Interpretation Of Quantum Mechanics Research Articles

Holistic Ensemble Interpretation of Quantum Mechanics and Bell’s Inequalities

The ensemble interpretation (EI) of quantum mechanics has been proposed by physicists and philosophers (e.g., A. Einstein, K. R. Popper, and A. Lande). However, it is not accepted widely among modern scientists. This is because the EI is regarded as a kind of the hidden variable theories. The scientists believe that the EI is inconsistent with violation of Bell's inequalities. The present paper points out that there are various types of the EI. Several of them can be consistent with the violation. The non-local type of the EI proposed by Shirai in 1998 is also consistent. We call it “holistic ensemble interpretation (HEI).” The non-locality in the HEI includes a temporal non-locality (i.e., a future dependence), implying that the present distributions depend on the future conditions. The concept of the future dependence would be so controversial that we discuss it deeply in the latter half of the paper. Many scientists may think of it as a doubtful concept, because it disagrees with the concept of “free will.” However, there are several reasons why we should consider the future dependence.

Философия науки. Интервью с Бригиттой Фалькенбург

Professor Dr. Brigitte Falkenburg is one of the leading philosophers of science, a representative of the German school of philosophy of science. She wrote or edited about twenty books, and published more than hundred articles on the most topical issues of philosophy of science, philosophy of physics and philosophy of consciousness. Her work is attractive for its clarity, precision and depth of scientific and philosophical analysis. Some of her prominent books include: “Particle metaphysics: A critical account of subatomic reality” (2007), “Kant’s cosmology: From the Pre-Critical System to the Antinomy of Pure Reason” (2020) etc. In this interview, Prof. Falkenburg talks about her career path, main directions of her research, her books and new projects. Topics such as neo-Kantian philosophy of physics, scientific realism, interpretations of quantum mechanics, reality of virtual particles, the hard problem of consciousness, inductive metaphysics, the limits of scientific knowledge and others are discussed.

Дискретность пространства и ее следствия

Based on the general principle of the unity of the nature of interacting entities and the principle of the relativity of motion, as well as following the requirement of an indissoluble and conditioning connection of space and time, the model of a discrete space-time consisting of identical interacting particles is proposed as the most acceptable one. We consider the consequences of the discreteness of space, such as: the occurrence of time quanta, the limiting speed of signal propa­gation, and the constancy of this speed, regardless of the motion of the reference frame. Regularly performed acts of particles of space-time (PST) interaction en­sure the connectivity of space, set the quantum of time and the maximum speed – the speed of light. In the process of PST communication, their mixing occurs, which ensures the relativity of inertial motion, and can also underlie quantum uncertainty. In this case, elementary particles are spatial configurations of an excited “lattice” of PST, and particles with mass must contain loop struc­tures in their configuration. A new interpretation of quantum mechanics is pro­posed, according to which the wave function determines the probability of de­struction of a spatial configuration (representing a quantum object) in its corresponding region, which leads to the contraction of the entire structure to a given, detectable component. Particle entanglement is explained by the appear­ance of additional links between the PST – the appearance of a local coordinate along which the distance between entangled objects does not increase. It is shown that the movement of a body should lead to an asymmetry of the tension of the bonds between the PST – to the asymmetry of its effective gravity, the es­tablishment of which is one of the possibilities for experimental verification of the proposed model. It is shown that the constancy of the speed of light in a vac­uum and the appearance of relativistic effects are based on ensuring the connec­tivity of space-time, i.e. striving to prevent its rupture.

An exploration of a special case in the relationship between Fisher information and quantum potential in the causal interpretation of quantum mechanics

Fisher information is a cornerstone of both statistical inference and physical theory, leading to debate about whether its latter role is active or passive. Motivated by connections between Fisher information, entropy, and the quantum potential in the de Broglie–Bohm causal interpretation of quantum mechanics, the purpose of this article is to derive the position probability density when there a is a close and ubiquitous bonding of Fisher information and quantum potential. This is done by exploring a case in which a particle moves in a straight line and the integrands in Fisher information and expected quantum potential are proportional. It is found that in this case the probability density given by the Schrodinger wave equation has a Laplace distribution and that quantum potential is a negative constant at all points and times. It is noted that the rate of change of the entropy of the particle is bounded above by a limit that is proportional to the square roots of both Fisher information and the absolute value of quantum potential. Unlike Fisher information, quantum potential is a measure of a real physical potential, and it is proposed that it is quantum potential that puts an upper bound on the rate of change of the particle’s entropy and that, being negative in this case, may also act to contain the particle on its straight-line path. It is suggested that Fisher information does not have an active role in the physics, at least in this case, and only provides information about entropy.

