Possible connections between relativity theory and a version of quantum theory based upon theoretical variables

Helland, Inge Svein

doi:10.32388/063pqj

Cited by 4 publications

References 25 publications

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A Simple Quantum Model Linked to Decisions

Helland

2022

Found Phys

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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.

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A Simple Quantum Model Linked to Decisions

Helland

2022

Found Phys

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On probabilities in quantum mechanics

Helland

2024

APL Quantum

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This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Khrennikov on the one hand and Stacey and Schack on the other hand. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, as seen from my point of view, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection, I also sketch some consequences of my approach toward the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation of quantum mechanics before I give some final remarks.

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An alternative foundation of quantum theory

Helland

2023

Preprint

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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 shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. 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.

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Possible connections between relativity theory and a version of quantum theory based upon theoretical variables

Cited by 4 publications

References 25 publications

A Simple Quantum Model Linked to Decisions

A Simple Quantum Model Linked to Decisions

On probabilities in quantum mechanics

An alternative foundation of quantum theory

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