Many-Worlds
What if Germany had won World War II? Or what would life be like if the asteroid that killed the dinosaurs sixty-five million years ago had not hit the earth? The idea of a parallel world that took a different course at some critical historical junction is a favorite theme of science-fiction authors. But as real science, I have always dismissed such ideas as frivolous nonsense. But to my surprise I find myself talking and thinking about just such matters. In fact this whole book is about parallel universes: the megaverse is a world of pocket universes that become disconnected—completely out of contact—as they recede beyond one another’s hori-zons.
I am far from the first physicist to seriously entertain the possibility that reality—whatever that means—contains, in addition to our own world of experience, alternate worlds with different history than our own. The subject has been part of an ongoing debate about the interpretation of quantum mechanics. Sometime in the middle 1950s, a young graduate student, Hugh Everett III, put forth a radical reinterpretation of quantum mechanics that he called the many-worlds interpretation. Everett’s theory is that at every junction in history the world splits into parallel universes with alternate histories. Although it sounds like fringe speculation, some of the greatest modern physicists have been driven by the weirdness of quantum mechanics to embrace Ever-ett’s ideas—among them, Richard Feynman, Murray Gell-Mann, Steven Weinberg, John Wheeler, and Stephen Hawking. The many-worlds interpretation was the inspiration for the Anthropic Principle when Brandon Carter first formulated it, in 1974.
The many-worlds of Everett seems, at first sight, to be quite a different conception than the eternally inflating megaverse. However, I think the two may really be the same thing. I have emphasized several times that quantum mechanics is not a theory that predicts the future from the past, but rather it determines the probabilities for the possible alternate outcomes of an observation. These probabilities are summarized in the basic mathematical object of quantum mechanics—the wave function.
If you have learned a little bit about quantum mechanics and know that Schrödinger discovered a wave equation describing electrons, then you have heard of wave functions. I want you to forget all that. Schrödinger’s wave function was a very special case of a much broader concept, and it is this more general idea that I want to concentrate on. At any given time—right now, for example—there are many things that one might observe about the world. I might choose to look out the window just above my desk and see if the moon is up. Or I might plan a two-slit experiment (see chapter 1) and observe the location of a particular spot on the screen. Yet another experiment would involve a single neutron that was prepared a certain time in the past—say, ten minutes ago. You may recall from chapter 1 that a neutron, not bound in a nucleus, is unstable. On the average (but only on the average), in twelve minutes it will decay into a proton, an electron, and an antineutrino. The observation in this case would be to determine whether, after ten minutes, the neutron has decayed or if it is still present in its original form. Each of these experiments or observations has more than one possible outcome. In its most general sense, the wave function is a list of the probabilities for all possible outcomes of all possible observations on the system under consideration. More exactly, it is a list of the square roots of all these probabilities.
The decaying neutron is a good illustration to start with. With a bit of simplification, we can suppose there are only two possible outcomes when we observe the neutron: either it has decayed or it hasn’t. The list of possibilities is a short one, and the wave function has only two entries. We start with the neutron in its undecayed form so that the wave function has value one for the first possibility and zero for the second. In other words initially the probability that the neutron is undecayed is one, while the probability that it has decayed (when we start) is zero. But after a short time, there is a small probability that the neutron has disappeared. The two entries to the wave function have changed from one and zero to something a bit less than one and something a bit more than zero. After about ten minutes the two entries have become equal. Go on for another ten minutes, and the probabilities will be reversed: the probability that the neutron is still intact will be close to zero, and the probability that it has become a proton/ electron/ antineutrino will be up near one. Quantum mechanics contains a set of rules for updating the wave function of a system as time unfolds. In its most general form, the system of interest is everything—the entire observable universe, including the observer doing the observations. Since there may be more than one lump of matter that might be called an observer, the theory must give rise to consistent observations. The wave function contains all of this and in a way that will prove consistent when two observers get together to discuss their findings.
Let’s examine the best known of all thought experiments in physics: the famous (or should I say infamous?) Schrödinger’s cat experiment. Imagine that at noon a cat is placed in a sealed box along with a neutron and a gun. When the neutron decays (randomly), the ejected electron activates a circuit that causes the gun to shoot and kill the cat.
A practitioner of quantum mechanics—call him S—would analyze the experiment by constructing a wave function: a list of the probabilities for the various outcomes. S cannot reasonably take the entire universe into account, so he limits the system to include only those things in the box. At noon only one entry would exist: “The cat is alive in the box with the loaded gun and the neutron.” Then S will do some mathematics analogous to solving Newton’s equations in order to find out what will happen next—say, at 12:10 p.m. But the result is not a prediction of whether the cat will be dead or alive. It is an updating of the wave function, which will now have two entries: “The neutron is intact/ the gun is loaded/ the cat is alive” and “The neutron has decayed/ the gun is empty/ the cat is dead.” The wave function has split into two branches—the dead and alive branches—whose numerical values give the square roots of the probabilities for the two outcomes.
