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causality and operationalism:from sets and functions to monads

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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?

This post has been migrated from (A51.SE)
asked Nov 27, 2011 in Theoretical Physics by user442920 (90 points) [ no revision ]
You haven't defined the category of the apparatus. A definition seems to be necessary before looking for a monad structure.

This post has been migrated from (A51.SE)
Sounds me as a sohisticated rehearsal of the old debate of operator against wave function, or Heisenberg vs Schroedinger pictures.

This post has been migrated from (A51.SE)
"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.

This post has been migrated from (A51.SE)

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