by John Gribbin
A (true) story that has become part of Oxford folklore tells how a Japanese film crew who came to interview Deutsch were so concerned by the mess that they offered to tidy it up. Deutsch explained that what looked like a mess to them was order to him, and he knew what was in each pile of papers; but he reluctantly agreed to their request, on condition that they promised to put everything back afterwards as they had found it. So they photographed everything, made notes like records of an archaeological dig, cleared away what they regarded as a mess—and, after the interview, restored everything to its original place, so that Deutsch could instantly locate anything in his “filing system.” I can empathize with his insistence, since I operate a similar system myself.
So how did Deutsch get into this position? He was born in 1953 in Haifa, Israel. After studying at William Ellis School in London, he took his first degree (in natural sciences) at the University of Cambridge, as a member of Clare College, staying on for the Part III in Mathematics (the Cambridge equivalent of a Master's degree), awarded in 1975. Deutsch then moved to Oxford, studying for his doctorate in mathematical physics under the supervision of Dennis Sciama. These studies also took him to the University of Texas at Austin, where he was supervised by John Wheeler—Everett's PhD supervisor who subsequently had doubts about the MWI—and stayed on to do post-doctoral research.
Always interested in fundamental physics, Deutsch had chosen for his thesis topic to investigate the theory of quantum fields in curved space-time, a problem that involves both quantum theory and the general theory of relativity, the two most fundamental theories of the world that we have. Unfortunately, at first sight the two theories seem to be incompatible with one another. The Holy Grail of physics—on which no one has yet laid hand—is the uniting of these two great theories in one package, quantum gravity. Deutsch hoped that understanding quantum fields in curved space-time would provide a clue to quantum gravity; that hope was not fulfilled, but in the course of his investigation he decided that quantum theory contained deeper truths about the nature of reality than the general theory of relativity did, and decided to focus on quantum theory in future.
While in Texas, Deutsch also worked under the supervision of Bryce DeWitt, who was almost single-handedly responsible for reviving Everett's MWI, largely ignored since its publication in his 1957 paper. From DeWitt Deutsch learned about MWI, and in 1977 he was in the audience when Everett gave a four-hour tour de force presentation of his ideas at a conference in Austin organized by DeWitt. This was the only major exposition of his ideas ever given by Everett, who had moved straight from his PhD studies in Princeton (before his MWI paper was even published) out of academia into the secret world of the Pentagon, working in the Weapons Systems Evaluation Group, at the height of the Cold War. Deutsch and Everett discussed the many universes idea over lunch, and Deutsch became convinced that this was the right way to understand quantum mechanics.
Almost immediately, Deutsch came up with the idea of a self-aware machine that could test the many worlds hypothesis. The idea had been thought untestable, and therefore arguably not “real science,” but by 1978 he had devised a thought experiment involving a machine which would be aware of the existence of more than one reality producing interference. Only later did he appreciate that this would, in fact, be a version of a quantum computer. Deutsch described this experiment in an interview with Paul Davies broadcast by the BBC in 1982.8 By then, he had returned to Oxford (in 1979), where he has been based ever since.
The experiment Deutsch described to Paul Davies “requires the observation of interference effects between two different states of an observer's memory.” The “observer” would be a machine operating on quantum principles—a quantum computer, although he did not use the term at that time. “The experiment hinges on observing an interference phenomenon inside the mind of this artificial observer…by his trying to remember various things so that he can conduct an experiment on his own brain while it's working.” Deutsch refers to a “quantum memory unit” which observes a feature of the state of an atomic system, such as its spin. The experiment can easily be set up so that the system is in a superposition, before interference occurs. In one of the parallel universes the brain will be aware that the atomic spin is up; in the other it will be aware that the atomic spin is down. But it will not observe both at once. At this stage, it can communicate with outside observers to confirm to its human colleagues that it is experiencing one possibility, and only one (in other words, it is not experiencing a superposition)—but it doesn't tell them which one, because interference can only take place in systems that are not entangled with the rest of the universe. Then, interference takes place, and in both universes the result is the same: equivalent, if Everett is correct, to the interference produced by electrons going through both holes of the double-slit experiment. The two universes have become identical to one another (at least in this respect), but although each of them records interference, each also contains proof that there was only one history in that universe:
If interference occurs he [the quantum computer] can infer that these two possibilities must have existed in parallel in the past—supporting the Everett interpretation. However, if the conventional interpretation is true,9 [the wave function will collapse and] although it'll still be true that he will write down “I am observing only one,” by the time he gets to the interference phenomenon it won't work (i.e. the interference won't occur). And so he will have demonstrated that the Everett interpretation is false.
