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Here’s where things get weird. At first blush, the combined results suggest that the display should simultaneously register the locations of both spikes. As in Figure 8.10, the words “Strawberry Fields” and “Grant’s Tomb” should flash simultaneously, one location commingled with the other, like the confused monitor of a computer that’s about to crash. Schrödinger’s equation also dictates how the probability waves of the photons emitted by the measuring device’s display entangle with those of the particles in your rods and cones, and subsequently those rushing through your neurons, creating a mental state reflecting what you see. Assuming unlimited Schrödinger hegemony, linearity applies here too, so not only will the device simultaneously display both locations but also your brain will be caught up in the confusion, thinking that the electron is simultaneously positioned at both.

Figure 8.10 An electron’s probability wave is spiked at two locations. The linearity of Schrödinger’s equation suggests that a measurement of the electron’s position would yield a confusing amalgam of both locations.

For yet more complicated wave shapes, the confusion becomes yet wilder. A shape with four spikes doubles the dizziness. With six, it triples. Notice that if you keep on going, putting wave spikes of various heights at every location in the model Manhattan, their combined shape fills out an ordinary, more gradually varying quantum wave shape, as schematically illustrated in Figure 8.11. Linearity still holds, and this implies that the final device reading, as well as your final brain state and mental impression, are dictated by the union of the results for each spike individually.

Figure 8.11 A general probability wave is the union of many spiked waves, each representing a possible position of the electron.

The device should simultaneously register the location of each and every spike—each and every location in Manhattan—as your mind becomes profoundly puzzled, being unable to settle on a single definite location for the electron.5

But, of course, this seems grossly at odds with experience. No properly functioning device, when taking a measurement, displays conflicting results. No properly functioning person, on performing a measurement, has the mental impression of a dizzying mélange of simultaneous yet distinct outcomes.

You can now see the appeal of Bohr’s prescription. Hold the Dramamine, he’d declare. According to Bohr, we don’t see ambiguous meter readings because they don’t happen. He’d argue that we’ve come to an incorrect conclusion because we’ve overextended the reach of Schrödinger’s equation into the domain of big things: laboratory equipment that takes measurements, and scientists who read the results. Although Schrödinger’s equation and its feature of linearity dictate that we should combine the results from distinct possible outcomes—nothing collapses—Bohr tells us that this is wrong because the act of measurement tosses Schrödinger’s math out the window. Instead, he’d pronounce, the measurement causes all but one of the spikes in Figure 8.10 or Figure 8.11 to collapse to zero; the probability that a particular spike will be the sole survivor is proportional to the spike’s height. That unique remaining spike determines the device’s unique reading, as well as your mind’s recognition of a unique result. Dizziness done.

But for Everett, and later DeWitt, the cost of Bohr’s approach was too high. Schrödinger’s equation is meant to describe particles. All particles. Why would it somehow not apply to particular configurations of particles—those constituting the equipment that takes measurements, and those in the experimenters who monitor the equipment? This just didn’t make sense. Everett therefore suggested that we not dispense with Schrödinger so quickly. Instead, he advocated that we analyze where Schrödinger’s equation takes us from a decidedly different perspective.

Many Worlds

The challenge we’ve encountered is that