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Minkowski Space from Quantum Mechanics 量子力学中的闵科夫斯基空间
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-05-04 DOI: 10.1007/s10701-024-00753-x
László B. Szabados
{"title":"Minkowski Space from Quantum Mechanics","authors":"László B. Szabados","doi":"10.1007/s10701-024-00753-x","DOIUrl":"10.1007/s10701-024-00753-x","url":null,"abstract":"<div><p>Penrose’s Spin Geometry Theorem is extended further, from <i>SU</i>(2) and <i>E</i>(3) (Euclidean) to <i>E</i>(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of <i>E</i>(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of <i>E</i>(1, 3)-<i>invariant basic observables</i>, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for <i>E</i>(1, 3)-<i>invariant elementary quantum mechanical systems</i> in terms of the <i>basic quantum observables</i> in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the <i>metric structure</i> of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-024-00753-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883827","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
Eliminativism and the QCD (theta _{text {YM}})-Term: What Gauge Transformations Cannot Do 消除主义与 QCD $$theta _{text {YM}}$-Term：量子变换无法做到的事情
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-04-24 DOI: 10.1007/s10701-024-00759-5
Henrique Gomes, Aldo Riello
{"title":"Eliminativism and the QCD (theta _{text {YM}})-Term: What Gauge Transformations Cannot Do","authors":"Henrique Gomes,&nbsp;Aldo Riello","doi":"10.1007/s10701-024-00759-5","DOIUrl":"10.1007/s10701-024-00759-5","url":null,"abstract":"<div><p>The eliminative view of gauge degrees of freedom—the view that they arise solely from descriptive redundancy and are therefore eliminable from the theory—is a lively topic of debate in the philosophy of physics. Recent work attempts to leverage properties of the QCD <span>(theta _{text {YM}})</span>-term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD <span>(theta _{text {YM}})</span>-term changes under “large” gauge transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the <span>(theta _{text {YM}})</span>-term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is <i>fully</i> gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the <span>(theta _{text {YM}})</span>-term shows the physical importance of bundle topology (or superpositions thereof) and thus counts against (a naive) eliminativism.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-024-00759-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140767576","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
A No-Go Result on Observing Quantum Superpositions 观测量子叠加的禁区结果
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-04-20 DOI: 10.1007/s10701-024-00760-y
Guang Ping He
{"title":"A No-Go Result on Observing Quantum Superpositions","authors":"Guang Ping He","doi":"10.1007/s10701-024-00760-y","DOIUrl":"10.1007/s10701-024-00760-y","url":null,"abstract":"<div><p>We give a general proof showing that if the evolution from one state to another is not reversible, then the projective measurements on the superposition of these two states are impossible. Applying this no-go result to the Schrödinger’s cat paradox implies that if something is claimed to be a real Schrödinger’s cat, there will be no measurable difference between it and a trivial classical mixture of ordinary cats in any physically implementable process, unless raising the dead becomes reality. Other similar macroscopic quantum superpositions cannot be observed either, due to the lack of non-commuting measurement bases. Our proof does not involve any quantum interpretation theory and hypothesis.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623087","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
Spatio-temporally Graded Causality: A Model 时空分级因果关系：一个模型
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-04-17 DOI: 10.1007/s10701-024-00761-x
Bartosz Jura
{"title":"Spatio-temporally Graded Causality: A Model","authors":"Bartosz Jura","doi":"10.1007/s10701-024-00761-x","DOIUrl":"10.1007/s10701-024-00761-x","url":null,"abstract":"<div><p>In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to use elements of a non-classical logic. Specifically, we focus here on causality, as a concept tightly related with the assumption of there being distinct, separate events, proposing a model according to which it can be considered to be spatio-temporally graded. It is outlined how this can be described using the formalism of fuzzy sets theory, with the degree of causality varying between 1, that is no separation between causes and effects, and 0, that is perfect separation between causes and their effects as in classical ’billiard balls’ models of physical systems, namely such based on the notion of ideal mathematical point. Our model posits that subjective moments of time are like fuzzy sets, with their extension determined by local degrees of causality, resulting from information integration processes extended gradually in space and time. This, we argue, is how a notion of causality could be, to a certain degree, spared and reconciled with a variant of Bergsonian duration theory as formulated in the theory of continuous change. Relation of the proposed viewpoint to other theories, as well as possible solutions it suggests to various problems, in particular the measurement problem, are also discussed.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612392","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 Stochastic Model of Mathematics and Science 数学与科学的随机模型
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-04-09 DOI: 10.1007/s10701-024-00755-9
David H. Wolpert, David B. Kinney
{"title":"A Stochastic Model of Mathematics and Science","authors":"David H. Wolpert,&nbsp;David B. Kinney","doi":"10.1007/s10701-024-00755-9","DOIUrl":"10.1007/s10701-024-00755-9","url":null,"abstract":"<div><p>We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves <i>stochastic mathematical systems</i> (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a “calibration” relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an “oracle” SMS that can be interpreted as deciding whether the question–answer pairs of the reasoner SMS are valid. To ground thinking, we understand the answers to questions given by this oracle to be the answers that would be given by an SMS representing the entire mathematical community in the infinite long run of the process of asking and answering questions. We then introduce a slight extension of SMSs to allow us to model both the physical universe and human reasoning about the physical universe. We then define a slightly different calibration relation appropriate for the case of scientific reasoning. In this case the first SMS represents a human scientist predicting the outcome of future experiments, while the second SMS represents the physical universe in which the scientist is embedded, with the question–answer pairs of that SMS being specifications of the experiments that will occur and the outcome of those experiments, respectively. Next we derive conditions justifying two important patterns of inference in both mathematical and scientific reasoning: (i) the practice of increasing one’s degree of belief in a claim as one observes increasingly many lines of evidence for that claim, and (ii) abduction, the practice of inferring a claim’s probability of being correct from its explanatory power with respect to some other claim that is already taken to hold for independent reasons.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569879","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
