Constructing deterministic models for quantum mechanical systems

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040007
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Essential Element ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Final States ◽  
Deterministic Models ◽  
Quantum Theories ◽  
Initial States ◽  
Quantum Mechanical Systems ◽  
Entire Theory

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential element of the deterministic interpretation, we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realization of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

scholarly journals ${\mathcal N}$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS

2012 ◽  
Vol 27 (19) ◽  
pp. 1250102 ◽  
Author(s):  
TOSHIAKI TANAKA
Keyword(s):  
Quantum Mechanics ◽  
Hermitian Matrix ◽  
Mechanical Systems ◽  
Quantum Systems ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Quantum Mechanical ◽  
Quantum Mechanical Systems ◽  
Ordinary Quantum

We formulate [Formula: see text]-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of [Formula: see text]-fold supersymmetry, namely, almost isospectrality and weak quasi-solvability. We construct explicitly the most general one- and two-fold supersymmetric quantum mechanical systems with reflections. In the case of [Formula: see text], we find that there are seven inequivalent such systems, three of which are characterized by three arbitrary functions having definite parity while the other four characterized by two arbitrary functions. In addition, four of the seven inequivalent systems do not reduce to ordinary quantum systems without reflections. Furthermore, in certain particular cases, they are essentially equivalent to the most general two-by-two Hermitian matrix two-fold supersymmetric quantum systems obtained previously by us.

scholarly journals CORRELATIONS IN ENTANGLED STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1496-1503
Author(s):  
B. C. SANCTUARY
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Hidden Variable ◽  
Phase Decoherence ◽  
Classical Correlations ◽  
Spin Pairs ◽  
Ensemble Interpretation

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

scholarly journals Barad, Bohr, and quantum mechanics

Synthese ◽  
2021 ◽  
Author(s):  
Jan Faye ◽  
Rasmus Jaksland
Keyword(s):  
Social Sciences ◽  
Quantum Mechanics ◽  
Science Studies ◽  
Niels Bohr ◽  
Quantum Mechanical ◽  
Strict Sense ◽  
Interpretation Of Quantum Mechanics ◽  
Feminist Science ◽  
Interpretations Of Quantum Mechanics ◽  
Agential Realism

AbstractThe last decade has seen an increasing number of references to quantum mechanics in the humanities and social sciences. This development has in particular been driven by Karen Barad’s agential realism: a theoretical framework that, based on Niels Bohr’s interpretation of quantum mechanics, aims to inform social theorizing. In dealing with notions such as agency, power, and embodiment as well as the relation between the material and the discursive level, the influence of agential realism in fields such as feminist science studies and posthumanism has been profound. However, no one has hitherto paused to assess agential realism’s proclaimed quantum mechanical origin including its relation to the writings of Niels Bohr. This is the task taken up here. We find that many of the implications that agential realism allegedly derives from a Bohrian interpretation of quantum mechanics dissent from Bohr’s own views and are in conflict with those of other interpretations of quantum mechanics. Agential realism is at best consistent with quantum mechanics and consequently, it does not capture what quantum mechanics in any strict sense implies for social science or any other domain of inquiry. Agential realism may be interesting and thought provoking from the perspective of social theorizing, but it is neither sanctioned by quantum mechanics nor by Bohr’s authority. This conclusion not only holds for agential realism in particular, it also serves as a general warning against the other attempts to use quantum mechanics in social theorizing.

Wave Function Realism in a Relativistic Setting

2020 ◽  
pp. 154-168
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Higher Dimensions ◽  
Recent Criticism ◽  
Interpretation Of Quantum Mechanics ◽  
Quantum Theories ◽  
Realist Interpretation ◽  
Wave Function Realism

The purpose of the present chapter is to respond to a thread of recent criticism against one candidate framework for interpreting quantum theories, a framework introduced and defended by David Albert and Barry Loewer: wave function realism, a framework for interpreting the ontology of quantum theories according to which what appears to be a nonseparable metaphysics ofentangled objects acting instantaneously across spatial distances is a manifestation of a more fundamental separable and local metaphysics in higher dimensions. Thechapterconsiders strategies for extending the wave function realist interpretation of quantum mechanics to the case of relativistic quantum theories, responding to arguments that this cannot be done.

scholarly journals Quantum Mechanics and an Ontology of Intersubjectivity: Perils and Promises

Open Theology ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 325-341
Author(s):  
Marc A. Pugliese
Keyword(s):  
Quantum Mechanics ◽  
New Physics ◽  
Relativity Theory ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Experimental Procedure ◽  
Interpretations Of Quantum Mechanics ◽  
Ontological Categories ◽  
Per Se ◽  
The Many