S can open the box and see if the cat is dead or alive. If the cat is alive, then S can throw away the dead-cat branch of the wave function. That branch, if advanced in time, would contain all the information about the world in which the cat was shot, but since S found the cat alive, he has no further need for this information. There is a term for this process of dropping the unobserved branches of the wave function whenever an observation is made. It is called the collapse of the wave function. It is a very convenient trick that allows the physicist to concentrate on only the things that can subsequently be of interest. For example, the live branch has information that may still interest S. If he advances this branch of the wave function a bit more in time, he would be able to determine the probability that the gun would subsequently misfire and shoot S (serves him right). The collapse of the wave function whenever an observation takes place is the primary ingredient of the famous Copenhagen interpretation of quantum mechanics championed by Niels Bohr.
But the collapse of the wave function is not a part of the mathematics of quantum mechanics. It is something extraneous to the mathematical rules, something that Bohr had to tack on in order to end the experiment with an observation. This arbitrary rule has bothered generations of physicists. A big part of the problem is that S limited his system to the things in the box, but at the end of the experiment S himself gets into the act by making the observation. It is now widely understood that a consistent description must necessarily include S as part of the system. Here is the way the new description would go:
The wave function now describes everything in the box as well as the physical lump of matter that we have been calling S. The initial wave function still has only one entry but it is now described as follows: “The live cat is in the box with the loaded gun and the neutron, and the mental state of S is blank.” Time goes on, and S opens the box. Now the wave function has two entries: “The neutron is intact/ the gun is loaded/ the cat is alive/ the mental state of S is aware of the live cat” and th
e second branch, “The neutron has decayed/ the gun is empty/ the cat is dead/the mental state of S is aware of the dead cat.” We have managed to describe S’s perceptions without collapsing the wave function.
But now suppose there is another observer named B. B has been out of the room while S has been doing his bizarre experiment. When he opens the door to look in what he sees is one of two outcomes. There is no point in keeping track of the unobserved branch of the wave function, so B collapses the wave function. It seems we have not avoided the extraneous operation. Evidently what we need to do is to include B in the wave function. The starting point would be a system composed of everything in the box and two lumps called S and B. The initial state is: “The live cat is in the box with the loaded gun and the neutron, the mental state of S is blank, and the mental state of B (who is out of the room) is blank.” When S opens the box, the wave function develops two branches: “The neutron is intact/ the gun is loaded/ the cat is alive/ the mental state of S is aware of the living cat/ B’s mental state is still blank” and “The neutron has decayed/ the gun is empty/ the cat is dead/ the mental state of S is aware of the dead cat/ B’s mental state is still blank.” Finally, B opens the door, and the first branch becomes: “The neutron is intact/ the gun is loaded/ the cat is alive/ the mental state of S is aware of the living cat/ B’s mental state is aware of the live cat and also S’s mental state.” I will leave it to the reader to work out the other branch. The important thing is that the experiment has been described without collapsing the wave function.
But now suppose there is another observer called E. Never mind. You should be able to see the pattern. What is evident is that the only way to avoid wave-function collapse is to include the entire observable universe as well as all the branches of the wave function in the quantum description. That is the alternative to Bohr’s pragmatic rule of terminating the story by collapsing the wave function.
In Everett’s way of thinking, the wave function describes an infinite branching tree of possible outcomes. Following Bohr, most physicists have tended to think of the branches as mathematical fictions, except for the actual branch that one finds oneself on after an observation. Collapsing the wave function is a useful device to cut away all the unneeded baggage, but to many physicists this rule seems to be an arbitrary external intervention by the observer—a procedure not in any way based on the mathematics of quantum mechanics. Why should the mathematics give rise to all the other branches if their only role is to be thrown away?
According to the advocates of the many-worlds interpretation, all the branches of the wave function are equally real. At each junction the world splits into two or more alternative universes, which forever live side by side. Everett’s vision was of a ceaselessly branching reality, but with the one proviso that the different branches never interact with one another after they have split. On the live-cat branch, the dead-cat branch will never come back to haunt S. Bohr’s rule is just a trick to cut away all the branches, which although quite real, will have no further effect on the observer.
One other point is worth noting. By the time we get to the present stage of history, the wave function has branched so many times that there are an enormous number of replicas of every possible eventuality. Consider poor B while he is out of the room. The wave function branched when S opened the box, thus splitting all of them, including B, into two branches. The number of branches containing you, sitting and reading this book, is practically infinite. In this framework the concept of probability makes perfect sense as the relative frequency of different outcomes. One outcome is more probable than another if more branches contain it.
