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By Root 2112 0

the combined wave depression is deep; and most important of all, where the peak of one crosses the trough of the other, the waves cancel and the water remains level. This is illustrated in Figure 8.3. If you were to insert a detector screen across the top of the figure that recorded the water’s agitation at each location—the larger the agitation, the brighter the reading—the result would be a series of alternating bright and dark regions on the screen. Bright regions would be where the waves reinforce each other, yielding much agitation; dark regions would be where the waves cancel, yielding no agitation. Physicists say the overlapping waves interfere with one another, and call the bright-dark-bright data they produce an interference pattern.

The similarity to Figure 8.2c is unmistakable, so in trying to explain the electron data we’re led to think about waves. Good. That’s a start. But the details are still murky. What kind of waves? Where are they? And what have they to do with particles such as electrons?

The next clue comes from the experimental fact I emphasized at the outset. Reams of data on the motion of particles show that regularities emerge only statistically. The same measurements performed on identically prepared particles will generally reveal them to be in different places; yet many such measurements establish that, on average, the particles have the same probability of being found at any given location. In 1926, the German physicist Max Born joined these two clues together and with them made a leap that nearly three decades later would earn him a Nobel Prize. You’ve got experimental evidence that waves play a role. You’ve got experimental evidence that probabilities play a role. Perhaps, Born suggested, the wave associated with a particle is a probability wave.

Figure 8.3 When two water waves overlap, they “interfere,” creating alternating regions of more or less agitation called an interference pattern.

It was an unprecedented and spectacularly original contribution. The idea is that in analyzing the motion of a particle we shouldn’t think of it as a rock hurtling from here to there. Instead, we should think of it as a wave undulating from here to there. Locations where the wave’s values are large, near its peaks and troughs, are locations where the particle is likely to be found. Locations where the probability wave’s values are small are locations where the particle is unlikely to be found. Locations where the wave’s values vanish are places where the particle won’t be found. As the wave rolls onward, the values evolve, going up in some locations, down in others. And since we’re interpreting the undulating values as undulating probabilities, the wave is justly called a probability wave.

To flesh out the picture, consider how it explains the double-slit data. As an electron travels toward the barrier in Figure 8.2c, quantum mechanics tells us to think of it as an undulating wave, as in Figure 8.4. When the wave encounters the barrier, two wave fragments make it through the slits and undulate onward toward the detector screen. What happens next is key. Much like overlapping water waves, the probability waves emerging from the two slits overlap and interfere, yielding a combined form that looks much like that in Figure 8.3: a pattern of high and low values that, according to quantum mechanics, corresponds with a pattern of high and low probabilities for where the electron will land. When electron after electron is fired, the cumulative landing positions conform to this probability profile. Many electrons land where the probability is high, few where it’s low, and none where the probability vanishes. The result is the bright and dark bands of Figure 8.2c.3

And that’s how quantum theory explains the data. The description makes manifest that each electron does “know” about both slits, since each electron’s probability wave passes through both. It’s the union of these two partial waves that dictates the probabilities for where the electrons land. That’s why the mere presence of a second slit affects