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Figure 8.4 When we describe the motion of an electron in terms of an undulating probability wave, the puzzling interference data are explained.

Not So Fast

Although I’ve focused on electrons, similar experiments have established the same probability-wave picture for all of nature’s basic constituents. Photons, neutrinos, muons, quarks—every fundamental particle—all are described by waves of probability. But before we declare victory, three questions immediately present themselves. Two are straightforward. One is a bear. It’s the latter that Everett sought to answer back in the 1950s, and it led him to a quantum version of parallel worlds.

First, if quantum theory is right and the world unfolds probabilistically, why is Newton’s nonprobabilistic framework so good at predicting the motion of things from baseballs to planets to stars? The answer is that probability waves for big things usually (but not always, as we will shortly see) have a very particular shape. They’re extraordinarily narrow, as in Figure 8.5a, meaning there’s a huge probability, just shy of 100 percent, that the object is located where the wave is peaked and a minuscule probability, just a shade above 0 percent, that it’s located anywhere else.4 Moreover, the quantum laws show that the peaks of such narrow waves move along the very same trajectories that emerge from Newton’s equations. And so, while Newton’s laws predict precisely the trajectory of a baseball, quantum theory offers only the most minimal refinement, saying there’s a nearly 100 percent probability that the ball will land where Newton says it should, and a nearly 0 percent probability that it won’t.

Figure 8.5 (a) The probability wave for a macroscopic object is generally narrowly peaked. (b) The probability wave for a microscopic object, say, a single particle, is typically widely spread.

In fact, the words “just shy” and “nearly” don’t do the physics justice. The chance of a macroscopic body deviating from Newton’s predictions is so fantastically tiny that if you’d been keeping tabs on the cosmos for the last few billion years, the odds are overwhelming that you’d have never seen it happen. But according to quantum theory, the smaller an object, the more spread-out its probability wave typically is. For example, a typical electron’s wave might look like that in Figure 8.5b, with substantial probabilities of being at a variety of locations, a totally foreign concept in a Newtonian world. And that’s why it’s the microrealm where the probabilistic nature of reality comes to the fore.

Second, can we see the probability waves on which quantum mechanics relies? Is there any way to directly access the unfamiliar probabilistic haze, such as that illustrated schematically in Figure 8.5b, in which a single particle has a chance of being found in a variety of locations? No. The standard approach to quantum mechanics, developed by Bohr and his group, and called the Copenhagen interpretation in their honor, envisions that whenever you try to see a probability wave, the very act of observation thwarts your attempt. When you look at an electron’s probability wave, where “look” means “measure its position,” the electron responds by snapping to attention and coalescing at one definite location. Correspondingly, the probability wave surges to 100 percent at that spot, while collapsing to 0 percent everywhere else, as in Figure 8.6. Look away, and the needle-thin probability wave rapidly spreads, indicating that once again there’s a reasonable chance of finding the electron at a variety of locations. Look back, and the electron’s wave collapses anew, eliminating the range of possible places the electron might be found in favor of its occupying a single definite spot. In short, every time you attempt to see the probabilistic haze it disappears—it collapses—and is supplanted by familiar reality. The detector screen in Figure 8.2c provides a case in point: it measures the impinging probability wave of an electron and thus immediately causes it to collapse. The detector forces the electron