An application of ideal experiments to quantum mechanical measurement theory

It is shown that the rule for obtaining probabilities by squaring amplitudes is deducible from ideal experiments in a mechanics of unitary motion in a complex-linear space, with tensor product for making compound systems. Difficulty with tensor product in undoctored quaternionic quantum mechanics makes the argument inapplicable there. Except for the replacement by ideal experiments of a more formal unitary equivalence, the discussion is similar to that of Everett (1957). Diagonal expression of a general vector in the tensor product of two spaces is related to polar form of a matrix, in the Appendix.