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14 pages, 857 KiB

Open AccessArticle

The Dirac Equation, Mass and Arithmetic by Permutations of Automaton States

by Hans-Thomas Elze

Entropy 2025, 27(4), 395; https://doi.org/10.3390/e27040395 - 7 Apr 2025

Viewed by 199

Abstract

The cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its underlying ontological states that evolve by permutations. They do not create would-be quantum mechanical superposition states. We review this with a classical automaton consisting of an Ising spin chain which is [...] Read more.

The cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its underlying ontological states that evolve by permutations. They do not create would-be quantum mechanical superposition states. We review this with a classical automaton consisting of an Ising spin chain which is then related to the Weyl equation in the continuum limit. Based on this and generalizing, we construct a new “Necklace of Necklaces” automaton with a torus-like topology that lends itself to represent the Dirac equation in 1 + 1 dimensions. Special attention has to be paid to its mass term, which necessitates this enlarged structure and a particular scattering operator contributing to the step-wise updates of the automaton. As discussed earlier, such deterministic models of discrete spins or bits unavoidably become quantum mechanical, when only slightly deformed. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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20 pages, 1356 KiB

Open AccessArticle

A Quantum Probability Approach to Improving Human–AI Decision Making

by Scott Humr, Mustafa Canan and Mustafa Demir

Entropy 2025, 27(2), 152; https://doi.org/10.3390/e27020152 - 2 Feb 2025

Viewed by 1462

Abstract

Artificial intelligence is set to incorporate additional decision space that has traditionally been the purview of humans. However, AI systems that support decision making also entail the rationalization of AI outputs by humans. Yet, incongruencies between AI and human rationalization processes may introduce [...] Read more.

Artificial intelligence is set to incorporate additional decision space that has traditionally been the purview of humans. However, AI systems that support decision making also entail the rationalization of AI outputs by humans. Yet, incongruencies between AI and human rationalization processes may introduce uncertainties in human decision making, which require new conceptualizations to improve the predictability of these interactions. The application of quantum probability theory (QPT) to human cognition is on the ascent and warrants potential consideration to human–AI decision making to improve these outcomes. This perspective paper explores how QPT may be applied to human–AI interactions and contributes by integrating these concepts into human-in-the-loop decision making. To capture this and offer a more comprehensive conceptualization, we use human-in-the-loop constructs to explicate how recent applications of QPT can ameliorate the models of interaction by providing a novel way to capture these behaviors. Followed by a summary of the challenges posed by human-in-the-loop systems, we discuss newer theories that advance models of the cognitive system by using quantum probability formalisms. We conclude by outlining areas of promising future research in human–AI decision making in which the proposed methods may apply. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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39 pages, 416 KiB

Open AccessArticle

“In Mathematical Language”: On Mathematical Foundations of Quantum Foundations

by Arkady Plotnitsky

Entropy 2024, 26(11), 989; https://doi.org/10.3390/e26110989 - 18 Nov 2024

Viewed by 1016

Abstract

The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the [...] Read more.

The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

14 pages, 2349 KiB

Open AccessArticle

Violation of Leggett–Garg Inequality in Perceiving Cup-like Objects and Cognitive Contextuality

by Likan Zhan, Andrei Khrennikov and Yingce Zhu

Entropy 2024, 26(11), 950; https://doi.org/10.3390/e26110950 - 5 Nov 2024

Viewed by 886

Abstract

This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, [...] Read more.

This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, i.e., exploring the methodology of quantum theory outside of physics. We examined the bistable perception of cup-like objects, which strongly depends on experimental contexts. Our experimental data confirmed the existence of cognitive hysteresis, the important role of memory, and the non-commutative structure of cognitive observables. In physics, quantum contextuality is assessed using Bell-CHSH inequalities, and their violation is incorrectly believed to imply the nonlocality of Nature. The violation of Bell-type inequalities in cognitive and social science strongly indicates that the metaphysical implications of these inequalities are quite limited. In our experiments, modified Leggett–Garg inequalities were also significantly violated, but this only means that experimental data from experiments performed in different contexts cannot be modeled by a unique set of noncontextual, jointly distributed random variables. In our experiments, we know the empirical probability distributions measured in different contexts; thus, we can obtain much more detailed and reliable information about contextuality in human cognition by performing nonparametric compatibility tests. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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20 pages, 1036 KiB

Open AccessArticle

Quantum Approach for Contextual Search, Retrieval, and Ranking of Classical Information

by Alexander P. Alodjants, Anna E. Avdyushina, Dmitriy V. Tsarev, Igor A. Bessmertny and Andrey Yu. Khrennikov

Entropy 2024, 26(10), 862; https://doi.org/10.3390/e26100862 - 13 Oct 2024

Viewed by 1512

Abstract

Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. [...] Read more.

Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the “entanglement” in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning algorithms. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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10 pages, 699 KiB

Open AccessArticle

Quantum State Combinatorics

by Gregory D. Scholes

Entropy 2024, 26(9), 764; https://doi.org/10.3390/e26090764 - 6 Sep 2024

Cited by 1 | Viewed by 907

Abstract

This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations [...] Read more.

This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations for the complex structure of non-classical multipartite correlations with surprisingly little information about the state. We show, with pegagogical examples, how known results from combinatorics can be used to reveal the expected structure of various correlations hidden in the ensemble described by a state. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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9 pages, 926 KiB

Open AccessArticle

Testing the Pauli Exclusion Principle across the Periodic Table with the VIP-3 Experiment

by Simone Manti, Massimiliano Bazzi, Nicola Bortolotti, Cesidio Capoccia, Michael Cargnelli, Alberto Clozza, Luca De Paolis, Carlo Fiorini, Carlo Guaraldo, Mihail Iliescu, Matthias Laubenstein, Johann Marton, Fabrizio Napolitano, Kristian Piscicchia, Alessio Porcelli, Alessandro Scordo, Francesco Sgaramella, Diana Laura Sirghi, Florin Sirghi, Oton Vazquez Doce, Johann Zmeskal and Catalina Curceanu Show full author list Hide full author list

Entropy 2024, 26(9), 752; https://doi.org/10.3390/e26090752 - 2 Sep 2024

Cited by 1 | Viewed by 1706

Abstract

The Pauli exclusion principle (PEP), a cornerstone of quantum mechanics and whole science, states that in a system, two fermions can not simultaneously occupy the same quantum state. Several experimental tests have been performed to place increasingly stringent bounds on the validity of [...] Read more.

The Pauli exclusion principle (PEP), a cornerstone of quantum mechanics and whole science, states that in a system, two fermions can not simultaneously occupy the same quantum state. Several experimental tests have been performed to place increasingly stringent bounds on the validity of PEP. Among these, the series of VIP experiments, performed at the Gran Sasso Underground National Laboratory of INFN, is searching for PEP-violating atomic X-ray transitions in copper. In this paper, the upgraded VIP-3 setup is described, designed to extend these investigations to higher-Z elements such as zirconium, silver, palladium, and tin. We detail the enhanced design of this setup, including the implementation of cutting-edge, 1 mm thick, silicon drift detectors, which significantly improve the measurement sensitivity at higher energies. Additionally, we present calculations of expected PEP-violating energy shifts in the characteristic lines of these elements, performed using the multi-configurational Dirac–Fock method from first principles. The VIP-3 realization will contribute to ongoing research into PEP violation for different elements, offering new insights and directions for future studies. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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11 pages, 245 KiB

Open AccessArticle

The Particle of Haag’s Local Quantum Physics: A Critical Assessment

by Gregg Jaeger

Entropy 2024, 26(9), 748; https://doi.org/10.3390/e26090748 - 1 Sep 2024

Cited by 1 | Viewed by 1275

Abstract

Rudolf Haag’s Local Quantum Physics (LQP) is an alternative framework to conventional relativistic quantum field theory for combining special relativity and quantum theory based on first principles, making it of great interest for the purposes of conceptual analysis despite currently being relatively limited [...] Read more.

Rudolf Haag’s Local Quantum Physics (LQP) is an alternative framework to conventional relativistic quantum field theory for combining special relativity and quantum theory based on first principles, making it of great interest for the purposes of conceptual analysis despite currently being relatively limited as a tool for making experimental predictions. In LQP, the elementary particles are defined as species of causal link between interaction events, together with which they comprise its most fundamental entities. This notion of particle has yet to be independently assessed as such. Here, it is captured via a set of propositions specifying particle characteristics and then compared to previous particle notions. Haag’s particle differs decisively with respect to mechanical intuitions about particles by lacking, among other things, even an approximate independent space–time location. This notion is thus found to differ greatly even from those of relativistic quantum mechanics and quantum field theory, which have been applied to the known elementary particles. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

Review

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46 pages, 15416 KiB

Open AccessReview

Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model

by Marian Kupczynski

Entropy 2024, 26(11), 991; https://doi.org/10.3390/e26110991 - 18 Nov 2024

Cited by 1 | Viewed by 2264

Abstract

In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and [...] Read more.

In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and I discuss some challenges and open questions in quantum foundations and in the Standard Model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes, many believe that when we reconcile general relativity with quantum theory we will have the correct theory of everything. Perhaps we should be much humbler. Our perceptions of reality are biased by our senses and by our brain, bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite, we can use a concept of a material point, but the point-like approximation breaks completely when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear and elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)

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