Note that de Broglie’s version of a hidden-variables theory is distinctly nonlocal.  In describing the movement of multiple particles, the guidance equation (the equation for de Broglie’s guiding wave, the pilot wave) for any given particle depends upon the simultaneous position of all of the other particles. So, as soon as a particle moves to a new position under the pilot wave, the motion of all of the other particles, which could be widely dispersed, depends upon the new position of the first particle, no matter how distant. So, de Broglie’s theory is essentially nonlocal, even though it assigns the local hidden variables of position and momentum to individual particles.

Returning to the double-slit experiment, if – and it should be strongly emphasized – if we believe de Broglie and Einstein were right in thinking that the electron really exists as a particle as it travels between the slits and the screen, then this would suggest an explanation for the apparent unpredictability of where each electron lands on the detecting screen. We would know at least in principle the precise position and momentum of the electron at each moment (which, remember, according to Heisenberg’s Uncertainty Principle, is impossible), and so we would indeed know exactly where the electron would land on each occasion. On its journey to the screen, it would be subject to all the random buffeting of any “turbulence” of the electromagnetic field in its path, and any other fields that happen to interact with the electron, and, just as we could in theory predict the outcome of every throw of a die if we could take into account each encounter with every air molecule and every muscle twitch of the hand that cast it, so we would be able to predict the electron’s drunken zig-zag route all the way to its ultimate destination on the detecting screen. In other words, the seemingly random fashion in which the pattern emerges on the detecting screen would in principle be predictable if we knew the exact location of all the stray fields that the electron would encounter en route.

It follows that, if the de Broglie explanation were true, then every event in our universe would in principle be predictable, meaning that our universe would be deterministic. However, I said earlier that the case for parallel universes depends upon our universe being indeterministic. In order to sort this out, we’re going to take a couple of diversions, starting with quantum spin.