In my last post and the previous one, I put one or two particles in various sorts of quantum superpositions, and claimed that some cases display quantum interference and some do not. Today we’ll start looking at these examples in detail to see why interference does or does not occur. We’ll also encounter a difficulty asking where the interference occurs — a difficulty which will lead us eventually to deeper understanding.
First, a lightning review of interference for one particle. Take a single particle in a superposition that gives it equal probability of being right of center and moving to the left OR being left of center and moving to the right. Its wave function is given in Fig. 1.
Then, at the moment and location where the two peaks in the wave function cross, a strong interference effect is observed, the same sort as is seen in the famous double slit-experiment.
The simplest way to analyze this is to approach it as a 19th century physicist might have done. In this pre-quantum version of the problem, shown in Fig. 3, the particle has a definite location and speed (and no wave function), with
- a 50 percent chance of being left of center and moving right, and
- a 50 percent chance of being right of center and moving left.
Nothing interesting, in either possibility, happens when the particle reaches the center. Either it reaches the center from the left and keeps on going OR it reaches the center from the right and keeps on going. There is certainly no collision, and, in pre-quantum physics, there is also no interference effect.
Still, something abstractly interesting happens there. Before the particle reaches the center, the top and bottom of Fig. 3 are different. But just when the particle is at x=0, the two possibilities in the superposition describe the same object in the same place. In a sense, the two possibilities meet. In the corresponding quantum problem, this is the precise moment where the quantum interference effect is largest. That is a clue.
(more…)
