Measurement Problem In Quantum Mechanics Research Articles

Bohr and von Neumann on the universality of quantum mechanics: materials for the history of the quantum measurement process

The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.

Collapse of neutrino wave functions under Penrose gravitational reduction

Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose’s description of gravitational collapse which proposes a decoherence time τ determined through Egτ∼ℏ, where Eg is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is σν,x≤2×10−12 m. Published by the American Physical Society 2024

Mathematical modeling of consciousness based on the human language- An interpreting measurement problem in quantum mechanics

Mathematical modeling of consciousness based on the human language- An interpreting measurement problem in quantum mechanics

Enter by the Narrow Gate, for Getting New Perspective to Bring Modern Technology Into Order

One of the main causes of issues about the today’s situation of technology comes from a big mismatch between the new technology based on quantum mechanics (laws in the micro world) and the old perspective (mechanistic viewpoint in the macro world) for more than a half century. I explain this circumstance and show how to settle this problem by solving the so-called measurement problem of quantum mechanics. These give us a new perspective which unify the laws of macro and micro worlds and bring the current technology into order. To go this way would be to enter by the narrow gate.

On the Evolution of States in a Quantum-Mechanical Model of Experiments

Ideas and results in the quantum theory of experiments are reviewed. To fix ideas, a concrete example of indirect measurements, an experiment devised by Guerlin et al. (Nature 448(7156):889–893, 2007), and theoretical interpretations thereof (Bauer and Bernard, Phys Rev A 84(4):044103, 2011; Bauer et al., Ann H Poincaré 14:639–679, 2013) are recalled. Subsequently two important elements of the Copenhagen interpretation of quantum mechanics, viz. the von Neumann- and the Lüders measurement postulates, are recalled and rendered more precise. Next, a model originally proposed by Gisin et al. (Phys Rev Lett 52:1657–1660, 1984) is described and shown to imply these postulates. It is then used to provide a theoretical description of the experiment in Guerlin et al. (Nature 448(7156):889–893, 2007) involving a “Heisenberg cut” differing from the one invoked in (Bauer and Bernard, Phys Rev A 84(4):044103, 2011; Bauer et al., Ann H Poincaré 14:639–679, 2013; J Stat Phys 162:924–958, 2016). Some technical issues in the analysis of Gisin’s model are elaborated upon. The paper concludes with remarks on a general principle that implies a universal law governing the stochastic time evolution of states of individual physical systems featuring events and leading to a solution of the so-called measurement problem in quantum mechanics.

Natural Law, the modeling relation, and two roots of perspectivism

Scientific perspectivism, or perspectival realism, is a view according to which scientific knowledge is neither utterly objective nor independent of the world “as it is”, but always tied to some particular ways of conceptualization and interaction with Nature. In the present paper, I employ Robert Rosen’s concept of the modeling relation for arguing that there are two basic reasons why our knowledge of natural systems is perspectival in this sense. The first of these pertains to the dualism between a system and its environment, which is necessarily imposed by a scientist focusing on the former. The second pertains to the complexity of complex systems; a complex system understood as a system in which different kinds of causal entailments intertwine together. As I discuss in the paper besides developing the argument, perspectivism thus understood ties together several issues ranging from organicism to emergentism and to processual philosophy, and from the ceteris paribus talk of biology to the measurement problem of quantum mechanics. I also discuss Rosen’s relational formalisms as a concrete example of how perspectival epistemology might directly suggest novel strategies and practices of doing theoretical science.

Measurement of a quantum system with a classical apparatus using ensembles on configuration space* *Contribution to the Special Collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’

Finding a physically consistent approach to modeling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical–quantum interactions which made use of the Koopman–von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.

Observability of spontaneous collapse in flavor oscillations and its relation to the [formula omitted] and [formula omitted] symmetries

Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations which, however, is not strong enough to be observed in the present accelerator facilities. In this Letter, we study how the violation of the CP symmetry in mixing changes the spontaneous collapse effect on flavor oscillations and its observability.

Search for Spontaneous Radiation from Wave Function Collapse in the Majorana Demonstrator.

