by Brian Greene
To keep the discussion accessible, I’ve focused on the position measurement of a single particle, and one that has a particularly simple probability wave. But Everett’s proposal applies generally. If you measured the position of a particle whose probability wave has any number of spikes, say, five, the result, according to Everett, would be five parallel realities differing only by the location registered on each reality’s device, and within the mind of each reality’s you. If one of these yous then measured the position of another particle whose wave had seven spikes, that you and that world would split again, into seven more, one for each possible outcome. And if you measured a wave like that of Figure 8.11, which can be partitioned into a great many tightly packed spikes, the result would be a great many parallel realities in which each possible particle location would be recorded on a device and read by a copy of you. In Everett’s approach, everything that is possible, quantum-mechanically speaking (that is, all those outcomes to which quantum mechanics assigns a nonzero probability), is realized in its own separate world. These are the “many worlds” of the Many Worlds approach to quantum mechanics.
Figure 8.12 In Everett’s approach, the measurement of a particle whose probability wave has two spikes yields both outcomes. In one world, the particle is found at the first location; in another world, it is found at the second.
If we apply the terminology we’ve been using in earlier chapters, these many worlds would properly be described as many universes, composing a multiverse, the sixth we’ve encountered. I’ll call it the Quantum Multiverse.
A Tale of Two Tales
In describing how quantum mechanics may generate many realities, I used the word “split.” Everett used it. So did DeWitt. Nevertheless, in this context it’s a loaded verb with the potential to grossly mislead, and I’d intended not to invoke it. But I gave in to temptation. In my defense, it’s sometimes more effective to use a sledgehammer to break down a barrier separating us from an unfamiliar proposal about the workings of reality, and to subsequently repair the damage, than it is to delicately carve a pristine window that directly reveals the new vista. I’ve been using that sledgehammer; in this and the next section I’ll undertake the necessary repairs. Some of the ideas are a touch more difficult than those we’ve so far encountered, and the explanatory chains are a bit longer as well, but I encourage you to stay with me. I’ve found that all too often, people who learn about, or are even somewhat familiar with, the Many Worlds idea have the impression that it emerged from speculation of the most extravagant sort. But nothing could be further from the truth. As I will explain, the Many Worlds approach is, in some ways, the most conservative framework for defining quantum physics, and it’s important to understand why.
The essential point is that physicists must always tell two kinds of stories. One is the mathematical story of how the universe evolves according to a given theory. The other, also essential, is the physical story, which translates the abstract mathematics into experiential language. This second story describes how the mathematical evolution will appear to observers like you and me, and more generally, what the theory’s mathematical symbols tell us about the nature of reality.6 In the time of Newton, the two stories were essentially identical, as I suggested with my remarks in Chapter 7 about Newtonian “architecture” being immediate and palpable. Every mathematical symbol in Newton’s equations has a direct and transparent physical correlate. The symbol x? Oh, that’s the ball’s position. The symbol v? The ball’s velocity. By the time we get to quantum mechanics, however, translation between the mathematical symbols and what we can see in the world around us becomes far more subtle. In turn, the language used and the concepts deemed relevant to each of the two stories become so different that you need both to acquire a full understanding. But it’s important to keep straight which story is which: to understand fully which ideas and descriptions are invoked as part of the theory’s fundamental mathematical structure and which are used to build a bridge to human experience.
Let’s tell the two stories for the Many Worlds approach to quantum mechanics. Here’s the first.
The mathematics of Many Worlds, unlike that of Copenhagen, is pure, simple, and constant. Schrödinger’s equation determines how probability waves evolve over time, and it is never set aside; it is always in effect. Schrödinger’s math guides the shape of probability waves, causing them to shift, morph, and undulate over time. Whether it’s addressing the probability wave for a particle, or for a collection of particles, or for the various assemblages of particles that constitute you and your measuring equipment, Schrödinger’s equation takes the particles’ initial probability wave shape as input and then, like the graphics program driving an elaborate screen saver, provides the wave’s shape at any future time as output. And that, according to this approach, is how the universe evolves. Period. End of story. Or, more precisely, end of first story.
Notice that in telling the first story I did not need the word “split” nor the terms “many worlds,” “parallel universes,” or “Quantum Multiverse.” The Many Worlds approach does not hypothesize these features. They play no role in the theory’s fundamental mathematical structure. Rather, as we will now see, these ideas are called upon in the theory’s second story, when, following Everett and others who’ve since extended his pioneering work, we investigate what the mathematics tells us about our observations and measurements.
Let’s start simply—or, as simply as we can. Consider measuring an electron that has a spiked probability wave, as in Figure 8.9. (Again, don’t worry about how it got this wave shape; just take it as a given.) As noted earlier, to tell the first story of even this measurement process in detail is beyond what we can do. We’d need to use Schrödinger’s math to figure out how the probability wave describing the positions of the huge number of particles that constitute you and your measuring device joins with the probability wave of the electron, and how their union evolves forward in time. My undergraduate students, many of whom are quite able, often struggle to solve Schrödinger’s equation for even a single particle. Between you and the device, there are something like 1027 particles. Working out Schrödinger’s math for that many constituents is virtually impossible. Even so, we understand qualitatively what the math entails. When we measure the electron’s position, we cause a mass particle migration. Some 1024 or so particles in the device’s display, like performers in a crisply choreographed halftime show, race to the appropriate spot so that they collectively spell out “Thirty-fourth Street and Broadway,” while a similar number in my eyes and brain do whatever’s required for me to develop a firm mental grasp of the result. Schrödinger’s math—however impenetrable explicit analysis of it might be when faced with so many particles—describes such a particle shift.
