Entropy

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14 pages, 517 KiB

Open AccessArticle

Notions of Completeness in the EPR Discussion

by Gerd Christian Krizek and Lukas Mairhofer

Entropy 2023, 25(4), 585; https://doi.org/10.3390/e25040585 - 29 Mar 2023

Viewed by 1217

We explore the different notions of completeness applied in the EPR discussion following and amending the thorough analysis of Arthur Fine. To this aim, we propose a classification scheme for scientific theories that provides a methodology for analyzing the different levels at which [...] Read more.

We explore the different notions of completeness applied in the EPR discussion following and amending the thorough analysis of Arthur Fine. To this aim, we propose a classification scheme for scientific theories that provides a methodology for analyzing the different levels at which interpretive approaches come into play. This allows us to contrast several concepts of completeness that operate on specific levels of the theory. We introduce the notion of theory completeness and compare it with the established notions of Born completeness, Schrödinger completeness and bijective completeness. We relate these notions to the recent concept of

ψ

-completeness and predictable completeness. The paper shows that the EPR argument contains conflicting versions of completeness. The confusion of these notions led to misunderstandings in the EPR debate and hindered its progress. Their clarification will thus contribute to recent debates on interpretational issues of quantum mechanics. Finally, we discuss the connection between the EPR paper and the Einstein–Rosen paper with regard to the question of completeness. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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16 pages, 769 KiB

Open AccessFeature PaperArticle

Models for Quantum Measurement of Particles with Higher Spin

by Theodorus M. Nieuwenhuizen

Entropy 2022, 24(12), 1746; https://doi.org/10.3390/e24121746 - 29 Nov 2022

Cited by 3 | Viewed by 1298

Abstract

The Curie–Weiss model for quantum measurement describes the dynamical measurement of a spin-

\frac{1}{2}

by an apparatus consisting of an Ising magnet of many spins

\frac{1}{2}

coupled to a thermal phonon bath. To measure the z-component [...] Read more.

The Curie–Weiss model for quantum measurement describes the dynamical measurement of a spin-

\frac{1}{2}

by an apparatus consisting of an Ising magnet of many spins

\frac{1}{2}

coupled to a thermal phonon bath. To measure the z-component

s = - l, - l + 1, \dots, l

of a spin l, a class of models is designed along the same lines, which involve

2 l

order parameters. As required for unbiased measurement, the Hamiltonian of the magnet, its entropy and the interaction Hamiltonian possess an invariance under the permutation

s \to s + 1

mod

2 l + 1

. The theory is worked out for the spin-1 case, where the thermodynamics is analyzed in detail, and, for spins

\frac{3}{2}, 2, \frac{5}{2}

, the thermodynamics and the invariance are presented. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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8 pages, 272 KiB

Open AccessFeature PaperArticle

On the Complete Description of Entangled Systems Part II: The (Meta)Physical Status and Semantic Aspects

by Karl Svozil

Entropy 2022, 24(12), 1724; https://doi.org/10.3390/e24121724 - 25 Nov 2022

Cited by 1 | Viewed by 1468

Abstract

We review some semantical aspects of probability bounds from Boole’s “conditions on possible experience” violated by quantum mechanics. We also speculate about emerging space-time categories as an epiphenomenon of quantization and the resulting breakdown of relativity theory by non-unitary and non-linear processes. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

16 pages, 346 KiB

Open AccessArticle

The Electromagnetic Vacuum Field as an Essential Hidden Ingredient of the Quantum-Mechanical Ontology

by Ana Maria Cetto and Luis de la Peña

Entropy 2022, 24(12), 1717; https://doi.org/10.3390/e24121717 - 24 Nov 2022

Cited by 7 | Viewed by 2471

Abstract

This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a [...] Read more.

This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the canonical variables of the particle into quantum operators satisfying the basic commutator

[\hat{x}, \hat{p}] = i ℏ

, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators

{\hat{a}}^{†}, \hat{a}

, satisfying

[\hat{a}, {\hat{a}}^{†}] = 1

. This allows for an explanation of quantum features such as quantum fluctuations, stationary states and transitions, and establishes a natural contact with (nonrelativistic) quantum electrodynamics. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

16 pages, 345 KiB

Open AccessArticle

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications

by Brian Drummond

Entropy 2022, 24(11), 1537; https://doi.org/10.3390/e24111537 - 26 Oct 2022

Viewed by 2833

Abstract

Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical states, and not yet explained. The concept of “statistical balance” is [...] Read more.

Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical states, and not yet explained. The concept of “statistical balance” is here explored, comparing its meaning since 2019 with its original meaning in 2001. Statistical balance now refers to a feature of contexts in which: (a) there is a prescribed probability other than 0 or 1 for the collective response of an ensemble to one measurement type; and (b) the collective response of the same ensemble to another measurement type demonstrates that no well-defined value can be attributed, for the property relevant to the original measurement type, to individual members of the ensemble. In some unexplained way, the outcomes of single runs of a measurement of the original type “balance” each other to give an overall result in line with the prescribed probability. Unexplained statistical balance prompts caution in assessing the conceptual implications of entanglement, measurement, uncertainty, and two-slit and Bell-type analyses. Physicists have a responsibility to the wider population to be conceptually precise about quantum mechanics, and to make clear that many possible conceptual implications are uncertain. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

16 pages, 457 KiB

Open AccessArticle

A Proposed Interpretation of the Wave–Particle Duality

by Kurt Jung

Entropy 2022, 24(11), 1535; https://doi.org/10.3390/e24111535 - 26 Oct 2022

Cited by 1 | Viewed by 2220

Abstract

Within the framework of quantum mechanics, the wave function squared describes the probability density of particles. In this article, another description of the wave function is given which embeds quantum mechanics into the traditional fields of physics, thus making new interpretations dispensable. The [...] Read more.

Within the framework of quantum mechanics, the wave function squared describes the probability density of particles. In this article, another description of the wave function is given which embeds quantum mechanics into the traditional fields of physics, thus making new interpretations dispensable. The new concept is based on the idea that each microscopic particle with non-vanishing rest mass is accompanied by a matter wave, which is formed by adjusting the phases of the vacuum fluctuations in the vicinity of the vibrating particle. The vibrations of the particle and wave are phase-coupled. Particles move on continuous approximately classical trajectories. By the phase coupling mechanism, the particle transfers the information on its kinematics and thus also on the external potential to the wave. The space dependence of the escorting wave turns out to be equal to the wave function. The new concept fundamentally differs from the pilot wave concept of Bohmian mechanics. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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8 pages, 431 KiB

Open AccessArticle

Observations of Bell Inequality Violations with Causal Isolation between Source and Detectors

by Marc Jean Jose Fleury

Entropy 2022, 24(9), 1230; https://doi.org/10.3390/e24091230 - 1 Sep 2022

Cited by 1 | Viewed by 2309

Abstract

We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH- [...] Read more.

We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH-

S = 2.30 \pm 0.07 > 2.00

. This result rules out theories that explain correlations with traveling communication between source and detectors, including super-luminal and instantaneous communication. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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27 pages, 9519 KiB

Open AccessArticle

Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons

by Hans De Raedt, Fengping Jin and Kristel Michielsen

Entropy 2022, 24(8), 1143; https://doi.org/10.3390/e24081143 - 17 Aug 2022

Cited by 3 | Viewed by 2395

Abstract

We present a comprehensive simulation study of the Newtonian and quantum model of a Stern–Gerlach experiment with cold neutrons. By solving Newton’s equation of motion and the time-dependent Pauli equation for a wide range of uniform magnetic field strengths, we scrutinize the role [...] Read more.

We present a comprehensive simulation study of the Newtonian and quantum model of a Stern–Gerlach experiment with cold neutrons. By solving Newton’s equation of motion and the time-dependent Pauli equation for a wide range of uniform magnetic field strengths, we scrutinize the role of the latter for drawing the conclusion that the magnetic moment of the neutron is quantized. We then demonstrate that a marginal modification of the Newtonian model suffices to construct, without invoking any concept of quantum theory, an event-based subquantum model that eliminates the shortcomings of the classical model and yields results that are in qualitative agreement with experiment and quantum theory. In this event-by-event model, the intrinsic angular momentum can take any value on the sphere, yet, for a sufficiently strong uniform magnetic field, the particle beam splits in two, exactly as in experiment and in concert with quantum theory. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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8 pages, 226 KiB

Open AccessFeature PaperArticle

There Is No Spooky Action at a Distance in Quantum Mechanics

by Stephen Boughn

Entropy 2022, 24(4), 560; https://doi.org/10.3390/e24040560 - 16 Apr 2022

Cited by 11 | Viewed by 3399

Abstract

Einstein became bothered by quantum mechanical action at a distance within two years of Schrödinger’s introduction of his eponymous wave equation. If the wave function represents the “real” physical state of a particle, then the measurement of the particle’s position would result in [...] Read more.

Einstein became bothered by quantum mechanical action at a distance within two years of Schrödinger’s introduction of his eponymous wave equation. If the wave function represents the “real” physical state of a particle, then the measurement of the particle’s position would result in the instantaneous collapse of the wave function to the single, measured position. Such a process seemingly violates not only the Schrödinger equation but also special relativity. Einstein was not alone in this vexation; however, the dilemma eventually faded as physicists concentrated on using the Schrödinger equation to solve a plethora of pressing problems. For the next 30 years, wave function collapse, while occasionally discussed by physicists, was primarily a topic of interest for philosophers. That is, until 1964, when Bell introduced his famous inequality and maintained that its violation proved that quantum mechanics and, by implication, nature herself are nonlocal. Unfortunately, this brought the topic back to mainstream physics, where it has remained and continues to muddy the waters. To be sure, not all physicists are bothered by the apparent nonlocality of quantum mechanics. So where have those who embrace quantum nonlocality gone wrong? I argue that the answer is a gratuitous belief in the ontic nature of the quantum state. Full article

(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)

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