An alternative foundation of quantum theory
- URL: http://arxiv.org/abs/2305.06727v9
- Date: Thu, 12 Oct 2023 10:07:38 GMT
- Title: An alternative foundation of quantum theory
- Authors: Inge S. Helland
- Abstract summary: A new approach to quantum theory is proposed in this paper.
The accessible variables are just ideal observations connected to an observer or to some communicating observers.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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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