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Time, Causality, and Entropy

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Time".

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 24013

Special Issue Editor


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Guest Editor
Laboratory of Physical Chemistry, ETH Zuerich, Vladimir-Prelog Weg 2, HCI F 225, CH-8093 Zurich, Switzerland
Interests: entropy; discrete time; structural biology

Special Issue Information

What is time? The nature of time, including the arrow of time, belongs to the unsolved mysteries of physics. Resolving this question may open a novel avenue toward a fundamental theory of physics. However, when talking about time, there appear inconsistencies. For example, time can be related to causality or even be interchanged, while causality appears to be absent in quantum mechanics because of the superposition principle, but there is time in the time-dependent Schrödinger equation. Entropy is the measure for the arrow of time, while microscopically, it is calculated by a statistical approach through the Boltzmann entropy interfering with causality, because it is applicable only for an ensemble representation of the system under investigation. Time is usually used continuously, while any measure of time—a clock—tics discretely, but a discrete time and other discrete approaches appear to have the caveat of interfering with Lorentz invariance. Albeit these and other apparent contradictions, physics theories with time being a continuous variable in the space–time vector of special and general relativity, with the Boltzmann entropy in statistical thermodynamics, as well as the superposition of quantum mechanics, predict (physical) experiments very well. An experiment is, however, only a subset of the real world, because amongst others, such as simple starting and end conditions, it is/must be reproducible, which by definition is a time-sensitive property.

It is the goal of this Special Issue to elaborate on our current understandings and non-understandings of time and entropy, on the character of an experiment versus the real world, and on problems that may arise between continuous and discrete time and on the nature of causality and its relationship with time.

Prof. Dr. Roland Riek
Guest Editor

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. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). 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

  • entropy
  • time
  • continuous
  • discrete
  • experiment
  • entropy
  • quantum mechanics
  • causality
  • Lorentz invariance

Published Papers (9 papers)

