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Entanglement of Observables: Quantum Conditional Probability Approach 可观测物的纠缠:量子条件概率方法
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-09-15 DOI: 10.1007/s10701-023-00725-7
Andrei Khrennikov, Irina Basieva
{"title":"Entanglement of Observables: Quantum Conditional Probability Approach","authors":"Andrei Khrennikov,&nbsp;Irina Basieva","doi":"10.1007/s10701-023-00725-7","DOIUrl":"10.1007/s10701-023-00725-7","url":null,"abstract":"<div><p>This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable <i>A</i> and <i>B</i>. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables <i>A</i> and <i>B</i>,  so this is <i>AB</i>-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the <i>AB</i>-entangled states as amplitude non-factorisable states. In the tensor product case, <i>AB</i>-entanglement implies standard entanglement, but not vise verse. <i>AB</i>-entanglement for dichotomous observables is equivalent to their correlation, i.e., <span>(langle ABrangle _{psi} not = langle Arangle _{psi} langle Brangle _{psi} .)</span> We describe the class of quantum states that are <span>(A_{u} B_{u})</span>-entangled for a family of unitary operators (<i>u</i>). Finally, observables entanglement is compared with dependence of random variables in classical probability theory.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00725-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796885","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: 1
Synchronization and Fundamental Time: A Connection Between Relativity and Quantum Mechanics 同步与基本时间:相对论与量子力学之间的联系
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-09-15 DOI: 10.1007/s10701-023-00724-8
Matteo Luca Ruggiero
{"title":"Synchronization and Fundamental Time: A Connection Between Relativity and Quantum Mechanics","authors":"Matteo Luca Ruggiero","doi":"10.1007/s10701-023-00724-8","DOIUrl":"10.1007/s10701-023-00724-8","url":null,"abstract":"<div><p>An interesting connection between special relativity and quantum mechanics was put forward by Louis de Broglie, about 60 years ago, who focused on the link between synchronization in a rotating frame and the quantization of the angular momentum. Here we generalise his approach to curved spacetime, using the gravitoelectromagnetic analogy, which can be applied to describe the weak gravitational field around rotating sources, and give a new interpretation of the results.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796886","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
The Non-vanishing Imprint of Gravitational Waves as the Result of Its Nonlinear Evolution in Space 引力波在空间中非线性演化的不消失印记
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-09-05 DOI: 10.1007/s10701-023-00714-w
Ioseph Gurwich
{"title":"The Non-vanishing Imprint of Gravitational Waves as the Result of Its Nonlinear Evolution in Space","authors":"Ioseph Gurwich","doi":"10.1007/s10701-023-00714-w","DOIUrl":"10.1007/s10701-023-00714-w","url":null,"abstract":"<div><p>This paper focuses on the nonlinear self-interaction of gravitational waves and explores its impact on the spectrum of the resulting gravitational wave. While many authors primarily investigate the nonlinear effects within the framework of \"gravitational memory,\" we take a different approach by conducting a comprehensive analysis of harmonic generation. Theoretical analysis indicates that higher harmonics do not possess suitable conditions for energy accumulation. However, our study presents intriguing evidence supporting the concept of \"nonlinear gravitational memory\": the conversion and accumulation of gravitational wave energy into a persistent metric deformation in the background space (specifically referred here to as zero harmonics). In simpler terms, a wave leaves a lasting imprint on the background space, even after the gravitational pulse subsides. Furthermore, our study estimates the significance of this effect and demonstrates that it should not be disregarded.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46196005","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
Is the Electron Magnetic Moment Unique? 电子磁矩是唯一的吗？
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-09-02 DOI: 10.1007/s10701-023-00723-9
V. A. Golovko
