Interpretation Of Quantum Mechanics Research Articles

Does Quantum Mechanics Require “Conspiracy”?

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.

Theoretical derivation of Planck’s constant based on brownian motion model and uncertainty relation

AbstractIn stochastic mechanics, one of the interpretations of realistic quantum mechanics, the Schrödinger equation can be derived by assuming the Brownian motion (BM) of minute particles. In this study, we theoretically derive Planck’s constant (h), a fundamental constant of quantum physics, by assuming same BM. Einstein investigated the BM of a resonator caused by photons in a black body; meanwhile, in this study, BM is considered to be caused by the particle and wave natures of light. As a result, as the functional form of h,$${h}_{N}=\frac{4\pi {e}^{2}}{c{\varepsilon }_{0}}\frac{1}{\beta }$$ h N = 4 π e 2 c ε 0 1 β (e: elementary charge, $${\varepsilon }_{0}$$ ε 0 : permittivity, c: speed of light) was derived, where the undetermined coefficient $$\frac{\beta }{2}$$ β 2 represents the probability that the interaction between electrons and electromagnetic waves becomes particle-like absorption in one cycle of oscillation. The theoretical value of h was calculated to be $$\frac{4\pi {e}^{2}}{c{\varepsilon }_{0}}\pi \sqrt{3}$$ 4 π e 2 c ε 0 π 3 by obtaining β from the transition conditions of the BM model and uncertainty relation. This theoretical value is within 0.3% of the most recent value of h. Besides, Nelson’s assumed diffusion coefficient in the stochastic mechanics, which is essential in obtaining Schrödinger’s equation, was proved to be obtained from the BM model and the uncertainty relation. This finding and the conclusion that the Planck’s constant can be mathematically derived, provide support for Nelson’s stochastic mechanics.

Quantum cosmology in teleparallel gravity with a boundary term

We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity: one wherein an arbitrary function of the boundary term, namely B, is present in the action, and in the other model, a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler–DeWitt (WDW) equations of the models. To correspond to the comprehensive classical and quantum levels, in the second model, we propose an appropriate initial condition for the wave packets and observe that they closely adhere to the classical trajectories and reach their peak. We quantify this correspondence using the de Broglie–Bohm interpretation of quantum mechanics. According to this proposal, the classical and Bohmian trajectories coincide when the quantum potential vanishes along the Bohmian paths. Furthermore, we apply the de-parameterization technique to our model in the realm of the problem of time in quantum cosmological models based on the WDW equation, utilizing the global internal time denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}, which represents a scalar field.

The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations

The Many-Worlds Interpretation of Quantum Mechanics: Current Status and Relation to Other Interpretations

Prime Matter and the Quantum Wavefunction

Prime matter plays an indispensable role in Aristotle’s philosophy, enabling him to avoid the pitfalls of both naïve Platonism and nominalism. Prime matter is best thought of as a kind of infinitely divisible and atomless bare particularity, grounding the distinctness of distinct members of the same species. Such bare particularity is needed in symmetrical situations, like a world consisting of indistinguishable Max Black spheres. Bare particularity is especially important in modern physics, given the homogeneity and isotropy of space. With the importance of fields in classical, relativistic, and quantum physics, we have good reason to prefer something like Aristotle’s continuous, infinitely divisible matter over indivisible particles. Mass and energy in relativistic physics also points in the direction of prime matter as the enduring substrate of these quantities. Recent work on Aristotelian interpretations of quantum mechanics, further underscores the contemporary relevance of prime matter.

Interacting quantum trajectories for particles with spin 1/2

In recent decades, the de Broglie-Bohm or ‘pilot wave’ interpretation of quantum mechanics–especially its concept of the ‘quantum trajectory’–has inspired a plethora of computational methods in molecular and chemical physics. One particularly promising subclass of such methods are the ‘interacting quantum trajectory’ (IQT) methods, for which an ensemble of trajectories is propagated independently of–and without any recourse to–an underlying wavefunction. In this work, an IQT version of the Pauli equation is developed–enabling spin to be incorporated into IQT theories for the first time, to the authors' knowledge. The new trajectory-based dynamical equations are then used to solve two iconic quantum problems involving spin: the ‘quantum spin flipper’, and the Stern-Gerlach experiment.

Toward local Madelung mechanics in spacetime

AbstractIt has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating the momentum into average and symmetric parts, and kinetic energy into classical kinetic and quantum potential parts. The two types of momentum naturally give rise to a single classical kinetic energy density, which contains the expected kinetic energy, even for stationary states, and we define the reduced quantum potential as the remaining part of the quantum kinetic energy density. We treat the quantum potential as a novel mode of internal energy storage within the fluid particles, which explains most of the nonclassical behavior of the Madelung fluid. For example, we show that in tunneling phenomena, the quantum potential negates the barrier so that nothing prevents the fluid from flowing through. We show how energy flows and transforms in this model, and that enabling local conservation of energy requires defining a quantum potential energy current that flows through the fluid rather than only flowing with it. The nonrelativistic treatment generally contains singularities in the velocity field, which undermines the goal of local dynamics, but we expect a proper relativistic treatment will bound the fluid particle velocities at c.

