scholarly journals The Geometric Algebra Lift of Qubits and Beyond

Author(s):  
Alexander Soiguine

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.

Author(s):  
Alireza Jamali

It is known since Madelung that the Schrödinger equation can be thought of as governing the evolution of an incompressible fluid, but the current theory fails to mathematically express this incompressibility in terms of the wavefunction without facing problem. In this paper after showing that the current definition of quantum-mechanical momentum as a linear operator is neither the most general nor a necessary result of the de Broglie hypothesis, a new definition is proposed that can yield both a meaningful mathematical condition for the incompressibility of the Madelung fluid, and nonlinear generalisations of Schrödinger and Klein-Gordon equations. The derived equations satisfy all conditions that are expected from a proper generalisation: simplification to their linear counterparts by a well-defined dynamical condition; Galilean and Lorentz invariance (respectively); and signifying only rays in the Hilbert space.


2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040007
Author(s):  
Gerard ’t Hooft

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.


2007 ◽  
Vol 05 (01n02) ◽  
pp. 157-167 ◽  
Author(s):  
THOMAS KESSEMEIER ◽  
THOMAS KRÜGER

Within the framework of a statistical interpretation of quantum mechanics, entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell's inequality Δ ≤ 2. How can these different viewpoints be reconciled? We first show that (non-)separability follows different laws to (non-)locality, and, moreover, it is much more difficult to characterize as long as the mostly employed operational rather than an ontic definition of separability is used. In consequence, (i) "entanglement" has two different meanings which may or may not be realized simultaneously on one and the same ensemble, and (ii) we have to disadvise the use of the common separability definition which is still employed by the majority of the physical community.


The probability density Π is calculated for quantum eigenstates near spatial boundaries of classically chaotic regions. By contrast with integrable systems, for which the classical Π diverges on classical boundaries, which are caustics, in chaotic systems the classical Π does not diverge but vanishes abruptly in a way that depends on the number of freedoms N ; the boundaries are anticaustics. Quantum mechanics softens anticaustics, to give Π in terms of a set of canonical diffraction patterns, one for each N ; these are studied in detail. The appropriate definition of Π involves averaging over eigenstates in an energy range larger than O ( h ) but smaller than O ( h ⅔ ) (where h is Planck’s constant), that is over a range of ∆ N states near the N th, where N 1-1 / N ≪ ∆ N ≪ N 1-⅔ N .


2006 ◽  
Vol 20 (11n13) ◽  
pp. 1496-1503
Author(s):  
B. C. SANCTUARY

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.


Synthese ◽  
2021 ◽  
Author(s):  
Jan Faye ◽  
Rasmus Jaksland

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.


Open Theology ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 325-341
Author(s):  
Marc A. Pugliese

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


2019 ◽  
Vol 17 (08) ◽  
pp. 1941003 ◽  
Author(s):  
Hans-Thomas Elze

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.


2011 ◽  
Vol 20 (05) ◽  
pp. 909-918 ◽  
Author(s):  
RODOLFO GAMBINI ◽  
LUIS PEDRO GARCÍA-PINTOS ◽  
JORGE PULLIN

In recent papers we put forth a new interpretation of quantum mechanics, colloquially known as "the Montevideo interpretation". This interpretation is based on taking into account fundamental limits that gravity imposes on the measurement process. As a consequence one has that situations develop where a reduction process is undecidable from an evolution operator. When such a situation is achieved, an event has taken place. In this paper we sharpen the definition of when and how events occur; more precisely we give sufficient conditions for the occurrence of events. We probe the new definition in an example. In particular we show that the concept of undecidability used is not "FAPP" (for all practical purposes), but fundamental.


Author(s):  
Nicholas Manton ◽  
Nicholas Mee

In this chapter, the mathematical machinery of quantum mechanics is further developed in order to address real-world 3-dimensional physics. 3-dimensional vector notation is used for quantum mechanical operators and the Schrödinger equation is presented in this notation. The density of states of a particle in a box is considered. The angular momentum operators are defined. The eigenfunctions of the Laplacian are found. The Schrödinger equation with a spherical potential is analysed and solved for a Coulomb potential. The spectroscopy of the hydrogen atom is discussed. The spin operators are introduced. The Stern–Gerlach experiment and the Zeeman effect are discussed. The quantum mechanics of identical particles is considered and fundamental particles are shown to behave as either bosons or fermions depending on their spin. The action and the Feynman path integral are shown to offer an alternative approach to quantum mechanics that elucidates the connection between quantum and classical physics.


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