Version Of Quantum Mechanics Research Articles

Remarks on quantum mechanics and non-reflexive logic

In this paper we discuss and outline a version of non-relativistic quantum mechanics based on a new non-reflexive logic, where the basic entities (elementary particles) lack identity conditions. Some relationships with quantum field theories are also sketched.

An algebraic formulation of nonassociative quantum mechanics

We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop Gel’fand–Naimark–Segal constructions. We describe Heisenberg and Schrödinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra.

Newton's Off-Center Circular Orbits and the Magnetic Monopole

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic monopole in the inverse stereographically projected problem. One finds also a phenomenological correspondence with that of the linearly damped Kepler model. The presence of the monopole field deforms the symmetry algebra by a central extension, and the quantum mechanical version of this algebra reveals a number of zero modes equal to that counted using the index theorem of elliptic operators.

According to Classical Logic, the Current Version of Quantum Mechanics is Inconsistent and 'Explosive'

According to Classical Logic, the Current Version of Quantum Mechanics is Inconsistent and 'Explosive'

The effects of the covariant generalized uncertainty principle on quantum mechanics

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we considered a covariant version of the GUP to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy–momentum dispersion relation was modified. Starting with the modified dispersion relation, the corrections to the wave function were obtained and the problems of the particle in a box and the hydrogen atom were revisited. Considering the minimal time may be an interesting new topic, which is not widely studied before. It may lead to new results that can open a new window into quantum gravity.

Does science need intersubjectivity? The problem of confirmation in orthodox interpretations of quantum mechanics

Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of ‘orthodox interpretations,’ which includes QBism, neo-Copenhagen interpretations, and some versions of relational quantum mechanics. We demonstrate that intersubjectivity fails in radical ways in these approaches, and we explain why intersubjectivity matters for empirical confirmation. We take a detailed look at the way in which belief-updating might work in the kind of universe postulated by an orthodox interpretation, and argue that observers in such a universe are unable to escape their own perspective in order to learn about the structure of the set of perspectives that is supposed to make up reality according to these interpretations. We also argue that in some versions of these interpretations it is not even possible to use one’s own relative frequencies for empirical confirmation. Ultimately we conclude that it cannot be rational to believe these sorts of interpretations unless they are supplemented with some observer-independent structure which underwrites intersubjective agreement in at least certain sorts of cases.

Relativistic composite-particle theory of the gravitational form factors of the pion: Quantitative results

We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain the gravitational form factors of the pion in a common approach to its electroweak and gravitational properties. In the preceding work [Phys. Rev. D 103, 014029 (2021)], we formulated the mathematical background, presented the principal scheme of calculation and testified the obtained qualitative results to satisfy the general constraints given by the principles of the theory of hadron structure. In the present work, we give the detailed calculation of the gravitational form factors in the large range of momentum transfer, their static limits, and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we take into account the gravitational structure of the constituent quarks. We show that the results are almost insensitive to the type of model two-quark wave function in a close analogy to the case of the pion electromagnetic form factor. We present a correct calculation of the form factor $D$ and corresponding matrix element of the energy-momentum tensor, going beyond the scope of the modified impulse approximation. Most of the parameters that we use for the calculation had been fixed even earlier in our works on the pion electromagnetic form factors. The only free parameter is the $D$-term of the constituent quark, which we fix by fitting the result for the slope at zero of the normalized to pion $D$-term form factor $D$ of the pion, to a chosen experimental value.

Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables

In 1992, Scholtz et al. (Ann. Phys., 213 (1992) 74) showed that a set of non-Hermitian operators can represent observables of a closed unitary quantum system, provided only that its elements are quasi-Hermitian (i.e., roughly speaking, Hermitian with respect to an ad hoc inner-product metric). We show that such a version of quantum mechanics admits a simultaneous closed-form representation of the metric and of the observables , in terms of auxiliary operators Z k with . At N = 2 the formalism degenerates to the well-known quantum mechanics using factorized metric , where is parity and where is charge.