{"title":"Is the Electron Magnetic Moment Unique?","authors":"V. A. Golovko","doi":"10.1007/s10701-023-00723-9","DOIUrl":"10.1007/s10701-023-00723-9","url":null,"abstract":"<div><p>There exist two methods for finding the magnetic moment of the electron. The first method employed in quantum electrodynamics consists in calculating the energy of the electron placed in a constant magnetic field, the extra energy due to the field being proportional to the magnetic moment. It is also possible to use the second method proceeding from the fact that the asymptotic form of the vector potential at infinity is proportional to the magnetic moment. If the electron were point-like, both the methods would yield identical results. In the present paper is studied the magnetic field created by the electron in hydrogen-like ions, which enables one to find the electron magnetic moment by the second method. The electron magnetic moment in this case proves to be different in different states of the electron in the Coulomb field of the ions and, moreover, is distinct from the magnetic moment calculated by the first method. The results of the paper show that the electron is not small and is deformable under action of external fields.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46265071","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
Electron Wave Trajectories Within Schrodinger’s Hydrogen Atom, and Relativistic Consequences 薛定谔氢原子内的电子波轨迹及其相对论性结果
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-26 DOI: 10.1007/s10701-023-00722-w
Leslie Smith
{"title":"Electron Wave Trajectories Within Schrodinger’s Hydrogen Atom, and Relativistic Consequences","authors":"Leslie Smith","doi":"10.1007/s10701-023-00722-w","DOIUrl":"10.1007/s10701-023-00722-w","url":null,"abstract":"<div><p>Quantum mechanics teaches that before detection, knowledge of particle position is, at best, probabilistic, and classical trajectories are seen as a feature of the macroscopic world. These comments refer to detected particles, but we are still free to consider the motions generated by the wave equation. Within hydrogen, the Schrodinger equation allows calculation of kinetic energy at any location, and if this is identified as the energy of the wave, then radial momentum, allowing for spherical harmonics, becomes available. The distance across the real zone of radial momentum is found to match semi-integer wavelengths of the adjusted matter wave, consistent with what is expected from a standing wave condition. The approach is extended to include orbital motions, where it is established that the underlying wave, which has direction and wavelength at each location, forms a series of connected trajectories, which are shown to be ellipses orientated at various angles to the equatorial plane. This suggests that wave trajectories, rather than particle trajectories, are still a feature of the hydrogen atom. The finding allows the reason for the coincidence between energy results derived by Sommerfeld’s classical trajectories and the Schrodinger wave equation to be appreciated. The result has implications when the relativistic situation is considered, as Sommerfeld’s correct deduction of the relativistic energy levels of hydrogen well before Dirac derived his wave equation has long been somewhat puzzling.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4996996","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
Emergent Phenomena in Nature: A Paradox with Theory? 自然涌现现象:理论悖论?
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-25 DOI: 10.1007/s10701-023-00721-x
Christiaan J. F. van de Ven
{"title":"Emergent Phenomena in Nature: A Paradox with Theory?","authors":"Christiaan J. F. van de Ven","doi":"10.1007/s10701-023-00721-x","DOIUrl":"10.1007/s10701-023-00721-x","url":null,"abstract":"<div><p>The existence of various physical phenomena stems from the concept called <i>asymptotic emergence</i>, that is, they seem to be exclusively reserved for certain limiting theories. Important examples are spontaneous symmetry breaking (SSB) and phase transitions: these would only occur in the classical or thermodynamic limit of underlying finite quantum systems, since for finite quantum systems, due to the uniqueness of the relevant states, such phenomena are excluded by Theory. In Nature, however, finite quantum systems describing real materials clearly exhibit such effects. In this paper we discuss these apparently “paradoxical” phenomena and outline various ideas and mechanisms that encompass both theory and reality, from physical and mathematical points of view.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00721-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4961208","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: 1
Mathematical Models of Photons 光子的数学模型
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-17 DOI: 10.1007/s10701-023-00708-8
Imants Bersons, Rita Veilande, Ojars Balcers
{"title":"Mathematical Models of Photons","authors":"Imants Bersons,&nbsp;Rita Veilande,&nbsp;Ojars Balcers","doi":"10.1007/s10701-023-00708-8","DOIUrl":"10.1007/s10701-023-00708-8","url":null,"abstract":"<div><p>Mathematics from the electromagnetic field quantization procedure and the soliton models of photons are used to construct a new 3D model of photons. Besides the interaction potential between the charged particle and the photons, which contains the annihilation and creation operators of photons, the new function for a description of free propagating photons is derived. This function presents the vector potential of the field, the function is a product of the harmonic oscillator eigenfunction with the well-defined coordinate of the oscillator and the Gaussian function of the polar radius in the transverse direction. In the article, the difference between the quantum mechanics of particles and photons is discussed.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43319486","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: 1