To visualize this transformation at the level of a probability wave is also far beyond reach. In Figure 8.9 and others in that sequence, I used two axes, the north-south and east-west street grid of our model Manhattan, to denote the possible positions of a single particle. The probability wave’s value at each location was denoted by the wave’s height. This already simplifies things because I’ve left out the third axis, the particle’s vertical position (whether it’s on the second floor of Macy’s, or the fifth). Including the vertical would have been awkward, because if I’d used it to denote position, I’d have no axis left for recording the size of the wave. Such are the limitations of a brain and a visual system that evolution has firmly rooted in three spatial dimensions. To properly visualize the probability wave for roughly 1027 particles, I’d need to include three axes for each, allowing me to account mathematically for every possible position each particle could occupy.* Adding even a single vertical axis to Figure 8.9 would have made it difficult to visualize; to contemplate adding a billion billion billion more is, well, silly.
But a mental image of the key ideas is important; so, however imperfect the result, let’s give it a try. In sketching the probability wave for the particles making up you and yo
ur device, I’ll abide by the two-axis flat-page limit but will use an unconventional interpretation of what the axes mean. Roughly speaking, I’ll think of each axis as comprising an enormous bundle of axes, tightly grouped together, which will symbolically delineate the possible positions of a similarly enormous number of particles. A wave drawn using these bundled axes will therefore lay out the probabilities for the positions of a huge group of particles. To emphasize the distinction between the many-particle and single-particle situations, I’ll use a glowing outline for the many-particle probability wave, as in Figure 8.13.
Figure 8.13 A schematic depiction of the combined probability wave for all the particles making up you and your measuring device.
The many-particle and single-particle illustrations have some features in common. Just as the spiked wave shape in Figure 8.6 indicates probabilities that are sharply skewed (being almost 100 percent at the spike’s location and almost 0 percent everywhere else), so the peaked wave in Figure 8.13 also denotes sharply skewed probabilities. 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 now be augmented to comprise not only a copy of you examining a device that’s undertaken a measurement, but also copies of the surrounding laboratory, the rest of the earth in orbit around the sun, and so on. This means that each spike, in story-two language, corresponds to what we’d traditionally call a bona fide universe. In one such universe, you see “Strawberry Fields” on the display’s reading; in the other, “Grant’s Tomb.”
Figure 8.14 (a) A schematic illustration of the evolution, dictated by Schrödinger’s equation, of the combined probability wave for all the particles making up you and the measuring device, when you measure the position of an electron. The electron’s own probability wave is spiked at Strawberry Fields.
Figure 8.14 (b) The corresponding physical, or experiential, story.
Figure 8.15 (a) The same type of mathematical evolution as in Figure 8.14a, but with the electron’s probability wave spiked at Grant’s Tomb.
Figure 8.15 (b) The corresponding physical, or experiential, story.
Figure 8.16 (a) A schematic illustration of the evolution of the combined probability wave of all the particles making up you and your device, when measuring the position of an electron whose probability wave is spiked at two locations.
Figure 8.16 (b) The corresponding physical, or experiential, story.
If the electron’s original probability wave had, say, four spikes, or five, or a hundred, or any number, the same would follow: the wave evolution would result in four, or five, or a hundred, or any number of universes. In the most general case, as in Figure 8.11, a spread-out wave is composed of spikes at every location, and so the wave evolution would yield a vast collection of universes, one for each possible position.7
As advertised, though, the only thing that happens in any of these scenarios is that a probability wave enters Schrödinger’s equation, his math goes to work, and out comes a wave with a modified shape. There’s no “cloning machine.” There’s no “splitting machine.” This is why I said earlier that such words can give a misleading impression. There’s nothing but a probability-wave-evolution “machine” driven by the lean mathematical law of quantum mechanics. When the resulting waves have a particular shape, as in Figure 8.16a, we retell the mathematical story in type-two language, and conclude that in each spike there’s a sentient being, situated within a normal-looking universe, certain he sees one and only one definite result for the given experiment, as in Figure 8.16b. If I could somehow interview all these sentient beings, I’d find each to be an exact replica of the others. Their only point of departure would be that each would attest to a different definite result.
And so, whereas Bohr and the Copenhagen gang would argue that only one of these universes would exist (because the act of measurement, which they claim lies outside of Schrödinger’s purview, would collapse away all the others), and whereas a first-pass attempt to go beyond Bohr and extend Schrödinger’s math to all particles, including those constituting equipment and brains, yielded dizzying confusion (because a given machine or mind seemed to internalize all possible outcomes simultaneously), Everett found that a more careful reading of Schrödinger’s math leads somewhere else: to a plentiful reality populated by an ever-growing collection of universes.
Prior to the publication of Everett’s 1957 paper, a preliminary version was circulated to a number of physicists around the world. Under Wheeler’s guidance, the paper’s language had been abbreviated so aggressively that many who read it were unsure as to whether Everett was arguing that all the universes in the mathematics were real. Everett became aware of this confusion and decided to clarify it. In a “note added in proof” that he seems to have slipped in just before publication, and apparently without Wheeler’s notice, Everett sharply articulated his stance on the reality of the different outcomes: “From the viewpoint of the theory, all … are ‘actual,’ none any more ‘real’ than the rest.”8
When Is an Alternative a Universe?
Besides the loaded words “splitting” and “cloning,” we’ve freely invoked two other grand terms in our type-two stories—“world” and, interchangeably in this context, “universe.” Are there guidelines for determining when this usage is appropriate? When we consider a probability wave for a single electron that has two (or more) spikes, we don’t speak of two (or more) worlds. Instead, we speak of one world—ours—containing an electron whose position is ambiguous. Yet, in Everett’s approach, when we measure or observe that electron, we speak in terms of multiple worlds. What is it that distinguishes the unmeasured and the measured particle, yielding descriptions that sound so radically different?