Complex eigenvalues in Kuryshkin-Wodkiewicz quantum mechanics

One of the possible versions of quantum mechanics, known as Kuryshkin-Wodkiewicz quantum mechanics, is considered. In this version, the quantum distribution function is positive, but, as a retribution for this, the von Neumann quantization rule is replaced by a more complicated rule, in which an observed value AA is associated with a pseudodifferential operator O^(A){\hat{O}(A)}. This version is an example of a dissipative quantum system and, therefore, it was expected that the eigenvalues of the Hamiltonian should have imaginary parts. However, the discrete spectrum of the Hamiltonian of a hydrogen-like atom in this theory turned out to be real-valued. In this paper, we propose the following explanation for this paradox. It is traditionally assumed that in some state ψ{\psi} the quantity AA is equal to λ{\lambda} if ψ{\psi} is an eigenfunction of the operator O^(A){\hat{O}(A)}. In this case, the variance O^((A-λ)2)ψ{\hat{O}((A-\lambda)2)\psi} is zero in the standard version of quantum mechanics, but nonzero in Kuryshkins mechanics. Therefore, it is possible to consider such a range of values and states corresponding to them for which the variance O^((A-λ)2){\hat{O}((A-\lambda)2)} is zero. The spectrum of the quadratic pencil O^(A2)-2O^(A)λ+λ2E^{\hat{O}(A2)-2\hat{O}(A)\lambda + \lambda 2 \hat{E}} is studied by the methods of perturbation theory under the assumption of small variance D^(A)=O^(A2)-O^(A)2{\hat{D}(A) = \hat{O}(A2) - \hat{O}(A) 2} of the observable AA. It is shown that in the neighborhood of the real eigenvalue λ{\lambda} of the operator O^(A){\hat{O}(A)}, there are two eigenvalues of the operator pencil, which differ in the first order of perturbation theory by ±i⟨D^⟩{\pm i \sqrt{\langle \hat{D} \rangle}}.

Collapses without measurements

In quantum mechanics the state vector evolves in a predictable and continuous way, according to the Schrödinger equation; only if a measurement takes place, the Schrödinger evolution is interrupted. Transitions between stationary states (transitions BSS) are accounted for time dependent perturbation theory (TDPT). It is often ignored that this theory requires measurements. As measurements demand either the intervention of an observer or the interaction between the quantum system with a measuring device, billions of observers and/or measuring devices would be necessary at every small corner of the universe where transitions BSS take place. Nevertheless, there is no evidence of their existence. We are thus led to conclude that transitions BSS are the result of causes different from the measurements required in TDPT. In the spontaneous projection approach, the version of quantum mechanics which we uphold, collapses to the stationary states result from the tendency of the system to jump to the eigenstates of the constants of the motion.

Everett, Lotteries, and Fairness

Defenders of the Everettian version of quantum mechanics generally hold that it makes no difference to what we ought to do. This paper will argue against this stance, by considering the use of lotteries to select the recipients of indivisible goods. On orthodox non-Everettian metaphysics this practice faces the objection that only actual and not probable goods matter to distributive justice. However, this objection loses all force within Everettianism. This result should be of interest to both philosophers of physics and to ethicists.

Everettian Quantum Mechanics and the Metaphysics of Modality

Abstract This article sits at a point of intersection between the philosophy of physics and the metaphysics of modality. There are clear similarities between Everettian quantum mechanics and various modal metaphysical theories, but there have hitherto been few attempts at exploring how the two topics relate. In this article, I build on a series of recent papers by Wilson ([2011], [2012], [2013]), who argues that Everettian quantum mechanics’ connections with traditional modal metaphysics are vital in defending it against objections. I show that Wilson’s preferred version of Everettian quantum mechanics has two problems. First, it is unable to account for the contingency of various intuitively contingent modal claims. Second, it fails to yield intuitive truth values on modal claims about the number of branches in a given Everettian multiverse. Since modal claims about branch number are instrumental in decision-theoretic solutions to Everettian quantum mechanics’ problem(s) with probability, this second problem has wider dialectical implications. I suggest amendments to the underlying metaphysics that overcome these problems. The result is a more robust version of Everettian quantum mechanics.

On the effect of decoherence on quantum tunnelling

This work proposes a series of quantum experiments that can, at least in principle, allow for examining microscopic mechanisms associated with decoherence. These experiments can be interpreted as a quantum-mechanical version of non-equilibrium mixing between two volumes separated by a thin interface. One of the principal goals of such experiments is in identifying non-equilibrium conditions when time-symmetric laws give way to time-directional, irreversible processes, which are represented by decoherence at the quantum level. The rate of decoherence is suggested to be examined indirectly, with minimal intrusions—this can be achieved by measuring tunnelling rates that, in turn, are affected by decoherence. Decoherence is understood here as a general process that does not involve any significant exchanges of energy and governed by a particular class of the Kraus operators. The present work analyses different regimes of tunnelling in the presence of decoherence and obtains formulae that link the corresponding rates of tunnelling and decoherence under different conditions. It is shown that the effects on tunnelling of intrinsic decoherence and of decoherence due to unitary interactions with the environment are similar but not the same and can be distinguished in experiments.

