The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos

by Brian Greene

  One quick answer is that for a single isolated electron, we don’t tell a type-two story because without a measurement or an observation there’s no link to human experience that’s in need of articulation. The type-one story of a probability wave evolving via Schrödinger’s math is all that’s needed. And without a type-two story, there’s no opportunity to invoke multiple realities. Although this explanation is adequate, it proves worthwhile to delve a little deeper, revealing a special feature of quantum waves that comes into play when many particles are involved.

  To grasp the essential idea, it’s easiest to look back at the double-slit experiment of Figures 8.2 and 8.4. Recall that an electron’s probability wave encounters the barrier, and two wave fragments make it through the slits and travel onward to the detector screen. Inspired by our Many Worlds discussion, you might be tempted to think of the two racing waves as representing separate realities. In one, an electron whisks through the left slit; in the other, an electron whisks through the right slit. But you promptly realize that the intermingling of these supposedly “distinct realities” profoundly affects the experiment’s outcome; the intermingling is why an interference pattern is produced. So it doesn’t make much sense, nor does it yield any particular insight, to consider the two wave trajectories as existing in separate universes.

  If we change the experiment, however, by placing a meter behind each slit that records whether or not an electron passes through it, the situation is radically different. Because macroscopic equipment is now involved, the two distinct trajectories of an electron generate differences in a huge number of particles—the huge number of particles in the meters’ displays that register “electron passed through left slit” or “electron passed through right slit.” And because of this, the respective probability waves for each possibility become so disparate that it’s virtually impossible for them to have any subsequent influence on each other. Much as in Figure 8.16a, the differences between the billions and billions of particles in the meters cause the waves for the two outcomes to shift away from each other, leaving negligible overlap. With no overlap, the waves don’t engage in any of the hallmark interference phenomena of quantum physics. Indeed, with the meters in place, the electrons no longer yield the striped pattern of Figure 8.2c; instead, they generate a simple, non-interfering amalgam of the results in Figure 8.2a and Figure 8.2b. Physicists say that the probability waves have decohered (something you can read about in more detail, for example, in Chapter 7 of The Fabric of the Cosmos).

  The point, then, is that once decoherence sets in, the waves for each outcome evolve independently—there’s no intermingling between the distinct possible outcomes—and each can thus be called a world or a universe of its own. For the case at hand, in one such universe the electron goes through the left slit, and the meter displays left; in another universe the electron goes through the right slit, and the meter records right.

  In this sense, and only in this sense, there’s resonance with Bohr. According to the Many Worlds approach, big things made of many particles do differ from small things made from one particle or a mere handful. Big things don’t stand outside the basic mathematical law of quantum mechanics, as Bohr thought, but they do allow probability waves to acquire enough variations that their capacity to interfere with one another becomes negligible. And once two or more waves can’t affect one another, they become mutually invisible; each “thinks” the others have disappeared. So, whereas Bohr argued away by fiat all but one outcome in a measurement, the Many Worlds approach, combined with decoherence, ensures that within each universe it appears as though the other outcomes have vanished. Within each universe, that is, it’s as if the probability wave has collapsed. But, compared with the Copenhagen approach, the “as if” provides for a very different picture of the expanse of reality. In the Many Worlds view, all outcomes, not just one, are realized.

  Uncertainty at the Cutting Edge

  This might seem like a good place to end the chapter. We’ve seen how the bare-bones mathematical structure of quantum mechanics leads us by the nose to a new conception of parallel universes. Yet you’ll note that the chapter still has a fair way to go. In those pages I’ll explain why the Many Worlds approach to quantum physics remains controversial; we will see that the resistance goes well beyond the queasiness some feel about the conceptual leap into such an unfamiliar perspective on reality. But in case you’ve reached saturation and feel compelled to skip ahead to the next chapter, here is a short summary.

  In day-to-day life, probability enters our thinking when we face a range of possible outcomes, but for one reason or another we’re unable to figure out which will actually happen. Sometimes we have enough information to determine which outcomes are more or less likely to occur, and probability is the tool that makes such insights quantitative. Our confidence in a probabilistic approach grows when we find that the outcomes deemed likely happen often and those deemed unlikely happen rarely. The challenge facing the Many Worlds approach is that it needs to make sense of probability—quantum mechanics’ probabilistic predictions—in a wholly different context, one that envisions all possible outcomes happening. The dilemma is simple to state: How can we speak of some outcomes being likely and others being unlikely when all take place?

  In the remaining sections, I’ll explain the issue more fully and discuss attempts to address it. Be warned: we are now deep into cutting-edge research, so opinions vary widely on where we currently stand.

  A Probable Problem

  A frequent criticism of the Many Worlds approach is that it’s just too baroque to be true. The history of physics teaches us that successful theories are simple and elegant; they explain data with a minimum of assumptions and provide an understanding that’s precise and economical. A theory that introduces an ever-growing cornucopia of universes falls way short of this ideal.

