A trajectory theory
The DeBroglie Bohm pilot wave theory is impressive and appealing but intrinsically inadequate. It describes a quantum particle travelling through the apparatus guided by a mysterious pilot wave. All the weird quantum behaviour is due to the pilot wave and its unexplained interaction with the particle. Both these aspects are not classical.
It is good because…
When you consider that quantum interference has been observed with large composite objects: Silver atoms, Bucky balls even insulin molecules. These are objects that have a fixed size, they are local. Their very existence and properties depends upon their precise and compact structure. These objects come from a source on one side of the apparatus and arrive at a detector on the other side. I claim the only logical explanation is that they travel through the apparatus by a trajectory that gives the interference effects. The alternative, that they don’t exist inside the apparatus, or that they are a smeared out object is untenable – well it is too me. The pilot wave theory describes trajectories like this.
But we need more…
The origin and action of the pilot wave needs to be derived from a more fundamental principle.
My proposal….
I have shown that non-orientable time-reversing structures (manifolds) can explain quantum theory in principle. What we need now is some mechanism that uses the acausal structure to give rise to non classical trajectories. We can already show that the twisting of the time direction gives the equations of electromagnetism, but we need more, we need a mechanism that gives a momentum dependent path that is universal, independent of the particle composition. In all the rest of physics such equations are derived from a variational principle and paths turn out to be those that minimise the action. That is the route I am currently pursuing.