Cellular automaton ontology, bits, qubits and the Dirac equation

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this with a classical Ising spin chain. It is shown that it can be related to the Weyl equation in the continuum limit. Yet, the model of discrete spins or bits unavoidably becomes a model of qubits by generating superpositions, if only slightly deformed. We study modifications of its signal velocity which, however, do not relate to mass terms. To incorporate the latter, we consider the Dirac equation in 1+1 dimensions and sketch an underlying discrete deterministic “necklace of necklaces” automaton that qualifies as ontological.

Geometric phases, Everett’s many-worlds interpretation of quantum mechanics, and wormholes

Geometric phases, Everett’s many-worlds interpretation of quantum mechanics, and wormholes

On the Copenhagen Interpretation of Quantum Measurement

We claim that quantum collapse, as per the Copenhagen interpretation of quantum mechanics, follows naturally from the energetics of measurement. We argue that a realistic device generates an interaction energy that drives a random walk in Hilbert space and generates the probabilistic interpretation of Born.

Solving Particle–Antiparticle and Cosmological Constant Problems

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space H with a positive definite metric; each physical quantity is defined by a self-adjoint operator in H; symmetry at the quantum level is defined by a representation of a real Lie algebra A in H such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit R→∞, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities (c,ℏ,R) are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if Λ=3/R2, i.e., Λ>0 and there is no freedom for choosing the value of Λ.

Quantum ontology without textbooks. Nor overlapping

In this paper, I critically assess two recent proposals for an interpretation-independent understanding of non-relativistic quantum mechanics: the overlap strategy (Fraser & Vickers, 2022) and the textbook account (Egg, 2021). My argument has three steps. I first argue that they presume a Quinean-Carnapian meta-ontological framework that yields flat, structureless ontologies. Second, such ontologies are unable to solve the problems that quantum ontologists want to solve. Finally, only structured ontologies are capable of solving the problems that quantum ontologists want to solve. But they require some dose of speculation. In the end, I defend the conservative way to do quantum ontology, which is (and must be) speculative and non-neutral.

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

Exploring Transformation in Flux-Like Pattern – A Review of The Chinese Biantong in Yijing

One of the central features of the _Yijing_ is its use of 陰陽 _yin-yang_ correlative cosmology, a fundamental concept in traditional Chinese philosophy. This cosmology involves the idea that all things in the universe are interconnected and interdependent, each possessing _yin_ (negative, feminine) and _yang_ (positive, masculine) energies. Moreover, these energies are constantly in flux and transformation, with their balance continually shifting. Bohm's wholeness, also known as Bohm's holomovement, is a concept developed by physicist David Bohm as part of his interpretation of quantum mechanics. According to Bohm, the universe is fundamentally interconnected and interdependent, with all aspects of the universe influencing and being influenced by one another. This interconnectedness is reflected in the behaviour of subatomic particles, which can exhibit non-local correlations that classical physics cannot explain. Bohm's wholeness is similar to other physics and philosophy theories that emphasise the universe's interconnectedness. For example, one such theory is non-dualism, which posits that there is no fundamental separation between the self and the universe and that the self is an expression of the underlying unity of all things. Finally, the concept of entanglement in quantum mechanics also suggests a fundamental interconnectedness between particles, with changes in the state of one particle instantaneously affecting the state of another particle, regardless of their spatial separation. The significance of 變通 _biantong_ in Chinese philosophy is explored in relation to _yin_ and _yang_ energies constantly transforming and balancing each other in a continuous cycle. Similarly, Bohm's holomovement concept highlights the universe's interconnectedness and constant flux. The flux-like variables provide insights into the system's macroscopic and microscopic details, where transformation and change are fundamental aspects of reality. The probabilistic nature of human affairs and subatomic particles implies that their properties continually change and transform in response to the surrounding environment, reflecting the integral interdependence of all things. This paper emphasizes the significance of transformation and changes in comprehending reality by examining the concepts of yin and yang energies, Bohm's wholeness, and flux-like variables. The dynamic and interconnected nature of the universe necessitates an understanding of this constant state of flux, whether on a macroscopic or microscopic scale. This knowledge is vital for understanding the behaviour of subatomic particles and the natural world.

A proof of Specker's principle.

