causality and operationalism:from sets and functions to monads

Question

When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing zeeman splitting. We normally use this behaviour to create a function, thinking of the system as being composed of a set of states. I am interested in a program which borrows some of the assumptions of quantum gravity. Namely, I am working towards a picture where states are not fundamental, but instead processes are. This leads us to the following picture. We take the turning of the knob as a morphism and the change in the data output as another morphism. The experiment, then, is a map from an arrow to an arrow and this is just an endofunctor on the category of the apparatus. Can we then use this endofunctor to create a monad and subsequently an algrebraic theory for the system under investigation?

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Comments

"Of course, states don't exist, only processes do." - That's one hell of a statement. Perhaps we would be better sticking to physics than philosophy.

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Sounds me as a sohisticated rehearsal of the old debate of operator against wave function, or Heisenberg vs Schroedinger pictures.

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You haven't defined the category of the apparatus. A definition seems to be necessary before looking for a monad structure.

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