, the uncertainty principle sets insurmountable limits to our knowledge, leaving plenty of room for chance in the universe. Particularly at the level of subatomic particles, we can never exactly pinpoint something (say an electron) and know everything about it; we can only specify the probabilities of finding the electron here or there or with one velocity or another. And that is true of all its relevant characteristics. In quantum mechanics, the collection of all the defining characteristics of something is called its state. For example, if that something happens to be your bicycle, its state will include all the relevant information about the bike—from it being in your garage, to its tires being pumped enough, whether it is standing upright or lying on its side, whether the brakes work, if the chain has been greased, and everything else you can think about it. Every combination of possibilities for all these features defines a definite “state” of the bike.
. Before we observe the electron, it is equally likely to be anywhere in the box. So if we divide up the length of the box into ten equal sections, there will be equal probability of 10 percent of it being in any one of those sections. Let’s represent that in another picture just below it by drawing a bunch of little rectangles at each position, all with equal heights corresponding to a probability of 10 percent.
Figure 15.1 Wave function collapse: Before observation (left panels), the electron is everywhere in the box simultaneously as shown in the upper left panel, and therefore its wavefunction gives a flat probability shown in the lower left panel. After observation (right panels), the electron is found to be definitely in cell 5, and its wavefunction collapses to give 100 percent probability there and 0 percent elsewhere, as shown in the lower right panel.
So before we make an observation, all the rectangles are the same, so the wavefunction is just flat, but as soon as we observe the electron, the wavefunction becomes very tall and sharply localized in just one region. It seems as if the little rectangles in the wavefunction sort of collapsed from a broad, flat distribution to stack up to form a very narrow and tall shape, as a result of the observation. That is why this is called “wavefunction collapse.” The act of observing causes the probability density and the associated wavefunction to collapse from a shape that is flat and spread out to one that is narrow and tall in a small region.
Actually, the probability corresponds to the absolute square of the wavefunction, but that is a detail that we will not bother with here.