The Majorana Demonstrator neutrinoless double-beta decay experiment comprises a 44kg (30kg enriched in ^{76}Ge) array of p-type, point-contact germanium detectors. With its unprecedented energy resolution and ultralow backgrounds, Majorana also searches for rare event signatures from beyond standard model physics in the low energy region below 100keV. In this Letter, we test the continuous spontaneous localization (CSL) model, one of the mathematically well-motivated wave function collapse models aimed at solving the long-standing unresolved quantum mechanical measurement problem. While the CSL predicts the existence of a detectable radiation signature in the x-ray domain, we find no evidence of such radiation in the 19-100keV range in a 37.5kg-y enriched germanium exposure collected between December 31, 2015, and November 27, 2019, with the Demonstrator. We explored both the non-mass-proportional (n-m-p) and the mass-proportional (m-p) versions of the CSL with two different assumptions: that only the quasifree electrons can emit the x-ray radiation and that the nucleus can coherently emit an amplified radiation. In all cases, we set the most stringent upper limit to date for the white CSL model on the collapse rate, λ, providing a factor of 40-100 improvement in sensitivity over comparable searches. Our limit is the most stringent for large parts of the allowed parameter space. If the result is interpreted in terms of the Diòsi-Penrose gravitational wave function collapse model, the lower bound with a 95%confidence level is almost an order of magnitude improvement over the previous best limit.

Entanglement, inelastic scattering of particles and measurement problem in quantum mechanics

In this paper, a constructive definition of entanglement for nonidentical particles is given. It is shown that particles arising in the process of inelastic scattering are entangled with each other. This property is a consequence of the symmetry of fundamental interactions. Considering detectors of elementary particles, it was concluded that only inelastic scattering can be the basis of a measuring instrument. In the process of inelastic scattering, the measuring instrument can acquire information about the particle (system), while in the case of elastic scattering, it cannot. The nonlinearity of inelastic scattering naturally solves the measurement problem in quantum mechanics.

Measurement Problem in Quantum Mechanics and the Surjection Hypothesis

Starting with unitary quantum dynamics, we investigate how to add quantum measurements. Quantum measurements have four essential components: the furcation, the witness production, an alignment projection, and the actual choice decision. The first two components still lie in the domain of unitary quantum dynamics. The decoherence concept explains the third contribution. It can be based on the requirement that witnesses reaching the end of time on the wave function side and the conjugate one have to be identical. In this way, it also stays within the quantum dynamics domain. The surjection hypothesis explains the actual choice decision. It is based on a two boundary interpretation applied to the complete quantum universe. It offers a simple way to reduce these seemingly random projections to purely deterministic unitary quantum dynamics, eliminating the measurement problem.

Does Consciousness-Collapse Quantum Mechanics Facilitate Dualistic Mental Causation?

One of the most serious challenges (if not the most serious challenge) for interactive psycho-physical dualism (henceforth interactive dualism or ID) is the so-called ‘interaction problem’. It has two facets, one of which this article focuses on, namely the apparent tension between interactions of non-physical minds in the physical world and physical laws of nature. One family of approaches to alleviate or even dissolve this tension is based on a collapse solution (‘consciousness collapse/CC) of the measurement problem in quantum mechanics (QM). The idea is that the mind brings about the collapse of a superposed wave function onto one of its eigenstates. Thus, it is claimed, can the mind change the course of things without violating any law figuring in physical theory. I will first show that this hope is premature because energy and momentum are probably not conserved in collapse processes, and that even if this can be dealt with, the violations are either severe or produce further ontological problems. Second, I point out several conceptual difficulties for interactionist CC. I will also present solutions for those problems, but it will become clear that those solutions come at a high cost. Third, I shall briefly list some empirical problems which make life even harder for interactionist CC. I conclude with remarks about why no-collapse interpretations of QM don’t help either and what the present study has shown is the real issue for ID: namely to find a plausible integrative view of dualistic mental causation and laws of nature.

Nanomechanical test of quantum linearity

Spontaneous wavefunction collapse theories provide the possibility to resolve the measurement problem of quantum mechanics. However, the best experimental tests have been limited by thermal fluctuations and have operated at frequencies far below those conjectured to allow the proposed cosmological origin of collapse to be identified. Here we propose to use high-frequency nanomechanical resonators to surpass these limitations. We consider a specific implementation that uses a breathing mode of a quantum optomechanical system cooled to near its motional ground state. The scheme combines phonon counting with efficient mitigation of technical noise, including nonlinear photon conversion and photon coincidence counting. It can resolve the exquisitely small phonon fluxes required for a conclusive test of collapse models as well as testing the hypothesis of a cosmological origin of the collapse noise.

Particle mixing and the emergence of classicality: A spontaneous-collapse-model view

Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamiltonian and a dissipator of the Lindblad form in an enlarged Hilbert space, we show that spontaneous collapse can induce the decay dynamics in both quantum state and master equations. Moreover, we show that the decay property of a flavor-oscillating system is intimately connected to the time (a)symmetry of the noise field underlying the collapse mechanism. This (a)symmetry, in turn, is related to the definition of the stochastic integral and can provide a physical intuition behind the It\=o-Stratonovich dilemma in stochastic calculus.