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Research

17 pages, 626 KiB  
Article
Causality in Schwinger’s Picture of Quantum Mechanics
by Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone and Alessandro Zampini
Entropy 2022, 24(1), 75; https://doi.org/10.3390/e24010075 - 01 Jan 2022
Cited by 5 | Viewed by 1838
Abstract
This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called [...] Read more.
This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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21 pages, 1830 KiB  
Article
Time and Causality: A Thermocontextual Perspective
by Harrison Crecraft
Entropy 2021, 23(12), 1705; https://doi.org/10.3390/e23121705 - 20 Dec 2021
Cited by 1 | Viewed by 3627
Abstract
The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects [...] Read more.
The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects follow causes and an arrow of causality, and this conflicts with time symmetry. The prevailing interpretations also fail to explain the empirical irreversibility of wavefunction collapse without invoking untestable and untenable metaphysical implications. They fail to reconcile nonlocality and relativistic causality without invoking superdeterminism or unexplained superluminal correlations. The TCI defines a system’s state with respect to its actual surroundings at a positive ambient temperature. It recognizes the existing physical interpretations as special cases which either define a state with respect to an absolute zero reference (classical and relativistic states) or with respect to an equilibrium reference (quantum states). Between these special case extremes is where thermodynamic irreversibility and randomness exist. The TCI distinguishes between a system’s internal time and the reference time of relativity and causality as measured by an external observer’s clock. It defines system time as a complex property of state spanning both reversible mechanical time and irreversible thermodynamic time. Additionally, it provides a physical explanation for nonlocality that is consistent with relativistic causality without hidden variables, superdeterminism, or “spooky action”. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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13 pages, 875 KiB  
Article
The Relativity of Indeterminacy
by Flavio Del Santo and Nicolas Gisin
Entropy 2021, 23(10), 1326; https://doi.org/10.3390/e23101326 - 11 Oct 2021
Cited by 8 | Viewed by 2271
Abstract
A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity—with its block-universe picture—as the failure of any indeterministic program in physics. On the contrary, in this paper, we note that upholding reasonable principles of [...] Read more.
A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity—with its block-universe picture—as the failure of any indeterministic program in physics. On the contrary, in this paper, we note that upholding reasonable principles of finiteness of information hints at a picture of the physical world that should be both relativistic and indeterministic. We thus rebut the block-universe picture by assuming that fundamental indeterminacy itself should also be regarded as a relative property when considered in a relativistic scenario. We discuss the consequence that this view may have when correlated randomness is introduced, both in the classical case and in the quantum one. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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9 pages, 241 KiB  
Article
Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle
by Roland Riek and Atanu Chatterjee
Entropy 2021, 23(9), 1212; https://doi.org/10.3390/e23091212 - 14 Sep 2021
Cited by 3 | Viewed by 1783
Abstract
Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in [...] Read more.
Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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13 pages, 1176 KiB  
Article
On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard
by Alexander Sobol, Peter Güntert and Roland Riek
Entropy 2021, 23(9), 1188; https://doi.org/10.3390/e23091188 - 09 Sep 2021
Viewed by 2212
Abstract
A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann–Gibbs. Due to the collisions, trajectories [...] Read more.
A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann–Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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13 pages, 664 KiB  
Article
The Matter of Time
by Arto Annila
Entropy 2021, 23(8), 943; https://doi.org/10.3390/e23080943 - 23 Jul 2021
Cited by 7 | Viewed by 3309
Abstract
About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably [...] Read more.
About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Thus, time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths (i.e., geodesics) to level out energy differences in the least amount of time. The corresponding flow equations can be written, but they cannot be solved. Since the flows affect their driving forces, affecting the flows, and so on, the forces (i.e., causes) and changes in motions (i.e., consequences) are inseparable. Thus, the future remains unpredictable. However, it is not all arbitrary but rather bounded by free energy. Eventually, when the system has attained a stationary state where forces tally, there are no causes and no consequences. Since there are no energy differences between the system and its surroundings, the quanta only orbit on and on. Thus, time does not move forward either but circulates. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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10 pages, 398 KiB  
Article
Is Causality a Necessary Tool for Understanding Our Universe, or Is It a Part of the Problem?
by Martin Tamm
Entropy 2021, 23(7), 886; https://doi.org/10.3390/e23070886 - 13 Jul 2021
Cited by 2 | Viewed by 2392
Abstract
In this paper, the concept of causality in physics is discussed. Causality is a necessary tool for the understanding of almost all physical phenomena. However, taking it as a fundamental principle may lead us to wrong conclusions, particularly in cosmology. Here, three very [...] Read more.
In this paper, the concept of causality in physics is discussed. Causality is a necessary tool for the understanding of almost all physical phenomena. However, taking it as a fundamental principle may lead us to wrong conclusions, particularly in cosmology. Here, three very well-known problems—the Einstein–Podolsky–Rosen paradox, the accelerating expansion and the asymmetry of time—are discussed from this perspective. In particular, the implications of causality are compared to those of an alternative approach, where we instead take the probability space of all possible developments as the starting point. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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18 pages, 360 KiB  
Article
Timelessness Strictly inside the Quantum Realm
by Knud Thomsen
Entropy 2021, 23(6), 772; https://doi.org/10.3390/e23060772 - 18 Jun 2021
Cited by 5 | Viewed by 3127
Abstract
Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects [...] Read more.
Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only limited reality. Quantum systems, which we know, are embedded in the everyday classical world. Their preparation as well as their measurement-phases leave durable records and traces in the entropy of the environment. The Landauer Principle then gives a quantitative threshold for irreversibility. With double slit experiments and tunneling as paradigmatic examples, it is proposed that a label of timelessness offers clues for rendering a Copenhagen-type interpretation of quantum physics more “realistic” and acceptable by providing a coarse but viable link from the fundamental quantum realm to the classical world which humans directly experience. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
11 pages, 249 KiB  
Article
On Explaining Quantum Correlations: Causal vs. Non-Causal
by Laura Felline
Entropy 2021, 23(5), 589; https://doi.org/10.3390/e23050589 - 10 May 2021
Cited by 3 | Viewed by 1614
Abstract
At the basis of the problem of explaining non-local quantum correlations lies the tension between two factors: on the one hand, the natural interpretation of correlations as the manifestation of a causal relation; on the other, the resistance on the part of the [...] Read more.
At the basis of the problem of explaining non-local quantum correlations lies the tension between two factors: on the one hand, the natural interpretation of correlations as the manifestation of a causal relation; on the other, the resistance on the part of the physics underlying said correlations to adjust to the most essential features of a pre-theoretic notion of causation. In this paper, I argue for the rejection of the first horn of the dilemma, i.e., the assumption that quantum correlations call for a causal explanation. The paper is divided into two parts. The first, destructive, part provides a critical overview of the enterprise of causally interpreting non-local quantum correlations, with the aim of warning against the temptation of an account of causation claiming to cover such correlations ‘for free’. The second, constructive, part introduces the so-called structural explanation (a variety of non-causal explanation that shows how the explanandum is the manifestation of a fundamental structure of the world) and argues that quantum correlations might be explained structurally in the context of an information-theoretic approach to QT. Full article
(This article belongs to the Special Issue Time, Causality, and Entropy)
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