One of the most convincing demonstrations of the particle nature of matter is the straight-line trajectories traced out in cloud chambers. How can you explain this with any kind of wave theory of matter?
One of the early great successes of the wave theory was the explanation of radioactive decay due to George Gamow. Gamow treated the uranium atom as a simple potential well, just like the ones we analyze in second-year physics. From the hyperphysics website, here is a picture of how it works:
This is the wave-theoretic explanation of how a uranium atom emits alpha particles, and it works very well. But what happens when we place the uranium atom next to a cloud chamber? According to this picture, the cloud chamber is innundated by a steady, ultra-low intensity alpha wave field, which decays over a period of some four billion years. During that same time period, the uranium, initially in its pritstine state, is subsequently found as a superposition of uranium and lead, with the lead component increasing gradually over that same four-billion year span. That's the wave picture of decay.
Ridiculous, you say? That seems to be the general opinion of the physics world. Following the Copenhagen interpretation, we reject the notion of a superposition of uranium and lead. We say that the wave picture represents merely the probability of a transition, and when a transition actually happens, it takes place with infinite suddenness. At once the uranium is gone, the lead is in its place, and a straight-line trace appears in the cloud chamber.
It's an interesting exercise to try and say exactly why the notion of a uranium-lead hybrid is so clearly impossible. Remember for one thing that such experiments are typically not carried out with single atoms, but with samples numbering in the millions or more. (With a mere million uranium atoms we would wait four thousand years for a single click in the geiger counter, so it would be an inconveniently small sample to work with.) Furthermore, there seems to be a respected point of view, based on density matrix theory, which holds that an ensemble of uranium mixed with lead is indistinguishable in principle from a corresponding ensemble of urnaium/lead superpositions. (I refer you to this discussion on stackexchange.com for more details).
But leaving aside the problematic question of the uranium/lead superposition, we are still left with the very vexing question: how can the wave theory of matter explain the straight-line tracks in the cloud chambers? Because according the wave picture, the cloud chamber is innundated by a very slow, steady, low-intensity alpha wave field. By what possible mechanism can this extremely tenuous field leave such obvious concentrated havoc in its wake? And if it can, why is it not doing it all the time and everywhere? Why do ionization events not occur here, there, and everywhere, continuously for four billion years? Why the lone single track, so clearly identifiable as a single concentrated particle?
In 1929, Nevill Mott published a paper that claimed to show the straight line tracks were not only consistent with the wave theory, but to be expected. Mott's analysis was widely recognized in its day, but it was not considered to be evidence of the wave nature of matter, nor did Mott intend it that way. His wave function is calculated in multi-dimensional phase space, and he clearly explains his analysis in terms of probabilities, with the wave function simply being used as a calculation tool to determine the probabilities of simultaneous ionization events. Following the Copenhagen school, Mott does not ascribe physical reality to his wave function.
I don't believe that physics takes place in multi-dimensional phase space. I believe it happens in real four-dimensional space-time, and that's where we have to be able to explain things. I don't see how you can have this intricate wave mechanics going on in abstract space, and then describe the physical reality by saying an alpha particle crashes into an obstacle and knocks out an electron. If that's all that's happening, then why do you need all that wave machinery to calculate it?
I think there must be a physical, real-time wave explanation to what goes on in the cloud chamber, and over the next few days I'm going to try and lay it out.