Quantum transition between spaces in a multidimensional Universe and spatial unconnectivity explain free will and solve the measurement problem of quantum mechanics

Spacetime is deterministic, but the Universe appears to be stochastic. How to reconcile free will with the determinism inherent to the Universe? In this essay, we postulate that free will can only emanate from the existence of multiple additional spatial dimensions constituting the Universe. As our space displaces through the temporal dimension, we can choose any of the infinite possibilities defined by the additional spatial dimensions, through a process we refer to as quantum transition between spaces. Reality would emerge from the specific materialization of this quantum transition, resulting in a time series of events. This materialization is based on a fundamental property of any space, independently of its dimensions, which we refer to as spatial unconnectivity. This property implies the inability of the constituents of a particular space to observe spaces located in other dimensions. Therefore, the unconnectivity between spaces would prevent the simultaneous observation of all possible events at a specific time point, as well as past and future events, resulting in a unique reality. It would be the observers who determine the temporal trajectory of events, thus providing themselves with free will. In the absence of observers, all possibilities are feasible, thus explaining the quantum properties of elementary particles when they are not directly observed. Our model reconciles quantum mechanics with relativistic physics and is the easiest way to understand how reality arises in our observable Universe.

An algebraic approach to Koopman classical mechanics

Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator algebra is introduced, which allows the construction of a Hilbert space as a representation space of a Heisenberg algebra, giving a noncommutative operator algebraic variant of the Koopman–von Neumann approach. In this form, the measurement theory for unary classical mechanics can be the same and inform that for quantum mechanics, expanding classical mechanics to include noncommutative operators so that it is close to quantum mechanics, instead of attempting to squeeze quantum mechanics into a classical mechanics mold. The measurement problem as it appears in unary classical mechanics suggests a classical signal analysis approach that can also be successfully applied to the measurement problem of quantum mechanics. The development offers elementary mathematics that allows a formal reconciliation of “collapse” and “no-collapse” interpretations of quantum mechanics.

The measurement problem in Quantum Mechanics: Convivial Solipsism

The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve (or to dissolve) it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. In this paper, I defend a new position, the “Convivial Solipsism”, according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett’s interpretation and sharing also some similarities with Rovelli’s relational interpretation and Quantum Bayesianism. I also show how “Convivial Solipsism” can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics.

The measurement problem in quantum mechanics

In this paper, we discuss the importance of measurement in quantum mechanics and the so-called measurement problem. Any quantum system can be described as a linear combination of eigenstates of an operator representing a physical quantity; this means that the system can be in a superposition of states that corresponds to different eigenvalues, i.e., different physical outcomes, each one incompatible with the others. The measurement process converts a state of superposition (not macroscopically defined) in a well-defined state. We show that, if we describe the measurement by the standard laws of quantum mechanics, the system would preserve its state of superposition even on a macroscopic scale. Since this is not the case, we assume that a measurement does not obey to standard quantum mechanics, but to a new set of laws that form a “quantum measurement theory”.

Dissolving the measurement problem is not an option for the realist

This paper critically assesses the proposal that scientific realists do not need to search for a solution of the measurement problem in quantum mechanics, but should instead dismiss the problem as ill-posed. James Ladyman and Don Ross have sought to support this proposal with arguments drawn from their naturalized metaphysics and from a Bohr-inspired approach to quantum mechanics. I show that the first class of arguments is unsuccessful, because formulating the measurement problem does not depend on the metaphysical commitments which are undermined by ontic structural realism, rainforest realism, or naturalism in general. The second class of arguments is problematic due to its refusal to provide an analysis of the term “measurement”. It turns out that the proposed dissolution of the measurement problem is in conflict not only with traditional forms of scientific realism but even with the rather minimal realism that Ladyman and Ross themselves defend. The paper concludes with a brief discussion of two related proposals: Healey's pragmatist approach and Bub's information-theoretic interpretation.

Pre-Born–Oppenheimer molecular structure theory

ABSTRACTIn pre-Born–Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical description of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate versions can provide an efficient theoretical description for molecule-positron interactions and, in general, it would circumvent the tedious computation and fitting of potential energy surfaces and non-adiabatic coupling vectors while it includes also the quantum nuclear motion also often called ‘molecular quantum dynamics’. To achieve these goals, the review points out important technical and fundamental open questions. Most interestingly, the reconciliation of pre-BO theory with the classical chemistry knowledge touches upon fundamental problems related to the measurement problem of quantum mechanics.