Specker's principle, the condition that pairwise orthogonal propositions must be jointly orthogonal (or rather, the 'exclusivity principle' that follows from it), has been much investigated recently within the programme of finding physical principles to characterize quantum mechanics. Specker's principle, however, largely appears to lack a physical justification. In this paper, I present a proof of Specker's principle from three assumptions (made suitably precise): the existence of 'maximal entanglement', the existence of 'non-maximal measurements' and no-signalling. I discuss these three assumptions and describe canonical examples of non-Specker sets of propositions satisfying any two of them. These examples display analogies with various approaches to the interpretation of quantum mechanics, including retrocausation. I also discuss connections with the work of Popescu & Rohrlich. The core of the proof (and the main example violating no-signalling) is illustrated by a variant of Specker's tale of the seer of Nineveh, with which I open the paper. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

An Examination of Two Competing Interpretations of Quantum Mechanics with a Critique of the Kochen-Specker Theorem

There is ongoing discourse in philosophical and physics literature about whether the probabilistic essence of quantum mechanics indicates that deterministic interpretations of nature must be false. In 1967 two mathematicians, Simon Kochen and Ernst Specker, developed a mathematical theorem to the effect that particles do not have well-defined property values at a given time. A logical consequence of this is that there can be no well-defined hidden variables responsible for the outcomes of mysterious quantum behaviors. The theorem is thus fatal to the many deterministic interpretations of quantum mechanics that assume hidden variables, including pilot wave mechanics, a quantum theory developed by Louis de Broglie and David Bohm a few decades prior to the formulation of the Kochen-Specker Theorem. The purpose of this essay is to evaluate the legitimacy of the logical basis of Kochen’s and Specker’s argument considering its severe implications. It is concluded that Kochen and Specker do not provide sufficient evidence that deterministic theories must fail, due to their misinterpretation of the axioms on which hidden variable theories rely. This paper also finds that pilot wave mechanics is mathematically successful while remaining consistent with the deterministic understanding of broader physics and deserving of more serious consideration as a quantum theory. Above all it is emphasized that the nonsensicality of absolute randomness and indeterminism should be acknowledged, and theorems purporting to prove their existence should be critically examined, for such a discovery would undermine the legitimacy of logic itself.

Ozawa’s Intersubjectivity Theorem as Objection to QBism Individual Agent Perspective

QBism’s foundational statement that “the outcome of a measurement of an observable is personal” is in the straight contraversion with Ozawa’s Intersubjectivity Theorem (OIT). The latter (proven within the quantum formalism) states that two observers, agents within the QBism terminology, performing joint measurements of the same observable A on a system S in the state ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi $$\\end{document} should get the same outcome A=x.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=x.$$\\end{document} In Ozawa’s terminology, this outcome is intersubjective and it can’t be treated as personal. This is the strong objection to QBism which can’t survive without updating its principles. The essential aspect in understanding of the OIT-impact on QBism’s foundations takes the notion of quantum observable. This paper comprises the complementary discussion highlighting the difference between the accurate, von Neumann, and inaccurate, noisy, quantum observables which are represented by PVMs and POVMs respectively. Moreover, we discuss the OIT-impact on the Copenhagen interpretation of quantum mechanics.

The groupoidal picture of quantum mechanics

The basic ingredients of the groupoid interpretation of Quantum Mechanics are discussed. Starting with the motivation to consider measure groupoids as the appropriate statistical and kinematical setting to describe quantum mechanical systems, the algebra of observables of the system is constructed as the von Neumann algebra of the groupoid. The interpretation of the theory for classical systems is briefly analysed. As a final application of these ideas, Feynman's sum-over-histories interpretation of the theory is discussed in the groupoid picture.

Probabilistic Interpretation of Entrepreneurial Opportunity Using the Many-Worlds Model

This research engages with the uncertainties and unknowable in entrepreneurship with literature on the philosophy of quantum mechanics in an analogical way. Often characterised as a journey into an uncertain future, entrepreneurship stands out as a dynamic and unpredictable domain driven by a compelling and indefinable force. This research’s central argument revolves around the notion that within the entrepreneurial landscape, many latent propensities exist, each carrying its distinct probability of manifesting into various outcomes. Unlike a deterministic process with a single predetermined outcome, entrepreneurship is a complex interplay of potentialities. To capture this multifaceted perspective, we leverage the principles and formalism of quantum mechanics, renowned for its emphasis on potentiality over actuality until subjected to observation and action. This philosophical framework describes the inherent potentialities embedded within entrepreneurial opportunities. This study introduces a groundbreaking Many-Worlds model inspired by the interpretations of quantum mechanics. In this model, the act of observation serves as a catalyst, unravelling a spectrum of potential outcomes, each characterised by its probability. These potentialities materialise based on entrepreneurs’ intentional actions and decisions, reflecting their commitment to shaping the future of their ventures. In summary, our study bridges the gap between entrepreneurship and quantum mechanics by proposing a novel framework that portrays entrepreneurship as an exploration of a quantum-like landscape of possibilities. By emphasising the significance of intentionality and action, our research sheds new light on entrepreneurship’s dynamic and unpredictable nature, illustrating how entrepreneurs play a pivotal role in transforming potential into reality.

Empirical analysis of quantum mechanics and harmonic applications

A brief review of the main ideas (interpretations) of quantum mechanics is given. Each of the considered interpretations contains a number of disputable provisions, the discussion of which allows us to develop our own understanding of the mechanism of paradoxical quantum phenomena. The article is addressed to all students who study the concepts of modern natural science, and to all readers interested in the questions what is the reality beyond the quantum mechanical experiment or if our perception really shapes the physical world in some way. The author believes that the development of quantum information technologies is impossible without answering these fundamental questions.