Probability Waves

I was thinking about quantum mechanics again. In the standard pop-science book the author usually asks the reader to visualize a flat surface with different heights of waves on them. These waves, unlike water waves which show higher points of energy, for example, actually show in this visualization, the differing probabilities of a particle being found at a different point in space. So when they say that light going through two slits (the standard interference pattern we’ve all seen time and time again) the light and dark patterns represent different places the photon particles land. The reinforcement – “constructive interference” is an increased probability. The dark patterns, destructive interference. But each photon taken in and  of itself, could land on any spots, it is just the averaged out probability of all of them that creates this pattern.

But what kind of waves are probability waves? Unlike water or sound or sports arena waves they do not require a medium. So in this respect they seem to be like electro-magnetic waves. But (due in large part to Bell’s Theorem)  probability waves appear to act in a non-local manner, that is, they propagate instantaneously to all parts of the universe, instead of propagating at the speed of light. So unlike electro-magnetic waves, which are the basis for special relativity, probability waves do not follow with the rules of locality as laid down by Einstein. How then do they (the cognosciendi) maintain these results? Simple. Probability waves are not things, not matter, not substance. Then no ‘thing’ is moving at superluminal speeds.

Where does that leave us? We are familiar with the high school science texts with pictures of the two-slit experiment linked above. But yet, the waves can’t actually be there. So what, exactly, is a probability wave? Do we answer Einstein’s famous quote with: yes, God does play dice?