On Efforts to Decouple Early Universe Cosmology and Quantum Gravity Phenomenology 论早期宇宙宇宙学与量子引力现象学的解耦
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-14 DOI: 10.1007/s10701-023-00720-y
Mike D. Schneider
{"title":"On Efforts to Decouple Early Universe Cosmology and Quantum Gravity Phenomenology","authors":"Mike D. Schneider","doi":"10.1007/s10701-023-00720-y","DOIUrl":"10.1007/s10701-023-00720-y","url":null,"abstract":"<div><p>The Big Bang singularity in standard model cosmology suggests a program of study in ‘early universe’ quantum gravity phenomenology. Inflation is usually thought to undermine this program’s prospects by means of a dynamical diluting argument, but such a view has recently been disputed within inflationary cosmology, in the form of a ‘trans-Planckian censorship’ conjecture. Meanwhile, trans-Planckian censorship has been used outside of inflationary cosmology to motivate alternative early universe scenarios that are tightly linked to ongoing theorizing in quantum gravity. Against the resulting trend toward early universe quantum gravity phenomenology within and without inflation, Ijjas and Steindhardt suggest a further alternative: a ‘generalized cosmic censorship’ principle. I contrast the generalized cosmic censorship principle with the logic of its namesake, the cosmic censorship conjectures. I also remark on foundational concerns in the effective field theory approach to cosmology beyond the standard model, which would be based on that principle.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41368532","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 Boundary of the Cosmos 关于宇宙的边界
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-12 DOI: 10.1007/s10701-023-00718-6
Daniel Linford
{"title":"On the Boundary of the Cosmos","authors":"Daniel Linford","doi":"10.1007/s10701-023-00718-6","DOIUrl":"10.1007/s10701-023-00718-6","url":null,"abstract":"<div><p>Intuitively, the totality of physical reality—the Cosmos—has a beginning only if (i) all parts of the Cosmos agree on the direction of time (the Direction Condition) and (ii) there is a boundary to the past of all non-initial spacetime points such that there are no spacetime points to the past of the boundary (the Boundary Condition). Following a distinction previously introduced by J. Brian Pitts, the Boundary Condition can be conceived of in two distinct ways: either topologically, i.e., in terms of a closed boundary, or metrically, i.e., in terms of the Cosmos having a finite past. This article proposes that the Boundary Condition should be posed disjunctively, modifies and improves upon the metrical conception of the Cosmos’s beginning in light of a series of surprising yet simple thought experiments, and suggests that the Direction and Boundary Conditions should be thought of as more fundamental to the concept of the Cosmos’s beginning than classical Big Bang cosmology.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42240712","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
Quantum Entanglement: An Analysis via the Orthogonality Relation 量子纠缠:基于正交关系的分析
IF 1.5 3区 物理与天体物理
Foundations of Physics Pub Date : 2023-08-07 DOI: 10.1007/s10701-023-00710-0
Shengyang Zhong
{"title":"Quantum Entanglement: An Analysis via the Orthogonality Relation","authors":"Shengyang Zhong","doi":"10.1007/s10701-023-00710-0","DOIUrl":"10.1007/s10701-023-00710-0","url":null,"abstract":"<div><p>In the literature there has been evidence that a kind of relational structure called a quantum Kripke frame captures the essential characteristics of the orthogonality relation between pure states of quantum systems, and thus is a good qualitative mathematical model of quantum systems. This paper adds another piece of evidence by providing a tensor-product construction of two finite-dimensional quantum Kripke frames. We prove that this construction is exactly the qualitative counterpart of the tensor-product construction of two finite-dimensional Hilbert spaces over the complex numbers, and thus show that composition of quantum systems, especially the phenomenon of quantum entanglement, can be modelled in the framework of quantum Kripke frames. The assumptions used in our construction hint that we need complex numbers in quantum theory. Moreover, for this construction, we give a new and interesting characterization of linear maps of trace 0 in terms of the orthogonality relation.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795781","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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