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  1. The Madelung Picture as a Foundation of Geometric Quantum Theory.Maik Reddiger - 2017 - Foundations of Physics 47 (10):1317-1367.
    Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given (...)
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  • On the Philosophical Inadequacy of Modern Physics and the Need for a Theory of Space.Henry H. Lindner - 2015 - Cosmos and History 11 (1):136-180.
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  • Classical and Non-Relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles.Sergio Hernández-Zapata & Ernesto Hernández-Zapata - 2010 - Foundations of Physics 40 (5):532-544.
    A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an (...)
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  • Intrinsic Properties of Quantum Systems.P. Hájíček & J. Tolar - 2009 - Foundations of Physics 39 (5):411-432.
    A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any version of Copenhagen interpretation would allow. A (...)
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  • Quantum Mechanics From Focusing and Symmetry.Inge S. Helland - 2008 - Foundations of Physics 38 (9):818-842.
    A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and (...)
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  • A Symmetrical Interpretation of the Klein-Gordon Equation.Michael B. Heaney - 2013 - Foundations of Physics 43 (6):733-746.
    This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...)
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  • $\Mathfrak{D}$ -Differentiation in Hilbert Space and the Structure of Quantum Mechanics.D. J. Hurley & M. A. Vandyck - 2009 - Foundations of Physics 39 (5):433-473.
    An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of $\mathcal{C}$ - and $\mathfrak{D}$ -differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as a special case, quantisation in arbitrary curvilinear coordinates when space is (...)
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  • Compact Time and Determinism for Bosons: Foundations. [REVIEW]Donatello Dolce - 2011 - Foundations of Physics 41 (2):178-203.
    Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose foundamental set-up is presented in this paper, turns out to be consistent with special (...)
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  • Probability in Relativistic Bohmian Mechanics of Particles and Strings.Hrvoje Nikolić - 2008 - Foundations of Physics 38 (9):869-881.
    Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian theory predicts subtle deviations from the statistical predictions of more conventional formulations of quantum theory, but it seems that no present experiment rules this theory out. The generalization to the case of many particles or strings is straightforward, provided that a preferred foliation of spacetime is given.
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  • Unconventional Approach to Orbital-Free Density Functional Theory Derived From a Model of Extended Electrons.Werner A. Hofer - 2011 - Foundations of Physics 41 (4):754-791.
    An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution in a non-relativistic model. To (...)
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  • A Novel Interpretation of the Klein-Gordon Equation.K. B. Wharton - 2010 - Foundations of Physics 40 (3):313-332.
    The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrödinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing an invariant joint probability distribution from the size of the solution space, it is shown that the usual measurement probabilities can nearly be recovered (...)
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  • Boson-Fermion Unification, Superstrings, and Bohmian Mechanics.Hrvoje Nikolić - 2009 - Foundations of Physics 39 (10):1109-1138.
    Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an (...)
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