Foundations of Physics最新文献

{"title":"On the Nonreality of the PBR Theorem","authors":"Marcoen J. T. F. Cabbolet","doi":"10.1007/s10701-023-00704-y","DOIUrl":"10.1007/s10701-023-00704-y","url":null,"abstract":"<div><p>The PBR theorem, which implies that the Einsteinian realist view on quantum mechanics (QM) is inconsistent with predictions of the standard Copenhagen view on QM, has been hailed as one of the most important theorems in the foundations of QM. Here we show that the special measurement, used by Pusey et al. to derive the theorem, is nonexisting from the Einsteinian view on QM.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00704-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4973406","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}

{"title":"Forewords for the Special Issue ‘Pilot-wave and Beyond: Louis de Broglie and David Bohm’s Quest for a Quantum Ontology’","authors":"Aurélien Drezet","doi":"10.1007/s10701-023-00685-y","DOIUrl":"10.1007/s10701-023-00685-y","url":null,"abstract":"","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4613329","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}

{"title":"Quantum Prey–Predator Dynamics: A Gaussian Ensemble Analysis","authors":"A. E. Bernardini,&nbsp;O. Bertolami","doi":"10.1007/s10701-023-00703-z","DOIUrl":"10.1007/s10701-023-00703-z","url":null,"abstract":"<div><p>Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then be identified. These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4618253","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}

{"title":"On the Cardinality of Future Worldlines in Discrete Spacetime Structures","authors":"Ahmet Çevik,&nbsp;Zeki Seskir","doi":"10.1007/s10701-023-00701-1","DOIUrl":"10.1007/s10701-023-00701-1","url":null,"abstract":"<div><p>We give an analysis over a variation of causal sets where the light cone of an event is represented by finitely branching trees with respect to any given arbitrary dynamics. We argue through basic topological properties of Cantor space that under certain assumptions about the universe, spacetime structure and causation, given any event <i>x</i>, the number of all possible future worldlines of <i>x</i> within the many-worlds interpretation is uncountable. However, if all worldlines extending the event <i>x</i> are ‘eventually deterministic’, then the cardinality of the set of future worldlines with respect to <i>x</i> is exactly <span>(aleph _0)</span>, i.e., countably infinite. We also observe that if there are countably many future worldlines with respect to <i>x</i>, then at least one of them must be necessarily ‘decidable’ in the sense that there is an algorithm which determines whether or not any given event belongs to that worldline. We then show that if there are only finitely many worldlines in the future of an event <i>x</i>, then they are all decidable. We finally point out the fact that there can be only countably many terminating worldlines.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00701-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4261557","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}

{"title":"Affine Geometry and Relativity","authors":"Božidar Jovanović","doi":"10.1007/s10701-023-00700-2","DOIUrl":"10.1007/s10701-023-00700-2","url":null,"abstract":"<div><p>We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between classical mechanics and theory of relativity, which is quite often hidden, despite its fundamental importance. We have emphasized a passage from the group of Galilean motions to the group of Poincaré transformations of a plane. In particular, a 1-parametric family of natural deformations of the Poincaré group is described. We also visualized the underlying groups of Galilean, Euclidean, and pseudo-Euclidean rotations within the special linear group.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4216093","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}

{"title":"On the Representations of Bell’s Operators in Quantum Mechanics","authors":"S. P. Sorella","doi":"10.1007/s10701-023-00699-6","DOIUrl":"10.1007/s10701-023-00699-6","url":null,"abstract":"<div><p>We point out that, when the dimension of the Hilbert space is greater than two, Bell’s operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson’s bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5055626","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}

{"title":"Information-Theoretic Interpretation of Quantum Formalism","authors":"Michel Feldmann","doi":"10.1007/s10701-023-00690-1","DOIUrl":"10.1007/s10701-023-00690-1","url":null,"abstract":"<div><p>We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4832825","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}

{"title":"Neo-classical Relativistic Mechanics Theory for Electrons that Exhibits Spin, Zitterbewegung, Dipole Moments, Wavefunctions and Dirac’s Wave Equation","authors":"James L. Beck","doi":"10.1007/s10701-023-00696-9","DOIUrl":"10.1007/s10701-023-00696-9","url":null,"abstract":"<div><p>In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The <i>electric</i> dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his <i>magnetic</i> dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection ","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00696-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4658035","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}

{"title":"The Position-Momentum Commutator as a Generalized Function: Resolution of the Apparent Discrepancy Between Continuous and Discrete Bases","authors":"Timothy B. Boykin","doi":"10.1007/s10701-023-00697-8","DOIUrl":"10.1007/s10701-023-00697-8","url":null,"abstract":"<div><p>It has been known for many years that the matrix representation of the one-dimensional position-momentum commutator calculated with the position and momentum matrices in a finite basis is not proportional to the diagonal matrix, contrary to what one expects from the continuous-space commutator. This discrepancy has correctly been ascribed to the incompleteness of any finite basis, but without the details of exactly why this happens. Understanding why the discrepancy occurs requires calculating the position, momentum, and commutator matrix elements in the continuous position basis, in which all are generalized functions. The reason for the discrepancy is revealed by replacing the generalized functions with sequences approaching them as their parameter approaches zero. Besides explaining the discrepancy in the discrete and continuous models, this investigation finds an unusual double-peaked sequence for the Dirac delta function.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-023-00697-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4950172","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}

{"title":"Dirac Theory in Hydrodynamic Form","authors":"Luca Fabbri","doi":"10.1007/s10701-023-00695-w","DOIUrl":"10.1007/s10701-023-00695-w","url":null,"abstract":"<div><p>We consider quantum mechanics written in hydrodynamic formulation for the case of relativistic spinor fields to study their velocity: within such a hydrodynamic formulation it is possible to see that the velocity as is usually defined can not actually represent the tangent vector to the trajectories of particles. We propose an alternative definition for this tangent vector and hence for the trajectories of particles, which we believe to be new and the only one possible. We discuss how these results are a necessary step to take in order to face further problems, like the definition of trajectories for multi-particle systems or ensembles, as they happen to be useful in many applications and interpretations of quantum mechanics.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4504933","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}