Stern–Gerlach, EPRB and Bell Inequalities: An Analysis Using the Quantum Hamilton Equations of Stochastic Mechanics 斯特恩-格拉赫、EPRB 和贝尔不等式：利用随机力学的量子汉密尔顿方程进行分析
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-03-14 DOI: 10.1007/s10701-024-00752-y
Michael Beyer, Wolfgang Paul
{"title":"Stern–Gerlach, EPRB and Bell Inequalities: An Analysis Using the Quantum Hamilton Equations of Stochastic Mechanics","authors":"Michael Beyer,&nbsp;Wolfgang Paul","doi":"10.1007/s10701-024-00752-y","DOIUrl":"10.1007/s10701-024-00752-y","url":null,"abstract":"<div><p>The discussion of the recently derived quantum Hamilton equations for a spinning particle is extended to spin measurement in a Stern–Gerlach experiment. We show that this theory predicts a continuously changing orientation of the particles magnetic moment over the course of its motion across the Stern–Gerlach apparatus. The final measurement results agree with experiment and with predictions of the Pauli equation. Furthermore, the Einstein–Podolsky–Rosen–Bohm thought experiment is investigated, and the violation of Bells’s inequalities is reproduced within this stochastic mechanics approach. The origin of the violation of Bell’s inequalities is traced to the the non-local nature of the velocity fields for an entangled state in the stochastic formalism, which is a result of a non-separable probability distribution of the considered particles.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-024-00752-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155877","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
Why the Global Phase is Not Real 为什么全球阶段不是真实的
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-03-05 DOI: 10.1007/s10701-024-00754-w
Shan Gao
{"title":"Why the Global Phase is Not Real","authors":"Shan Gao","doi":"10.1007/s10701-024-00754-w","DOIUrl":"10.1007/s10701-024-00754-w","url":null,"abstract":"<div><p>In this paper, I present a new analysis of the meaning of the phase in quantum mechanics. First, I give a simple but rigorous proof that the global phase is not real in <span>(psi)</span>-ontic quantum theories. Next, I argue that a similar strategy cannot be used to prove the reality of the global phase due to the existence of the tails of the wave function. Finally, I argue that the relative phase is not a nonlocal property of two regions together, and adding a relative phase to one local branch of a superposition only changes the local properties at the boundary of the region of the branch.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046470","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
Reconstruction of f(R) Gravity from Cosmological Unified Dark Fluid Model 从宇宙学统一暗流模型重构 f(R) 引力
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-02-19 DOI: 10.1007/s10701-023-00751-5
Esraa Ali Elkhateeb
{"title":"Reconstruction of f(R) Gravity from Cosmological Unified Dark Fluid Model","authors":"Esraa Ali Elkhateeb","doi":"10.1007/s10701-023-00751-5","DOIUrl":"10.1007/s10701-023-00751-5","url":null,"abstract":"<div><p>In this work, we reconstruct the cosmological unified dark fluid model proposed previously by Elkhateeb (Astrophys Space Sci 363(1):7, 2018) in the framework of <i>f</i>(<i>R</i>) gravity. Utilizing the equivalence between the scalar-tensor theory and the <i>f</i>(<i>R</i>) gravity theory, the scalar field for the dark fluid is obtained, whence the <i>f</i>(<i>R</i>) function is extracted and its viability is discussed. The <i>f</i>(<i>R</i>) functions and the scalar field potentials have then been extracted in the early and late times of asymptotically de Sitter spacetime. The ability of our function to describe early time inflation is also tested. The early time scalar field potential is used to derive the slow roll inflation parameters. Our results of the tensor-to-scalar ratio <i>r</i> and the scalar spectral index <span>(n_s)</span> are in good agreement with results from Planck-2018 TT+TE+EE+lowE data for the model parameter <span>(n &gt; 2)</span>.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00751-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139917982","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
Schrödinger Cats and Quantum Complementarity 薛定谔猫与量子互补性
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-01-25 DOI: 10.1007/s10701-023-00750-6
Lorenzo Maccone
{"title":"Schrödinger Cats and Quantum Complementarity","authors":"Lorenzo Maccone","doi":"10.1007/s10701-023-00750-6","DOIUrl":"10.1007/s10701-023-00750-6","url":null,"abstract":"<div><p>Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead <i>and</i> alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00750-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583537","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
Fundamental Units in Gravitational, Electromagnetic and Weak (Fermi) Interactions 引力、电磁和弱（费米）相互作用的基本单位
IF 1.2 3区 物理与天体物理
Foundations of Physics Pub Date : 2024-01-22 DOI: 10.1007/s10701-023-00741-7
M. Novello, V. Antunes
{"title":"Fundamental Units in Gravitational, Electromagnetic and Weak (Fermi) Interactions","authors":"M. Novello,&nbsp;V. Antunes","doi":"10.1007/s10701-023-00741-7","DOIUrl":"10.1007/s10701-023-00741-7","url":null,"abstract":"<div><p>In analogy with Planck’s construction of fundamental quantities in gravitation, we construct fundamental quantities associated with (1) theories of electrodynamics in which the electromagnetic field has a maximum value (e.g. Born-Infeld theory), and (2) the Fermi interaction. This gives us a maximum intensity of the electromagnetic field, and also reveals a close relationship between the fundamental lengths associated with the gravitational and weak interactions, supporting the connection between these two interactions.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139555391","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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