaud Amblard, Aurélien Drezet
{"title":"From Hamilton-Jacobi to Bohm: Why the Wave Function Isn’t Just Another Action","authors":"Arnaud Amblard,&nbsp;Aurélien Drezet","doi":"10.1007/s10701-025-00865-y","DOIUrl":"10.1007/s10701-025-00865-y","url":null,"abstract":"<div><p>This paper examines the physical meaning of the wave function in Bohmian mechanics (BM), addressing the debate between causal and nomological interpretations. While BM postulates particles with definite trajectories guided by the wave function, the ontological status of the wave function itself remains contested. Critics of the causal interpretation argue that the wave function’s high-dimensionality and lack of back-reaction disqualify it as a physical entity. Proponents of the nomological interpretation, drawing parallels to the classical Hamiltonian, propose that the wave function is a “law-like\" entity. However, this view faces challenges, including reliance on speculative quantum gravity frameworks (e.g., the Wheeler-DeWitt equation) and conceptual ambiguities about the nature of “nomological entities\". By systematically comparing BM to Hamilton-Jacobi theory, this paper highlights disanalogies between the wave function and the classical action function. These differences—particularly the wave function’s dynamical necessity and irreducibility—support a <i>sui generis</i> interpretation, where the wave function represents a novel ontological category unique to quantum theory. The paper concludes that the wave function’s role in BM resists classical analogies, demanding a metaphysical framework that accommodates its non-local, high-dimensional, and dynamically irreducible nature.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167877","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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