  Proponents of the Many Worlds approach argue, credibly, that in assessing the complexity of a scientific proposal, you shouldn’t focus on its implications. What matters is the fundamental features of the proposal itself. The Many Worlds approach assumes that a single equation—Schrödinger’s—governs all probability waves all the time, so for simplicity of formulation and economy of assumptions, it’s hard to beat. The Copenhagen approach is surely no simpler. It, too, invokes Schrödinger’s equation, but it also includes a vague, ill-defined prescription for when Schrödinger’s equation should be turned off, and then an even less detailed prescription regarding the process of wave collapse that is meant to take its place. That the Many Worlds approach leads to an exceptionally rich picture of reality is no more a black mark against it than the rich diversity of life on earth is a black mark against Darwinian natural selection. Mechanisms that are fundamentally simple can give rise to complicated consequences.

  Nevertheless, while this establishes that Occam’s razor isn’t sharp enough to pare away the Many Worlds approach, the proposal’s surfeit of universes does yield a potential problem. Earlier I said that in applying a theory, physicists need to tell two kinds of stories—the story describing how the world evolves mathematically and the story that links the math to our experiences. But there’s actually a third story, related to these two, that the physicist must also tell. It’s the story of how we’ve come to have confidence in a given theory. For quantum mechanics, the third story generally goes like this: our confidence in quantum mechanics comes from its phenomenal success in explaining data. If a quantum expert uses the theory to calculate that in repeating a given experiment we expect one outcome to happen, say, 9.62 times more often than another, that’s what experimenters invariably see. Turning this around, had results not agreed with the quantum predictions, experimenters would have concluded that quantum mechanics wasn’t right. Actually, being careful scientists, they would have been more cautious. They would have called it doubtful that quantum mechanics was right but would have noted that their results didn’t rule out the theory definitively. Even a fair coin tossed 1,000 times can have
surprising runs that defy the odds. But the larger the deviation, the more one suspects the coin is not fair; the larger the experimental deviations from those predicted by quantum mechanics, the more strongly the experimenters would have suspected that quantum theory was mistaken.

  That confidence in quantum mechanics could have been undermined by data is essential; with any proposed scientific theory that has been suitably developed and understood, we should be able to say, at least in principle, that if upon doing such and such an experiment we don’t find such and such results, our belief in the theory should diminish. And the more that observations deviate from predictions, the greater the loss of credibility should be.

  The potential problem with the Many Worlds approach, and the reason it remains controversial, is that it may undercut this means for assessing the credibility of quantum mechanics. Here’s why. When I flip a coin, I know there’s a 50 percent chance that it will land heads and a 50 percent chance that it will land tails. But that conclusion rests on the usual assumption that a coin toss yields a unique result. If a coin toss yields heads in one world and tails in another, and moreover, if there’s a copy of me in each world who witnesses the outcome, what sense can we make of the usual odds? There’ll be someone who looks just like me, has all my memories, and emphatically claims to be me who sees heads, and another being, equally convinced that he’s me, who sees tails. Since both outcomes happen—there’s a Brian Greene who sees heads and a Brian Greene who sees tails—the familiar probability of there being an equal chance that Brian Greene will see either heads or tails seems nowhere to be found.

  The same concern applies to an electron whose probability wave is hovering near Strawberry Fields and Grant’s Tomb, as in Figure 8.16b. Traditional quantum reasoning says that you, the experimenter, have a 50 percent chance of finding the electron at either location. But in the Many Worlds approach, both outcomes happen. There’s a you who will find the electron at Strawberry Fields and another you who will find the electron at Grant’s Tomb. So, how can we make sense of the traditional probabilistic predictions, which in this case say that with equal odds you’ll see one result or the other?

  The natural inclination of many people when they first encounter this issue is to think that among the various yous in the Many Worlds approach, there’s one who’s somehow more real than the others. Even though each you in each world looks identical and has the same memories, the common thought is that only one of these beings is really you. And, this line of thought continues, it’s that you, who sees one and only one outcome, to whom the probabilistic predictions apply. I appreciate this response. Years ago, when I first learned about these ideas, I had it too. But the reasoning runs completely counter to the Many Worlds approach. Many Worlds practices minimalist architecture. Probability waves simply evolve by Schrödinger’s equation. That’s it. To imagine that one of the copies of you is the “real” you is to slip in through the back door something closely akin to Copenhagen. Wave collapse in the Copenhagen approach is a brutish means for making one and only one of the possible outcomes real. If in the Many Worlds approach you imagine that one and only one of the yous is really you, you’re doing the same thing, just a little more quietly. Such a move would erase the very reason for introducing the Many Worlds scheme. Many Worlds emerged from Everett’s attempt to address the failings of Copenhagen, and his strategy was to invoke nothing beyond the battle-tested Schrödinger equation.

  This realization shines an uncomfortable light on the Many Worlds approach. We have confidence in quantum mechanics because experiments confirm its probabilistic predictions. Yet, in the Many Worlds approach, it’s hard to see how probability even plays a role. How, then, can we tell the third kind of story, the one that should provide the basis of our confidence in the Many Worlds scheme? That’s the quandary.