The many-worlds interpretation cannot be experimentally distinguished from the more conventional Copenhagen interpretation. Everyone agrees that, in practice, the Copenhagen rule correctly gives the probabilities of experimental outcomes. But the two theories profoundly disagree about the philosophical meaning of these probabilities. The Copenhageners take the conservative view that probabilities refer to the statistics of a large number of repeated experiments. Think of flipping a coin. If the coin is “fair,” the probability for either outcome (heads or tails) is one-half. This means that if the coin is flipped a large number of times, the fraction of heads and tails will each be about one-half. The larger the number of trials, the closer the answer will be to the ideal half-half result. Similar things apply when rolling dice. If one rolls a single die many times, one-sixth of the time (within the margin of error) the die will show each of the six possible outcomes. Ordinarily no one would apply statistics to a single coin flip or a single roll of the die. But the many-worlds interpretation does just that. It deals with single events in a way that would seem ridiculous for coin flipping. The idea that when a coin is flipped, the world splits into two parallel worlds—a heads-world and a tails-world—does not seem to be a useful idea.
Why then are physicists so bothered by the probabilities that occur in quantum mechanics that they are driven to strange ideas like the many-worlds interpretation? Why was Einstein so insistent that “God does not play dice?” To understand the puzzlement that attends quantum mechanics, it is helpful to ask why, in a Newtonian world of absolute certainty, one would ever discuss probability at all. The answer is simple: probabilities enter Newtonian physics for the simple reason that one is almost always ignorant of the exact initial conditions of an experiment. In the coin flipping experiment, if one knew the exact details of the hand that threw the coin, the air currents in the room, and all the other relevant details, there would be no need for probabilities. Each throw would lead to a definite outcome. Probability is a convenient trick to compensate for our practical inability to know the details. It has no fundamental place in the Newtonian laws.
But quantum mechanics is different. Because of the Uncertainty Principle, there is no way to predict the outcome of an experiment—no way, in principle. The fundamental equations of the theory determine a wave function and nothing more. Probability enters the theory at the outset. It is not a trick of convenience used to compensate our ignorance. Moreover, the equations that determine how the wave function changes with time have no provision for suddenly collapsing the unobserved branches. The collapse of the wave function is the trick of convenience.
The problem becomes especially acute in the cosmological context. Ordinary experiments, similar to the two-slit experiment that I described in chapter 1, can be repeated over and over, just like the coin toss. In fact each photon that goes through the apparatus can be thought of as a separate experiment. There is no problem accumulating enormous amounts of statistical data. But the problem with this conception of quantum mechanics is that we cannot apply it to the great cosmic experiment. We can hardly repeat the Big Bang over and over and gather statistics on the outcomes. For this reason many thoughtful cosmologists have adopted the philosophical underpinnings of the many-worlds interpretation.
Carter’s early pioneering idea for synthesizing the Anthropic Principle with the many-worlds interpretation was this: suppose the wave function includes branches not only for such ordinary things as the location of an electron, the decay or nondecay of the neutron, or the life and death of a cat, but also for different Laws of Physics. If one assumes all the branches are equally real, then there are worlds with many alternative environments. In modern language we would say there are branches (as well as real worlds) for every location on the Landscape. The rest of the story is no different than what I have explained earlier in the book, except instead of talking about different regions of the megaverse, one would talk about different branches of reality. To make the point let me quote from chapter 1 and then modify the quote with some replacements. The original quote was, “Somewhere in the megaverse, the constant equals this number: somewhere else it is that number. We live in one tiny pocket where the value of the constant is consistent with our kind of life.” The modified quote is: “Somewhere in the wave function, the constant equals this number: somewhere else it is that number. We live in
one tiny branch where the value of the constant is consistent with our kind of life.” Although the two quotes seem very similar, they are referring to two apparently completely different ideas of alternate universes. It seems that we have more than one way to achieve the kind of diversity that would allow anthropic reasoning to make sense. I might add that different proponents of the Anthropic Principle have different opinions about which version is the one true theory of parallel universes. My opinion? I believe the two versions are complementary versions of exactly the same thing.
Let’s look at the situation in a bit more detail. Earlier in this chapter I described two views of eternally inflating history, the parallel and series views. The parallel view recognizes the entire megaverse with all its multiple pocket universes, which once they are separated by horizons are out of contact. That sounds quite a lot like the many-worlds of Everett. But what about the series view?
Let’s consider an example. Suppose that a bubble of space has formed, with properties associated with some valley in the landscape. It will help to have some names for the valley and its neighbors, so let’s call it Central Valley. To the east and west of Central Valley lie East and West valleys, each at somewhat lower altitudes. From West Valley two other nearby valleys can be reached, one called Shangri La and the other Death Valley. Death Valley is not really a valley but rather a flat plateau at exactly zero altitude. East Valley also has a few neighbors that can be easily reached, but we won’t bother naming them.
Imagine yourself in Central Valley as your pocket universe inflates. Because there are nearby lower valleys, your vacuum is metastable: bubbles can form and engulf you. After some period you might look around and observe the properties of your environment. You may find that you are still in Central Valley. Or you may find that you have made a transition to East Valley or to West Valley. The decision as to which valley you now inhabit is determined randomly according to quantum mechanics, in much the same way that quantum mechanics determined the fate of S’s cat.
The Cosmic Landscape Page 34
