Dr. R,
I know what you are saying, and I am well informed on Liouville's theorem. I also know about the attempts that have been made by Bohm using de Broglie's "pilot" wave. Whether you call it "uncertainty" or "indeterminacy" does not solve the ontological problems you have with all the approaches from Copenhagen to Bohm.
According to my insight the problem has all along been the interpretation that matter consist of particles, and that the (delta)p gives the uncertainty or indeterminacy of the momentum of the particle. It just cannot do that for a time-independent (stationary) wave, because for matter waves (having mass) momentum is determiined by relativity; i.e. by how fast the observer is moving relative to the matter or vice-versa. This is not a problem for light because light is always travelling at a speed c relative to any observer. Thus, if (delta)p gives the uncertainty in momentum, is this uncertainty the same relative to any inertial reference frame? Hardly likely.
These problems disappear when it is assumed that a free electron is a localised wave with a centre of charge. The ground-state energy of the wave is then the electron's mass and therefore the electron also has a centre of mass. It acts like a point particle when "viewed from outside" the localised wave (classical mechanics and electrodynamics apply as we know from numerous experiments), while quantum mechanics kick in when the wave functions start to overlap by a critical amount.
Thus instead of assuming there are electrons "whizzing around the nucleus" (and that they are doing this without radiating light in total violation of Maxwell's equations) the electron-charge distributed within the intensity of the electron-orbital and is thus stationary as it should be.
What the uncertainty relationship for "momentum" and position gives is just the size of the wave; and as for any other wave, this is determined by the boundary conditions. Thus a free electron is a localised entity as can be verified experimentally, while when encountering a double split it spreads to go through both and then superpose on the other side. When, however, making a measurement on the other side before superposition occurs the electron becomes localised again and no diffraction pattern develops.
What I find strange is that science has come to doubt experimental results and, since Bohr, Born and Heisenberg, resorted to "magic" (Voodo inerpretations): i.e. things happen when we dont look which we cannot fathom and even if we look we still cannot fathom what is happening except if we look many times. In fact, by discarding the concept of particles and postulating waves that can change their spatial extent when the boundary conditions change, leads to a total causal interpretation for quantum mechanics. There should not be any doubt that when an entity passes a double slit and contributes to the formation of a diffraction patter, then this entity MUST have gone through both slits. This is what we know from experiment and this is what we have to conclude as experimental philosophers.