AbstractContemporary theology has realized the importance of integrating what we know from the “new physics”-quantum mechanics and relativity theory-into the metaphysical and ontological categories used by theology to consider God, the world, and the God-world relationship. The categories of subjectivity and relationality have risen to prominence in these discussions. Both academic and popular presentations can obscure the vital distinction between what physicists agree on concerning quantum mechanics and the contested interpretation of quantum mechanics, or what quantum mechanics reveals about reality. After (1) summarizing the significant distinction between quantum mechanics per se and the interpretations of quantum mechanics and (2) the agreed upon quantum mechanical experimental procedure and its attendant mathematical formalism, as well as a few of the foremost interpretations, this paper (3) attempts a minimalist culling of some rudimentary but clear ontological principles and categories from what is agreed upon in quantum mechanics, without appeals-tacit or explicit-to one of the many controversial interpretations or to contestable philosophical assumptions and deductions, and these are: experience, subjectivity, relationship, and event. The paper closes by (4) commending one speculative scheme that is especially conducive to developing an interpretation of quantum mechanics consonant with the ontological principles and categories so derived, that of Alfred North Whitehead

scholarly journals Causality in Schwinger’s Picture of Quantum Mechanics

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 75
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo ◽  
Luca Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Von Neumann Algebra ◽  
Operator Algebras ◽  
Quantum Mechanical ◽  
Von Neumann ◽  
Triangular Operator ◽  
Quantum Mechanical Systems ◽  
Causal Structures ◽  
Incidence Theorem

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed.

scholarly journals THE MAIN LEITMOTIFS OF CHINESE MEDICINE IN THE CONTEXT OF THE DEVELOPMENT OF MODERN SCIENCE

2020 ◽  
Vol 73 (5) ◽  
pp. 1000-1003
Author(s):  
Ihor A. Sniehyrov ◽  
Inna А. Plakhtiienko ◽  
Viktoriia O. Kurhanska ◽  
Yurii V. Smiianov
Keyword(s):  
Quantum Mechanics ◽  
Qualitative Difference ◽  
Modern Science ◽  
Periodic Wave ◽  
Dissipative Structures ◽  
Living System ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Mechanical Systems ◽  
Integral Quantum

The aim: To demonstrate the limitations of pharmacological (chemical) therapy and the atomistic paradigm of science (in particular medicine) on the methodological basis of modern interdisciplinary directions (the theory of dissipative structures, chaos, autopoiesis), quantum mechanics, as well as the basic patterns of oriental medicine. Materials and methods: The principles used in the article include self-organization, emergence, quantum mechanics (the Heisenberg uncertainty principle), the principle of consistency; principles of using coherent millimeter waves of low power, etc. Theoretical methods of analysis and synthesis, idealization, abstraction, induction and deduction are also used. Сonclusions: The concept of “integrable system” is equivalent to the concept of “integral quantum-mechanical system”; Integral quantum-mechanical systems (nuclei, atoms, molecules, living objects) in the ground state are described by periodic wave functions of the type exp (jwt); The traditional paradigm, for the most part, eliminates the qualitative difference between living and dead matter; Any living system functioning as a whole is simultaneously a macroscopic quantum-mechanical object and a millimeter-wave laser.

scholarly journals Signatures of Quantum Mechanics in Chaotic Systems

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 618 ◽  
Author(s):  
Kevin M. Short ◽  
Matthew A. Morena
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Chaotic Systems ◽  
Measurement Problem ◽  
Quantum Systems ◽  
Analytical Tool ◽  
Quantum Mechanical ◽  
Unstable Periodic Orbits ◽  
Classical Correspondence ◽  
Quantum Mechanical Systems

We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.

scholarly journals Qubit exchange interactions from permutations of classical bits

2019 ◽  
Vol 17 (08) ◽  
pp. 1941003 ◽  
Author(s):  
Hans-Thomas Elze
Keyword(s):  
Quantum Mechanics ◽  
Cellular Automaton ◽  
Series Expansion ◽  
Spin Chain ◽  
Exchange Interactions ◽  
Theoretical Models ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Many Body ◽  
Ising Spins

In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’t[Formula: see text]Hooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

scholarly journals $$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Soumangsu Chakraborty ◽  
Amiya Mishra
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Partition Function ◽  
Linear Combination ◽  
Mechanical Systems ◽  
General Linear ◽  
Quantum Mechanical ◽  
Partition Functions ◽  
Flow Equations ◽  
Quantum Mechanical Systems

Abstract In this paper, we continue the study of $$ T\overline{T} $$ T T ¯ deformation in d = 1 quantum mechanical systems and propose possible analogues of $$ J\overline{T} $$ J T ¯ deformation and deformation by a general linear combination of $$ T\overline{T} $$ T T ¯ and $$ J\overline{T} $$ J T ¯ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and U(1) gauge theory.

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