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Approaches towards Quantum Foundations

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A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Foundations of Quantum Mechanics and Quantum Gravity".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 6879

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Prof. Dr. Inge Svein Helland

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Guest Editor

Department of Mathematics, University of Oslo, Oslo, Norway
Interests: foundations of science; interpretation and foundation of quantum mechanics; philosophical foundation of statistics; communication between scientists; machine learning; applied science

Prof. Dr. Jim Al-Khalili

E-Mail Website
Guest Editor

Department of Physics, University of Surrey, Guildford GU2 7XH, UK
Interests: theoretical nuclear physics; quantum biology; open quantum systems; foundations of quantum mechanics; history of science; philosophy of science; science communication

Special Issue Information

Dear Colleagues,

Richard Feynman has emphasized the difficulty of understanding quantum mechanics. However, in the last decade, several approaches towards such an understanding have appeared.

Many different meanings can be given to the term ‘understand’. One goal might be to arrive at an understanding which can be explained to scientists outside the quantum community. It may seem that ordinary Hilbert space formalism is not the most useful point of departure here.

Quantum foundation is an important topic. It is a fact that many mutually excluding interpretations of quantum theory exist. In our opinion, before we can start a serious ‘final’ discussion on interpretation, it is important that we first try to agree on the question of foundation.

A Special Issue of the journal Universe with the title ‘Approaches towards Quantum Foundations’, where these problems will be explored, is now being planned.

We hereby invite researchers to contribute to this Special Issue by writing articles on their own approaches towards quantum foundation or their views on this topic. Their reasoning must be underpinned by the necessary mathematics, or to a reference where the mathematics can be found.

One special problem that may be of relevance is to ‘understand’ the results of the Bell experiments, which have now been performed in a complexly loophole-free manner.

Prof. Dr. Inge Svein Helland
Prof. Dr. Jim Al-Khalili
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

bell experiments
foundation
Hilbert space formalism
mathematical models
physical axioms
quantum mechanics
simplicity

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Published Papers (4 papers)

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Research

6 pages, 205 KiB

Open AccessCommunication

On the Copenhagen Interpretation of Quantum Measurement

by Michael L. Walker

Universe 2024, 10(3), 113; https://doi.org/10.3390/universe10030113 - 1 Mar 2024

Viewed by 1314

Abstract

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 [...] Read more.

(This article belongs to the Special Issue Approaches towards Quantum Foundations)

20 pages, 624 KiB

Open AccessArticle

Superdeterminism without Conspiracy

by Tim Palmer

Universe 2024, 10(1), 47; https://doi.org/10.3390/universe10010047 - 18 Jan 2024

Cited by 2 | Viewed by 1534

Abstract

Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties

λ

of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial [...] Read more.

Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties

λ

of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique

λ

. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where

λ

defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping

λ

and y fixed but disappear with any coarse-graining of

λ

, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics. Full article

(This article belongs to the Special Issue Approaches towards Quantum Foundations)

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11 pages, 333 KiB

Open AccessArticle

Study of He–Mckellar–Wilkens Effect in Noncommutative Space

by Jian Jing, Qing Wang, Zi-Gang Yuan and Shi-Hai Dong

Universe 2023, 9(12), 494; https://doi.org/10.3390/universe9120494 - 27 Nov 2023

Cited by 1 | Viewed by 1367

Abstract

The He–McKellar–Wilkens (HMW) effect in noncommutative space has been explored through two distinct methodologies. One approach treats the neutral particle, which harbors a permanent electric dipole moment, as an unstructured entity, while the other approach considers the neutral particle as a composite system consisting of a pair of oppositely charged particles. To preserve gauge symmetry, we apply the Seiberg–Witten map. Surprisingly, both of these approaches converge on the same result. They independently confirm that, up to the first order of the noncommutative parameter (NCP), no corrections are observed in the phase of the HMW effect. Remarkably, these two approaches, although founded on fundamentally different mechanisms, yield identical conclusions. Full article

(This article belongs to the Special Issue Approaches towards Quantum Foundations)

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32 pages, 886 KiB

Open AccessArticle

Cosmic-Time Quantum Mechanics and the Passage-of-Time Problem

by Marek Czachor

Universe 2023, 9(4), 188; https://doi.org/10.3390/universe9040188 - 16 Apr 2023

Cited by 1 | Viewed by 1790

Abstract

A new dynamical paradigm merging quantum dynamics with cosmology is discussed. We distinguish between a universe and its background space-time. The universe here is the subset of space-time defined by

Ψ_{τ} (x) \neq 0

, where [...] Read more.

