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 Ontological states and dynamics of discrete (pre-) quantum systems

2017 ◽  
Vol 15 (08) ◽  
pp. 1740013 ◽  
Author(s):  
Hans-Thomas Elze
Keyword(s):  
Quantum Mechanics ◽  
Equations Of Motion ◽  
Superposition Principle ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
First Order ◽  
Mechanical Models ◽  
Superposition States ◽  
Ising Spins

The notion of ontological states is introduced here with reference to the Cellular Automaton Interpretation of Quantum Mechanics (QM) proposed by ’t Hooft. A class of discrete deterministic “Hamiltonian” Cellular Automata (CA) is defined that has been shown to bear many features in common with continuum quantum mechanical models, however, deformed by the presence of a finite discreteness scale [Formula: see text], such that for [Formula: see text], the usual properties result e.g. concerning linearity, dispersion relations, multipartite systems, and Superposition Principle. We argue that within this class of models, only very primitive realizations of ontological states and their dynamics can exist, since the equations of motion tend to produce superposition states that are not ontological. The most interesting, if not the only way out seems to involve interacting multipartite systems composed of two-state “Ising spins”, which evolve by a unitary transfer matrix. Thus, quantum like and ontological models appear side by side here, but distinguished by second-order and first-order dynamics, respectively.

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 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.

scholarly journals The universe from a single particle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Michael Freedman ◽  
Modjtaba Shokrian Zini
Keyword(s):  
Quantum Mechanics ◽  
Single Particle ◽  
Quantum Mechanical ◽  
Local Minima ◽  
Quantum Mechanical System ◽  
Many Body ◽  
Gaussian Unitary Ensemble ◽  
Interacting Systems ◽  
The Universe ◽  
Unitary Ensemble

Abstract We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.

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 Multipartite cellular automata and the superposition principle

2016 ◽  
Vol 14 (04) ◽  
pp. 1640001 ◽  
Author(s):  
Hans-Thomas Elze
Keyword(s):  
Quantum Mechanics ◽  
Cellular Automata ◽  
Tensor Product ◽  
Continuum Limit ◽  
Superposition Principle ◽  
Continuum Models ◽  
Quantum Mechanical ◽  
Many Body ◽  
Mechanical Models ◽  
Deterministic Automata

Cellular automata (CA) can show well known features of quantum mechanics (QM), such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of “natural” Hamiltonian CA, which are based entirely on integer-valued variables and couplings and derived from an action principle, can be mapped reversibly to continuum models with the help of sampling theory. This results in “deformed” quantum mechanical models with a finite discreteness scale l, which for [Formula: see text] reproduce the familiar continuum limit. Presently, we show, in particular, how such automata can form “multipartite” systems consistently with the tensor product structures of non-relativistic many-body QM, while maintaining the linearity of dynamics. Consequently, the superposition principle is fully operative already on the level of these primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement.

scholarly journals The Geometric Algebra Lift of Qubits and Beyond

2022 ◽  
Author(s):  
Alexander Soiguine
Keyword(s):  
Quantum Mechanics ◽  
Geometric Algebra ◽  
Wave Diffraction ◽  
Three Dimensions ◽  
Quantum Mechanical ◽  
Complex Numbers ◽  
Interpretation Of Quantum Mechanics ◽  
Diffraction Patterns ◽  
Definition Of

The Geometric Algebra formalism opens the door to developing a theory upgrading conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions; unambiguous definition of states, observables, measurements bring into reality clear explanations of conventional weird quantum mechanical features, particularly the results of double split experiments where particles create diffraction patterns inherent to wave diffraction. This weirdness of the double split experiment is milestone of all further difficulties in interpretation of quantum mechanics.

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