Fuzzy Logic in the Quantum Mechanical Worldview; Related to Zadeh, Wittgenstein, Moore, Saussure, Quine, Lewis Carroll, etc.

Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.

Many-Worlds Interpretation of Quantum Mechanics and Wave-Particle Dualism.

Based on the wave-particle duality and the principle of quantum superposition, it is shown that an elementary particle is an oscillator in which a periodic process of energy conversion takes place. Then, the transition from particle to wave, that is, the transition from one quantum state to another, is a simple change in the oscillator when the frame of reference is changed. Consequently, the many-worlds interpretation of quantum mechanics does not make sense, since there is one real Universe with elementary particles exhibiting wave and corpuscular properties.

Erratum to: An exploration of a special case in the relationship between Fisher information and quantum potential in the causal interpretation of quantum mechanics

On the last page of the article, there is a mistake in the first equation (QED).

Possibility of Geometrical Interpretation of Quantum Mechanics and Geometrical Meaning of “Hidden Variables”

Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in three-dimensional Euclidean space as its topological defect having stochastic and wave-corpuscular properties of quantum particle. All possible deformations (homeomorphisms) of closed topological manifold play the role of “hidden variables”, responsible for statistical character of the theory.

The Quantum Handshake: An Electric Charge/Transactional Interpretation of the Single Electron Double-Slit Experiment

A new and falsifiable realist interpretation of quantum mechanics is examined in relation to the sum over histories concept, pilot wave theory and the many-worlds interpretation. This electric charge/transactional model explains how the single electron double-slit experiment produces extremely localized endpoints from diffracted wavicles, why these endpoints are scattered around the entire surface of the absorber screen, and why these points of contact result in the characteristic fringe pattern as they accumulate. Advanced waves and substantive electric charge effects in the double-slit experiment are postulated, then this hypothesis is supported by a quantitative analysis of electron emission in comparison to lightning. The wider implications if advanced waves and electric charge distribution prove to be significant factors in the double-slit experiment are discussed, including possible parallels with meteorological and neurological phenomena.

Does accepting Fuzzy Time-Particle interpretation of Quantum Mechanics, refute the other interpretations? (Is fuzziness of time checkable experimentally?)

Does accepting Fuzzy Time-Particle interpretation of Quantum Mechanics, refute the other interpretations? (Is fuzziness of time checkable experimentally?)

Indistinguishability and Counting: Teaching the role of different interpretations in Quantum Mechanics

The theme of indistinguishability in the context of Quantum Mechanics as opposed to a distinguishability in the context of Classical Mechanics has been treated for almost a century in terms of an essential difference between the way of counting in Quantum and Classical Mechanics. Such differences are based on the adoption of the principles of Heisenberg, Duality and Complementarity. In this work, we show that it is possible to avoid such considerations and derive the same results considering only the Correspondence Principle. This is done considering that, in the classic context, the quantum discrete energy levels become continuous or almost continuous. From these results, we indicate how to develop a discussion within the scope of teaching Quantum Mechanics that involves such principles and concepts and possible comparisons, working on ideas related to the interpretation of Quantum Mechanics with regard to this phenomenon, rarely developed in traditional courses.

Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

This paper intends to show how the fabled violation of Bell’s inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect. I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt. Designed to assess consequences of Einstein’s principle of local realism, the inequality pertains to a linear combination of four polarization products on the same pair of photons arising in a gedankenexperiment. My assessment displays that in this context, the summands of the relevant CHSH quantity s(λ) inhere four symmetric functional relations which have long been neglected in analytic considerations. Its expectation E[s(λ)] is not the sum of four “marginal” expectations from a joint distribution, as quantum theory explicitly avoids such a specification. Rather, I show that E[s(λ)] has four distinct representations as the sum of three expectations of polarization products plus the expectation of a fourth which is restricted to equal a function value determined by the other three. Analysis using Bruno de Finetti’s fundamental theorem of prevision (FTP) yields only a bound for E(s) within (1.1213,2] , surely not at all as is commonly understood. I exhibit slices of the 4-dimensional polytope of joint P++ probabilities actually motivated by quantum theory at the four stipulated angle settings, as it passes through 3-dimensional space. Bell’s inequality is satisfied everywhere within the convex hull of extreme distributions cohering with quantum theoretic specifications, even while in keeping with local realism. Aspect’s proposed “estimation” of E(s) near to is based on polarization products from different photon pairs that do not have embedded within them the functional relations inhering in the relevant gedankenexperiment. When one actively embeds the restrictions into Aspect’s estimation procedure, it yields an estimate of 1.7667, although this is not and cannot be definitive. While my analysis supports the subjectivist construction of probability as clarifying issues relevant to the interpretation of quantum theory, the error resolved herein is purely mathematical. It pertains to the reconsideration of Bell violation irrespective of one’s attitude toward the meaning of probability.

