Unique transition probabilities in the modal interpretation

The modal interpretation of quantum theory ascribes at each instant physical magnitudes with definite values to quantum systems. Starting from certain natural requirements, I determine unique solutions for the evolution of these possessed magnitudes in free systems and in special cases of interacting systems. The evolution is given in terms of transition probabilities that relate the values of the possessed magnitudes at one instant to the values at a second instant. I also determine a joint property ascription to a composite system and its separate subsystems. Finally, I give a proof that the predictions of the modal interpretation with respect to measurement outcomes agree with the predictions of the standard interpretation.
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