Ψ_{τ} (x) \neq 0

, where

Ψ_{τ} (x)

is a solution of a Schrödinger equation, x is a point in n-dimensional Minkowski space, and

τ \geq 0

is a dimensionless ‘cosmic-time’ evolution parameter. We derive the form of the Schrödinger equation and show that an empty universe is described by a

Ψ_{τ} (x)

that propagates towards the future inside some future-cone

V_{+}

. The resulting dynamical semigroup is unitary, i.e.,

\int_{V_{+}} d^{4} x {| Ψ_{τ} (x) |}^{2} = 1

for

τ \geq 0

. The initial condition

Ψ_{0} (x)

is not localized at

x = 0

. Rather, it satisfies the boundary condition

Ψ_{0} (x) = 0

for

x \notin V_{+}

. For

n = 1 + 3

the support of

Ψ_{τ} (x)

is bounded from the past by the ‘gap hyperboloid’

ℓ^{2} \sqrt{τ} = c^{2} t^{2} - x^{2}

, where ℓ is a fundamental length. Consequently, the points located between the hyperboloid and the light cone

c^{2} t^{2} - x^{2} = 0

satisfy

Ψ_{τ} (x) = 0

, and thus do not belong to the universe. As

τ

grows, the gap between the support of

Ψ_{τ} (x)

and the light cone increases. The past thus literally disappears. Unitarity of the dynamical semigroup implies that the universe becomes localized in a finite-thickness future-neighbourhood of

ℓ^{2} \sqrt{τ} = c^{2} t^{2} - x^{2}

, simultaneously spreading along the hyperboloid. Effectively, for large

τ

the subset occupied by the universe resembles a part of the gap hyperboloid itself, but its thickness

Δ_{τ}

is non-zero for finite

τ

. Finite

Δ_{τ}

implies that the three-dimensional volume of the universe is finite as well. An approximate radius of the universe,

r_{τ}

, grows with

τ

due to

Δ_{τ} r_{τ}^{3} = Δ_{0} r_{0}^{3}

and

Δ_{τ} \to 0

. The propagation of

Ψ_{τ} (x)

through space-time matches an intuitive picture of the passage of time. What we regard as the Minkowski-space classical time can be identified with

c t_{τ} = \int d^{4} x x^{0} {| Ψ_{τ} (x) |}^{2}

, so

t_{τ}

grows with

τ

as a consequence of the Ehrenfest theorem, and its present uncertainty can be identified with the Planck time. Assuming that at present values of

τ

(corresponding to 13–14 billion years)

Δ_{τ}

and

r_{τ}

are of the order of the Planck length and the Hubble radius, we estimate that the analogous thickness

Δ_{0}

of the support of

Ψ_{0} (x)

is of the order of 1 AU, and

r_{0}^{3} \sim {(c t_{H})}^{3} \times 10^{- 44}

. The estimates imply that the initial volume of the universe was finite and its uncertainty in time was several minutes. Next, we generalize the formalism in a way that incorporates interactions with matter. We are guided by the correspondence principle with quantum mechanics, which should be asymptotically reconstructed for the present values of

τ

. We argue that Hamiltonians corresponding to the present values of

τ

approximately describe quantum mechanics in a conformally Minkowskian space-time. The conformal factor is directly related to

| Ψ_{τ} {(x) |}^{2}

. As a by-product of the construction, we arrive at a new formulation of conformal invariance of

m \neq 0

fields. Full article

(This article belongs to the Special Issue Approaches towards Quantum Foundations)

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