  On reflection, it’s not surprising that we’ve bumped into this wall. There’s nothing at all chancy in the Many Worlds approach. Waves simply evolve from one shape to another in a manner described fully and deterministically by Schrödinger’s equation. No dice are thrown; no roulette wheels are spun. By contrast, in the Copenhagen approach, probability enters through the hazily defined measurement-induced wave collapse (again, the larger the wave’s value at a given location, the larger the probability that the collapse will put the particle there). That’s the point in the Copenhagen approach where “dice throwing” makes an appearance. But since the Many Worlds approach abandons collapse, it abandons the traditional entry point for probability.

  So, is there a place for probability in the Many Worlds approach?

  Probability and Many Worlds

  Everett surely thought there was. The bulk of his 1956 draft dissertation, as well as the truncated 1957 version, was devoted to explaining how to incorporate probability in the Many Worlds approach. But a half century later, the debate still rages. Among those physicists and philosophers who spend their professional lives puzzling over the issue, there is a wide range of opinions on how, and whether, Many Worlds and probability come together. Some have argued that the problem is insoluble, and so the Many Worlds approach should be discarded. Others have argued that probability, or at least something that masquerades as probability, can indeed be incorporated.

  Everett’s original proposal provides a good example of the difficult points that arise. In everyday settings, we invoke probability because we generally have incomplete knowledge. If, when a coin is tossed, we know enough details (the coin’s precise dimensions and weight, precisely how the coin was thrown, and so on), we’d be able to predict the outcome. But since we generally don’t have that information, we resort to probability. Similar reasoning applies to the weather, the lottery, and every other familiar example where probability plays a role: we deem the outcomes chancy only because our knowledge of each situation is limited. Everett argued that probabilities find their way into the Many Worlds approach because an analogous ignorance, from a thoroughly different source, necessarily creeps in. Inhabitants of the Many Worlds only have access to their own single world; they do not experience the others. Everett argued that with such a limited perspective comes an infusion of probability.

  To get a feel for how, leave quantum mechanics for a moment and consider an imperfect but helpful analogy. Imagine that aliens from the planet Zaxtar have succeeded in building a cloning machine that can make identical copies of you, me, or anyone. Were you to step into the cloning machine, and were two of you then to step out, both would be absolutely convinced that they were the real you, and both would be right. The Zaxtarians delight in subjecting less intelligent life-forms to existential dilemmas, so they swoop down to earth and make you the following offer. Tonight, when you go to sleep, you’ll be carefully wheeled into the cloning machine; five minutes later two of you will be wheeled out. When one of you awakes, life will be normal—except that you will have been granted any wish of your choosing. When the other you awakes, life won’t be normal; you will be escorted to a torture chamber back on Zaxtar, never to leave. And no, your lucky clone is not allowed to wish for your release. Do you accept the offer?

  For most people, the answer is no. Since each of the clones really, truly is you, in accepting the offer you’d be guaranteeing that there will be a you who awakens to a lifetime of torment. Sure, there will also be a you who awakens to your usual life, augmented by the unlimited power of an arbitrary wish, but for the you on Zaxtar there’ll be nothing but torture. The price is too high.

  Anticipating your reluctance, the Zaxtarians up the ante. Same deal, but now they’ll make a million and one copies of you. A million will wake up on a million identical-looking earths, with the power to fulfill any wish; one will get the Zaxtarian torture. Do you accept? At this point, you begin to waver. “Heck,” you think, “the odds seem pretty good that I won’t end up on Zaxtar but instead will wake up right here at home, wish in hand.”

  This last intuition is particularly relevant to the Many Worlds approach. If odds entered your th
inking because you imagine that only one of the million and one clones is the “real” you, then you’ve not taken in the scenario fully. Each copy is you. There’s a 100 percent certainty that one of you will wake up to an unbearable future. If this was indeed what led you to think in terms of odds, you need to let it go. However, probability may have entered your thinking in a more refined way. Imagine that you just agreed to the Zaxtarian offer and are now contemplating what it will be like to wake up tomorrow morning. Curled up under a warm duvet, just regaining consciousness but not yet having opened your eyes, you’ll remember the Zaxtarian deal. At first it will seem like an unusually vivid nightmare, but as your heart starts to pound you’ll recognize that it is real—that a million and one copies of you are in the process of waking up, with one of you destined for Zaxtar and the others about to be granted extraordinary power. “What are the odds,” you’ll ask yourself nervously, “that when I open my eyes I’ll be shipping out to Zaxtar?”

  Before the cloning there was no sensible way to speak of whether it was or wasn’t likely that you’d be Zaxtar bound—it is absolutely certain that there will be such a you, so how could it be unlikely? But after the cloning, the situation seems different. Each clone experiences itself as the real you; indeed, each is the real you. But each copy is also a separate and distinct individual who can inquire about his or her own future. Each of the million and one copies can ask for the probability that they will go to Zaxtar. And since each knows that only one of the million and one will wake up to that outcome, each reckons that the odds of being that unlucky individual are low. Upon waking, a million will find their cheery expectation confirmed, and only one will not. So although there’s nothing uncertain, nothing chancy, nothing probabilistic in the Zaxtarian scenario—again, no dice are rolled and no roulette wheels spun—probability nevertheless seems to enter. It does so through the subjective ignorance experienced by each individual clone regarding which outcome he or she will witness.