Symmetry and the Hilbert space basis of quantum theory

What is it about?

The ordinary text book foundation of quantum mechanics is very abstract and formal: States are defined as unit vectors in an abstract Hilbert space, and variables are associated with operators in the same space. This article is the starting point for a program which aims at replacing this formal language with a simpler and more intuitive language. In the article I define a conceptual variable as any variable difined by some person or a group of communicating persons. These variables may be accessible - it is possible by experiment to find numerical values for them -. or inaccessible. From this, combined with some group theory and group representation theory, essential elements of the formal quantum language are derived.

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Why is it important?

It is very important to have a simple language behind scientific theories. When the language is simple, discussions about interpretations are also simpler to understand. The discussions about the interpretation of quantum mechanics has been intense for many years, and these discussions have partly been very difficult to understand for the general public. In this paper I promote a general epistemic interpretation of quantum theory: The theory is not about physical reality itself, but about our knowledge of reality. Another aspect of this programme is that a simple language facilitates comparison between scientific theories. One aim is to do comparisons between quantum theory and statistical infence theory. Up to now there has been little communication between the corresponding scientific communities.

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