Understanding Quantum Theory

There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are: Classical ontology, Indeterminism, Probability, Predictions, The necessity of classical concepts, Minimal interpretation, Lattice, Physical objects, Alternatives to quantum theory?, Measurement, Realism. One of the main points of this paper is the role of predictions in understanding any theory of physics.

Quantum Mechanical Postulates towards Realization of Artificial Wisdom on Incorporating Desire in Intelligence: A Hypothetical Study

This paper is a hypothetical study to present postulates to have mathematical formulation towards realization of artificial wisdom. On referring quantum mechanics (QM) a mathematical foundation of wisdom is being defined to have the wisdom machine that can work like creative human. Creation may be defined as the desire to have new. Wisdom is differentiated from intelligence on adding desire. Desire is defined as something more than need on encompassing knowledge of self and unbiased reasoning. Each component of desire has an embedded part that is defined as hallucination need (defined as wandering of mind around unreal, acting with attachments, having deluded mind with egoism, performing as foolish follower). This research is viewing wisdom as the tool-kit to realize the “Survival of the fittest.” That is wisdom allows developing own-self on desire base. QM allows probabilistic approximation of multiple interacting events. Human behavior and creativity is a product of multiple events occurring simultaneously and/or in cascade with mutual interferences. Quantum mechanical interpretation of human behavior may be possible on describing it with dual aspects of desire (conscious or the real need and unconscious or the hallucination need) and uncertainties in simultaneous measurement of them. This paper is presenting nine postulates. These postulates and more to develop in future research may make it possible to mathematically encode human wisdom of creativity, so that there may be artificial wisdom.

Foundations of the Quaternion Quantum Mechanics.

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the past hypothesis, PH) to account for the temporal asymmetry. In this article, I show that the PH also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce ‘density-matrix realism’, the thesis that the quantum state of the universe is objective and impure. This stands in sharp contrast to wave-function realism, the thesis that the quantum state of the universe is objective and pure. Second, I suggest that the PH is sufficient to determine a natural density matrix, which is simple and unique. This is achieved by what I call the ‘initial projection hypothesis’: the initial density matrix of the universe is the (normalized) projection onto the PH-subspace (in the Hilbert space). Third, because the initial quantum state is unique and simple, we have a strong case for the nomological thesis: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, theoretical unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement.

ONE-PARTICLE WAVE FUNCTIONS IN THE RELATIONAL PARADIGM

We discuss a quantum description of free particles in pseudo-Finslerian momentum spaces appearing in one of relational approaches to physics and geometry of space-time. It is shown that, for wave functions of such particles, we can define an invariant unitary scalar product which ensures the standard quantum mechanical probabilistic interpretation. As the simplest example, the description of a spinless particle is considered.

The Montevideo Interpretation: How the Inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem

We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.

Realism and causality. I. Pilot wave and retrocausal models as possible facilitators

Of all basic principles of classical physics, realism should arguably be the last to be given up when seeking a better interpretation of quantum mechanics. We examine the de Broglie-Bohm pilot wave theory as a well developed example of a realistic theory. We present three challenges to a naive reading of pilot-wave theory, each based on a system of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges can be answered. However this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function as if they were particles, and conversely travel through particles as if they were waves. More generally, the "particles" of pilot wave theory are led by the guidance equation to move in ways no classical particle would, involving apparent violations of the principles of inertia and momentum conservation.We next argue that the aforementioned cost can be avoided within a retrocausal model. In the proposed version of the pilot wave theory, the particle is guided by a combination of advanced and retarded waves. The resulting account for quantum physics seems to have greater heuristic power, it demands less damage to intuition, and moreover provides some general hints regarding spacetime and causality. This is the first of two papers. In the second [1] we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can coexist with a strict irreversibility of causal processes.

Husserl, the mathematization of nature, and the informational reconstruction of quantum theory

As is well known, the late Husserl warned against the dangers of reifying and objectifying the mathematical models that operate at the heart of our physical theories. Although Husserl’s worries were mainly directed at Galilean physics, the first aim of our paper is to show that many of his critical arguments are no less relevant today. By addressing the formalism and current interpretations of quantum theory, we illustrate how topics surrounding the mathematization of nature come to the fore naturally. Our second aim is to consider the program of reconstructing quantum theory, a program that currently enjoys popularity in the field of quantum foundations. We will conclude by arguing that, seen from this vantage point, certain insights delivered by phenomenology and quantum theory regarding perspectivity are remarkably concordant. Our overall hope with this paper is to show that there is much room for mutual learning between phenomenology and modern physics.