Abstract
A new foundation of quantum mechanics for systems symmetric under a compact symmetry group is proposed. The foundation is given by a link to classical statistics and coupled to the concept of parameter. A vector ϕ of parameters is called an inaccessible c-variable if experiments can be provided for the single parameter, but no experiment can be provided for ϕ. This is related to the concept of complementarity in quantum mechanics, but more generally to contrafactual parameters. Using these concepts and some weak assumption, the Hilbert space of quantum mechanics is constructed. The complete set of axioms of quantum mechanics is provided by proving Born's formula under weak assumptions.
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