In a recent paper Griffiths [38] has argued, based on the consistent histories interpretation, that Hilbert space quantum mechanics (QM) is noncontextual. According to Griffiths the problem of contextuality disappears if the apparatus is "designed and operated by a competent experimentalist" and we accept the Single Framework Rule (SFR). We will argue from a representational realist stance that the conclusion is incorrect due to the misleading understanding provided by Griffiths to the meaning of quantum contextuality and its relation to physical reality and measurements. We will discuss how the quite general incomprehension of contextuality has its origin in the "objective-subjective omelette" created by Heisenberg and Bohr. We will argue that in order to unscramble the omelette we need to disentangle, firstly, representational realism from naive realism, secondly, ontology from epistemology, and thirdly, the different interpretational problems of QM. In this respect, we will analyze what should be considered as Meaningful Physical Statements (MPS) within a theory and will argue that Counterfactual Reasoning (CR) -considered by Griffiths as "tricky"- must be accepted as a necessary condition for any representational realist interpretation of QM. Finally we discuss what should be considered as a problem (and what not) in QM from a representational realist perspective.
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of
p-mechanics which is a consistent physical theory capable of describing both classical and quantum mechanics simultaneously.
p-Mechanics starts from the observation that the one dimensional representations of the Heisenberg group play the same role in classical mechanics which the infinite dimensional representations play in quantum mechanics. In this thesis we introduce the idea of states to
p-mechanics.
p-Mechanical states come in two forms: elements of a Hilbert space and integration kernels. In developing
p-mechanical states we show that quantum probability amplitudes can be obtained using solely functions/distributions on the Heisenberg group. This theory is applied to the examples of the forced, harmonic and coupled oscillators. In doing so we show that both the quantum and classical dynamics of these systems can be derived from the same source. Also using
p-mechanics we simplify some of the current quantum mechanical calculations. We also analyse the role of both linear and non-linear canonical transformations in
p-mechanics. We enhance a method derived by Moshinsky for studying the passage of canonical transformations from classical to quantum mechanics. The Kepler/Coulomb problem is also examined in the
p-mechanical context. In analysing this problem we show some limitations of the current
p-mechanical approach. We then use Klauder's coherent states to generate a Hilbert space which is particularly useful for the Kepler/Coulomb problem.