Quantum Foundations

Work on formulating general probabilistic theories in an operational context has tended to concentrate on the probabilistic aspects (convex cones and so on) while remaining relatively naive about how the operational structure is built up (combining operations to form composite systems, and so on). In particular, an unsophisticated notion of a background time is usually taken for granted. It pays to be more careful about these matters for two reasons. First, by getting the foundations of the operational structure correct it can be easier to prove theorems. And second, if we want to construct new theories (such as a theory of Quantum Gravity) we need to start out with a sufficiently general operational structure before we introduce probabilities. I will present an operational structure which is sufficient to provide a foundation for the probabilistic concepts necessary to formulate quantum theory. According to Bob Coecke, this operational structure corresponds to a symmetric monoidal category. I will then discuss a more general operational framework (which I call Object Oriented Operationalism) which provides a foundation for a more general probabilistic framework which may be sufficient to formulate a theory of Quantum Gravity. This more general operational structure does not admit an obvious category theoretic formulation.

I will rephrase the question, "What is a quantal reality?" as "What is a quantal history?" (the word history having here the same meaning as in the phrase sum-over-histories). The answer I will propose modifies the rules of logical inference in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical logic, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.

Researchers in quantum foundations claim (D'Ariano, Fuchs, ...): Quantum = probability theory + x and hence: x = Quantum - probability theory Guided by the metaphorical analogy: probability theory / x = flesh / bones we introduce a notion of quantum measurement within x, which, when flesing it with Hilbert spaces, provides orthodox quantum mechanical probability calculus.

Removing the mystery from quantum mechanics, the Bohmian perspective – a way of describing the motion of quantum particles, and applying this to spacetime singularities (where gravity becomes infinite) like those inside a black hole.

The nature of time, probability and quantum mechanics, philosophy of physics and metaphysics, especially issues involving the role of mathematical tools like symmetry in physics, and applying this formal apparatus to the philosophy of mind.