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

Helland, Inge Svein

doi:10.32388/063pqj.2

An Alternative Foundation of Quantum Theory

Helland

2023

Found Phys

3

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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 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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An alternative foundation of quantum theory

Helland¹

2023

Preprint

Self Cite

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A new approach to quantum theory is proposed in this paper. The basis is first taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an actor to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an actor or to some communicating actors. 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. To focus only on physical variables rather than mathematical variables, the concept of inaccessible variables is then replaced by the concept of notions, and in this connection, aspects of category theory partly replace group 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.

show abstract

An alternative foundation of quantum theory

Helland

2023

Preprint

Self Cite

5

0

View full text Add to dashboard Cite

A new approach to quantum theory is proposed in this paper. The basis is first taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an actor to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an actor or to some communicating actors. 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. To focus only on physical variables rather than mathematical variables, the concept of inaccessible variables is then replaced by the concept of notions, and in this connection, aspects of category theory partly replace group 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.

show abstract

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

Cited by 6 publications

References 27 publications

An Alternative Foundation of Quantum Theory

An Alternative Foundation of Quantum Theory

An alternative foundation of quantum theory

An alternative foundation of quantum theory

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