Modal Logic and Quantum Mechanics

meAnd here I am again. ¬†Yes this is me today. It’s too late to hide now.

Today I’d like to talk about modal logic. My introduction to symbolic logic and the predicate calculus began in a philosopy & logic class in the late Seventies. But that was merely true-false logic.

Modal logic is a generalization of simple logic, going beyond whether statements are true or not, but whether it is possible for them to be true, or necessary that they be true.

modal1

The combination of these operators yields some interesting theorems:

modal2

If this sounds more like philosophy (epistemology) as well as Quantum Mechanics, then perhaps it is. For example, one way to state the principle of “mixed states” such as we find in the “uncollapsed state vectors” might be the following:

modal3

Conversely, if one passes a beam of spinning particles such as electrons through a magnetic field so as to cause the “spin up” particles to deflect one way and the “spin-down” particles to deflect the other way, then the states are no longer mixed. In this case, looking at either one of the diverged result beams, we find that it is no longer possible to observe both “up” and “down” states:

modal4

More on this later –MRK

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