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arXiv:2206.04918 · Foundations of Physics

A Simple Quantum Model Linked to Decisions

Inge Svein Helland

Published Dec 1, 2022• 16 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1007/s10701-022-00658-7

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Abstract 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.
A general theory based upon 6 postulates is introduced. The basical 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 [1][2]. Three possible applications of the general theory can be given; 1) The variables may be decision variables connected to the decisions of a person or of a group of persons. 2) The variables may be statistical parameters or future data, but most importantly here: 3) The variables are physical variables in some context. This last application gives a completely new foundation for quantum mechanics, a foundation which, in my opinion, is much more easy to understand than the ordinary formalism. The other applications seem also to give interesting consequences of the approach. 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 experiment and of the Bell experiment are provided. Finally, references and links to relativity theory and to quantum field theory are given.
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.
In the Preface of this book, we have mentioned several approaches [ 1 , 2 , 3 , 4 ] to the problem of connecting quantum theory and general relativity theory. In our opinion, before a final thinking around this problem, it is vital to make some efforts to find a new and less formal foundation of quantum theory. This has now been done by the first author in a process starting with the book [ 5 ] and further developed in a series of articles. A summary of the theory is now given in [ 6 ]. Central to the theory is a simple model of the mind of an observer, a model which may be generalized to the mind of any person. It first relies on what is called theoretical variables , which may be physical variables, but in the process of planning, doing, or interpreting experiments, the variables are also assumed to exist in the mind of a relevant actor. From a mathematical point of view, our only requirement for the theoretical variables is the following: If λ is a theoretical variable and θ = f ( λ ) for some fixed function f , then θ is also a theoretical variable.
A general theory based upon 7 postulates is introduced. The basical 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 [9, 10]. Three possible applications of the general theory can be given; 1) The variables may decision variables connected to the decisions of a person or of a group of persons. 2) The variables may be statistical parameters or future data, But most importantly here: 3) The variables are physical variables in some context. This last application gives a completely new foundation of quantum mechanics, a foundation which in my opinion is much more easy to understand than the ordinary formalism.The other applications seem also to give interesting consequences of the approach. Socalled 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 experiment and of the Bell experiment are provided. Finally, references to links towards relativity theory and to quantum field theory are given. The concluding remarks point at further possible developments.
I sketch the foundation of quantum mechanics as it is presented in various books and articles. Then a new approach to quantum foundation is described, a foundation that relies on 4 simple postulates related to the mind of an observer or to the joint minds of a group of communicating observers. One of these postulates may appear to be strong, but it turns out to be more natural when it is placed in a religious setting. This assumes the existence of an omnipotent God. These arguments are further discussed, and they are shown also to give a foundation of Quantum Decision Theory.