Foundation of quantum mechanics

What is it about?

A complete new foundation of quantum theory is described with all mathematical details included. The basis is the notion of theoretical variables, variables that can be attached to an agent or to a group of communicating agents. They may be ordinary physical variables. In a decision setting they may be decision variables. In a statistiical setting they may be parameters or future data. Theoretical variables may be accessible, possible to measure/realize, or they may be inaccessible. It is assumed that there exists an inaccessible variable phi such that all the accessible ones can be seen as functions of phi. The first main theorem is: Under weak symmetry assumptions consider a siuiation with two different, maximal, accessible variables. Then there exists a Hilbert space H such that all accessible variables have operators in H associated with them. The eigenvalues of the operators are the possible values of the variable. A variable is maximal if and only if all eigenspaces are one-dimensional.

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Why is it important?

It is very important to have a foundation of quantum mechanics which can be explained to outsiders. The foundation also implies reasonable views on the interpretation, which can lead to less debate on the interpretation issue.

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