My programme is to understand the CPT symmetry in a purely classical (non-quantum-field-theoretical) context. This is motivated by the fact that there seems to be nothing in the CPT symmetry that requires any non-classical treatment. Although the empirical evidence verifying the CPT-symmetry comes from kaon collisions modeled in quantum field theory, the critical element that distinguishes quantum field theory from its predecesors like the Dirac theory of the electron is its incorporation of particle annihilation and creation. There is seemingly nothing about the CPT symmetry that requires particle annihilation and creation. It's true that the signature phenomena that confirm the hypothesis that our laws are CPT symmetric are particle experiments, but this doesn't imply that permitting particle creation is necessary for a set of laws to be CPT symmetric, nor that a classical theory of CPT would be unfruitful.

One of the specific projects my programme suggests is to determine a way of embedding both Galilean spacetime and Minkowski spacetime within a higher dimensional space such that charge-conjugation is modeled as a reflection of the physical fields across the (non-temporal, non-spatial) higher dimensions. Modeling charge conjugation as a geometrical operation on the base manifold will hopefully make it such that the geometrical objects representing the physical fields will be trivially symmetric under CPT or at least that, insofar as the laws are concerned, any CPT asymmetry in the physical fields will play no role in the dynamics.

There are potentially many interesting questions this programme may bear on:

• Can we write formulate all of non-relativistic quantum mechanics in terms of a five-dimensional Galilean spacetime?
• What theory of classical mechanics can be formulated in five dimensions?
• Can one formulate a Galilean theory of electromagnetic waves such that the underlying electromagnetic potential has the same transformation properties as it has to have in so far as the potentials serve as a background field for non-relativistic quantum mechanics.
• What is the structure in the higher dimensional theory that makes the field ontology readily interpretable in terms of particles?
• Can the five dimensional theory really avoid a particle ontology?
• Should we really interpret an electron going forward in time as a positron going backward in time?
• Is there a classical solution to the inconsistency of classical electromagnetic theory?
• Can Einstein's field equations and Newtonian gravity be reinterpreted in such a way that they can be related in a higher dimensional theory just like the Klein-Gordon and Schroedinger's equations are related by the Klein shift?
• Will we be able to interpret all physical fields in such a way that their improper transformations (like C, P, and T) can be read off in a straightforward way from their corresponding geometrical representations (like elements of a geometric algebra)?
• Why do particles have mass iff they interact via the weak force? Does this signify a deep connection between gravity and the weak force?
• What is the relationship between the phase space of non-relativistic quantum theory and the extra dimensions?
• Can we form a Bohmian interpretation of non-relativistic quantum mechanics into a relativistic theory by way of the Klein shift. Does this require that we reconceive the Bohm theory as something other than a world-particle or particle positions moving through space?
• Is there an explanation available to explain why the existence of mass (and other forms of energy) constrain the spacetime metric in a dynamic way? Is it because the higher dimensional manifold has a non-dynamical metric?