The Quantum-Like Revolution (original) (raw)
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Frontiers in Physics 5:19, 2017
The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, that may be helpful or even necessary there or in physics itself. I shall, in closing, suggest one possible type of such models, singularized probabilistic models, SP-models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.
Towards a Proper Quantum Theory
Quantum Mechanics, A Half Century Later, 1977
The history of quantum physics has been deeply conditioned by the change in scientific practice as a social activity during the past fifty years. As a result the theory has not been allowed full maturing; both its formal and empirical advances have not resulted in a comparable conceptual progress. The recasting of quantum theory thus appears as an epistemological necessity. One of the main aspects of this process is to clear quantum theory from its persisting classical connections in order to endow it with an autonomous and intrinsic status. Problems related to the foundations, description, interpretation and approximations of quantum theory are considered in turn, and various recent works are reviewed which contribute to the proposed endeavour. Dialectica Vol. 30, No 2/3 (197~ * This article was prepared as a contribution to the Colloquium "Half a
A simple quantum model linked to a theory of decisions
Foundations of Physics, 2023
This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions from a quite different, much simpler model. This model is connected to the mind of an observer, or to the joint minds of a group of communicating observers. The model is based upon conceptual variables, and an important aspect is that an observer (a group of observers) must decide on which variable to measure. The model is then linked more generally to a theory of decisions. The results are discussed from several angles. In particular, macroscopic consequences are treated briefly.
An alternative foundation of quantum theory
arXiv (Cornell University), 2023
A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is indicated here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. In case, this simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The essential use of inaccessible variables can be avoided by basing the approach on some simple category theory.The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations.
The Quantum Revolution in Philosophy
The Philosophical Review, 2020
In this thought-provoking book, Richard Healey proposes a new interpretation of quantum theory inspired by pragmatist philosophy. Healey puts forward the interpretation as an alternative to realist quantum theories on the one hand such as Bohmian mechanics, spontaneous collapse theories, and many-worlds interpretations, which are different proposals for describing what the quantum world is like and what the basic laws of physics are, and non-realist interpretations on the other hand such as quantum Bayesianism, which proposes to understand quantum theory as describing agents' subjective epistemic states. The central idea of Healey's proposal is to understand quantum theory as providing not a description of the physical world but a set of authoritative and objectively correct prescriptions about how agents should act. The book provides a detailed development and defense of that idea, and it contains interesting discussions about a wide range of philosophical issues such as representation, probability, explanation, causation, objectivity, meaning, and fundamentality. Healey's project is at the intersection of physics and philosophy. The book is divided into two parts. Part I of the book discusses the foundational questions in quantum theory from the perspective of the prescriptive interpretation. In Part II, Healey discusses the philosophical implications of the view. Both parts are written in a way that is largely accessible to non-specialists. In this brief book review, I will focus on two questions: (1) How does Healey's idea work? (2) What reasons are there to believe in it?
A new approach toward the quantum foundation and some consequences
Academia Quantum, 2024
A general theory based on six postulates is introduced. The basic notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From these postulates, the ordinary formalism of quantum theory is derived. The mathematical derivations are not given in this article, but I refer to the recent articles. Three possible applications of the general theory can be given as follows: (1) the variables may be decision variables connected to the decisions of a person or a group of persons, (2) the variables may be statistical parameters or future data, and (3) most importantly, the variables are physical variables in some context. The last application gives a completely new foundation of quantum mechanics, a foundation which in my opinion is much easier to understand than ordinary formalism. So-called paradoxes like that of Schrödinger’s cat can be clarified under the theory. Explanations of the outcomes of David Bohm’s version of the EPR (Einstein–Podolsky–Rosen) experiment and the Bell experiment are provided. Finally, references to links toward relativity theory and quantum field theory are given. The concluding remarks point to further possible developments.
De rerum (incerta) natura A tentative approach to the concept of quantum-like
Preprints.org, 2021
In recent years, the term quantum-like has been increasingly used in different disciplines, including neurosciences, psychological and socio-economical disciplines, claiming that some investigated phenomena show “something” in common with quantum processes and, therefore, they can be modeled using a sort of quantum formalism. Therefore, the increasing use of the term quantum-like calls for defining and sharing its meaning in order to properly adopt it and avoid possible misuse. In our opinion, the concept of quantum-like may be successfully applied to macroscopic phenomena and empirical sciences other than physics when at least two conditions are satisfied: a) the behavior of the investigated phenomena show logical analogies with quantum ones; b) it is possible to find a criterion of truth based on an experiential/scientific approach applied to a probabilistic model of description of the phenomena. This is only a first, small step in the approach to the concept of quantum-like, hopefully helpful to promote further discussion and achieve a better definition.
Quantum Mechanics, Mathematics, Cognition and Action
Quantum Mechanics, Mathematics, Cognition and Action, 2002
This is what the epistemological universality of quantum mechanics consists of. By no means does it consist, as is often asserted, of the fact that any material system is made of microsystems-which is a physical circumstance, not an epistemological one. The feeling of essentiality conveyed by the quantum mechanical formalism to those who can read it, does not stem from this physical circumstance; it stems exclusively from the universal character of the peculiar cognitive situation dealt with in quantum mechanics. And, while reflections of it are encrypted in the general features of the formalism considered as a whole, this cognitive situation marks also directly the specific formal features that are pointed toward by the expressions "quantum probabilities" and "quantum logic". These simply are not intelligible in terms of what is classically called probabilities and logic. This manifests strikingly that the general epistemological consequences of the quantum mechanical formalism, if elaborated, modify the structure of our classical representations of probabilities and of logic, the two most basic and worked out representations of domains of our everyday thinking and acting. Indeed, when the universal representation of the very first stage of our conceptualization processes, drawn by generalization from quantum mechanics, is injected into classical probabilities and classical logic, they undergo a sort of spectral decomposition; and this places into evidence that, far down beneath language, probabilistic and logical conceptualization merge REMARKS ABOUT THE PROGRAM FOR A FORMALIZED EPISTEMOLOGY *
A Simple Quantum Model Linked to Decisions
Foundations of Physics
This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions from a quite different, much simpler model. This model is connected to the mind of an observer, or to the joint minds of a group of communicating observers. The model is based upon conceptual variables, and an important aspect is that an observer (a group of observers) must decide on which variable to measure. The model is then linked more generally to a theory of decisions. The results are discussed from several angles.