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By Root 2013 0

But you need to exercise care, because understanding based on the single-particle illustrations can take you only so far. For example, based on Figure 8.6 it is natural to think that Figure 8.13 represents particles that are all clustered around the same location. Yet, that’s not right. The peaked shape in Figure 8.13 symbolizes that each of the particles making up you and each of the particles making up the device starts out in the ordinary, familiar state of having a position that is nearly 100 percent definite. But they are not all positioned at the same location. The particles constituting your hand, shoulder, and brain are, with near certainty, clustered within the location of your hand, shoulder, and brain; the particles constituting the measuring device are, with near certainty, clustered within the location of the device. The peaked wave shape in Figure 8.13 denotes that each of these particles has only the most remote chance of being found anywhere else.

If you now perform the measurement illustrated in Figure 8.14, the many-particle probability wave (for the particles inside you and the device), by virtue of the interaction with the electron, evolves (as illustrated schematically in Figure 8.14a). All the particles involved still have nearly definite positions (within you; within the device), which is why the wave in Figure 8.14a maintains a spiked shape. But a mass particle rearrangement occurs that results in the words “Strawberry Fields” forming in the device’s readout and also in your brain (as in Figure 8.14b). Figure 8.14a represents the mathematical transformation dictated by Schrödinger’s equation, the first kind of story. Figure 8.14b illustrates the physical description of such mathematical evolution, the second kind of story. Similarly, if we perform the experiment in Figure 8.15, an analogous wave shift takes place (Figure 8.15a). This shift corresponds to a mass particle rearrangement that spells out “Grant’s Tomb” in the display and generates within you the associated mental impression (Figure 8.15b).

Now use linearity to put the two together. If you measure the position of an electron whose probability wave is spiked at two locations, the probability wave for you and your device commingles with that of the electron, resulting in the evolution shown in Figure 8.16a—the combined evolutions depicted in Figure 8.14a and Figure 8.15a. So far, this is nothing but an illustrated and annotated version of the first type of quantum story. We start with a probability wave of a given shape, Schrödinger’s equation evolves it forward in time, and we end up with a probability wave of a new shape. But the details we’ve overlaid now let us tell this mathematical story in more qualitative, type-two story language.

Physically, each spike in Figure 8.16a represents a configuration of an enormous number of particles that results in a device having a particular reading and your mind acquiring that information. In the left spike, the reading is Strawberry Fields; in the right, it’s Grant’s Tomb. Besides that difference, nothing distinguishes one spike from the other. I emphasize this because it’s essential to realize that neither is somehow more real than the other. Nothing but the device’s particular reading, and your reading of that reading, distinguishes the two multiparticle wave spikes.

Which means that our type-two story, as illustrated in Figure 8.16b, involves two realities.

In fact, the focus on the device and your mind is merely another simplification. I could also have included the particles that make up the laboratory and everything therein, as well as those of the earth, the sun, and so on, and the whole discussion would have been the same, essentially verbatim. The only difference would have been that the glowing probability wave in Figure 8.16a would now have information about all those other particles, too. But because the measurement we’re discussing has essentially no impact on them, they’d just come along for the ride. It’s useful to include those particles, though, because our second story can