Observing a superposition

The bare theory is a no-collapse version of quantum mechanics which predicts certain puzzling results for the introspective beliefs of human observers of superpositions. The bare theory can be interpreted to claim that an observer can form false beliefs about the outcome of an experiment which produces a superpositional result. It is argued that, when careful consideration is given to the observer’s belief states and their evolution, the observer does not end up with the beliefs claimed. This result leads to questions about whether there can be any allure for no-collapse theories as austere as the bare theory.

Pion gravitational form factors in a relativistic theory of composite particles

We extend our relativistic theory of electroweak properties of composite systems to describe simultaneously the gravitational form factors of hadrons. The approach is based on a version of the instant-form relativistic quantum mechanics and makes use of the modified impulse approximation. We exploit the general method of the relativistic invariant parametrizaton of local operators to write the energy-momentum tensor of a particle with an arbitrary spin. We use the obtained results to calculate the gravitational form factors of the pion assuming point-like constituent quarks. All but one parameters of our first-principle model were fixed previously in works on electromagnetic form factors. The only free parameter, $D_{q}$, is a characteristic of the gravitational form factor of a constituent quark. The derived form factors of the pion satisfy the constraints given by the general principles of the quantum field theory of hadron structure. The calculated gravitational form factors and gravitational mean-square radius are in a reasonable agreement with known results.

Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and c → ∞ Limit

We present the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg–Weyl symmetry with position and momentum operators transforming as Minkowski four-vectors. The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation, with the matching representation of an extension of the group C*-algebra giving the algebra of observables. The key feature is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. The language of pseudo-Hermitian quantum mechanics is adopted for a clear illustration of the aspect, with a metric operator obtained as really the manifestation of the Minkowski metric on the space of the state vectors. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product. The associated covariant harmonic oscillator Fock state basis has all the standard properties in exact analog to those of a harmonic oscillator with Euclidean position and momentum operators. Galilean limit and the classical limit are retrieved rigorously through appropriate symmetry contractions of the algebra and its representation, including the dynamics described through the symmetry of the phase space.

Susy for Non-Hermitian Hamiltonians, with a View to Coherent States

We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.

Quantum Mechanical Coherence of K+ Ion Wave Packets Increases Conduction in the KcsA Ion Channel

We simulate the transmission of K+ ions through the KcsA potassium ion channel filter region at physiological temperatures, employing classical molecular dynamics (MD) at the atomic scale together with a quantum mechanical version of MD simulation (QMD), treating single ions as quantum wave packets. We provide a direct comparison between both concepts, embedding the simulations into identical force fields and thermal fluctuations. The quantum simulations permit the estimation of coherence times and wave packet dispersions of a K+ ion over a range of 0.5 nm (a range that covers almost 50% of the filter domains longitudinal extension). We find that this observed extension of particle delocalization changes the mean orientation of the coordinating carbonyl oxygen atoms significantly, transiently suppressing their ‘caging action’ responsible for selective ion coordination. Compared to classical MD simulations, this particular quantum effect allows the K+ ions to ‘escape’ more easily from temporary binding sites provided by the surrounding filter atoms. To further elucidate the role of this observation for ion conduction rates, we compare the temporal pattern of single conduction events between classical MD and quantum QMD simulations at a femto-sec time scale. A finding from both approaches is that ion permeation follows a very irregular time pattern, involving flushes of permeation interrupted by non-conductive time intervals. However, as compared with classical behavior, the QMD simulation shortens non-conductive time by more than a half. As a consequence, and given the same force-fields, the QMD-simulated ion current appears to be considerably stronger as compared with the classical current. To bring this result in line with experimentally observed ion currents and the predictions based on Nernst–Planck theories, the conclusion is that a transient short time quantum behavior of permeating ions can successfully compromise high conduction rates with ion selectivity in the filter of channel proteins.

On the Hellmann-Feynman theorem in statistical mechanics

In this paper we develop the Hellmann-Feynman theorem in statistical mechanics without resorting to the eigenvalues and eigenvectors of the Hamiltonian operator. Present approach does not require the quantum-mechanical version of the theorem at T=0 and bypasses any discussion about degenerate states.

-extension of double-graded supersymmetric and superconformal quantum mechanics

In the recent paper (Bruce and Duplij 2019 (arXiv:1904.06975 [math-ph])), Bruce and Duplij introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an extension of Lie superalgebraic nature of SQM to a -graded superalgebra. In this work, we propose an extension of Bruce–Duplij model to higher values of . Furthermore, it is shown that our construction of double-graded SQM is a special case of the method which converts a given Lie superalgebra to a -graded superalgebra. By employing this method one may convert a model of superconformal mechanics to its double-graded version. The simplest example of double-graded superconformal mechanics is studied in some detail.