This is not easy to get your head around, but in his book The Beginning of Infinity Deutsch offers a simpler proof of the reality of parallel worlds. It's all based on the properties of half-silvered mirrors.
A half-silvered mirror is the basis of the “one-way” mirror, which looks like a mirror from one side but can be seen through like a sheet of plain glass from the other side. It works because half of the photons that hit the mirror are reflected, and half are transmitted through it. By tilting the mirror at 45 degrees to a beam of light, it can be arranged for the reflected photons to be deflected at a right-angle, while the transmitted photons go straight on, as in the top diagram. If photons are fired one at a time towards the mirror, half of them are transmitted along path X and half deflected along path Y, but you cannot have half a photon, so no individual photon divides to follow both paths. There is, of course, no way to tell in advance which path an individual photon will follow; there is a 50:50 chance of its following either path. But if you fire a million photons through the experiment you can be sure that almost exactly half a million will go each way.
Semi-silvered mirror
Mach-Zehnder interferometer
Now comes the interesting part. Four mirrors can be set up in a square arrangement, called a Mach-Zehnder interferometer, as in the bottom figure. The mirrors at top left and bottom right of this diagram are half-silvered; the other two are conventional mirrors that reflect all the photons that strike them. If the top left mirror is removed and photons are sent along path X towards the top right mirror, they are reflected downwards and emerge from the bottom right mirror (half-silvered, remember) either to the right or downwards with 50:50 probability. In the same way, without the top left mirror, a photon sent down along path Y will arrive at the bottom right mirror and emerge either to the right or downwards with 50:50 probability. But with all the mirrors in place, as in the diagram, all the photons emerge traveling to the right, even when they are fired in one at a time. This can be explained in terms of the interference between path X and path Y, although I shall not go into the details here.10 But since the effect is observed for single photons, which cannot be divided, how can both paths affect the outcome of the experiment? Deutsch argues persuasively that it is because of interference between parallel universes, in some of which the photon(s) take path X and in some of which the photon(s) take path Y. “The fact that the intermediate histories X and Y both contribute to the deterministic final outcome makes it inescapable that both are happenin
g at the intermediate time.” In other words, “the multiverse is no longer perfectly partitioned into histories” during such an experiment. “Quantum interference phenomena constitute our main evidence for the existence of the multiverse and what its laws are.”
In 1985, Deutsch published a scientific paper that is now regarded as marking the beginning of the quest for a quantum computer.11 The inspiration for the paper came from a conversation with Charles Bennett of IBM, who opened Deutsch's eyes to the physical significance of the “Church-Turing principle”—in Turing's words, that “it is possible to invent a single machine which can be used to compute any computable sequence.” In the mid-1930s, Turing's insight pointed the way towards universal classical computers; in the mid-1980s, Deutsch's insight pointed the way towards universal quantum computers. He described a quantum generalization of the Turing machine, and showed that a “universal quantum computer” could be built in accordance with the principle that “every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means…. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any [classical] Turing machine,” although they would also be able to simulate perfectly any such Turing machine. He stressed that a strong motivation for developing such machines is that “classical physics is false.” And in particular he drew attention to the way in which “quantum parallelism” would allow such computers to perform certain tasks faster than any classical computer.
This parallelism is the reason for Deutsch's interest in quantum computing. He is not interested in the practicalities of building such computers or the things they might achieve, except as evidence for the existence of the Multiverse. In his landmark 1985 paper he stated baldly that “quantum theory is a theory of parallel interfering universes,” and posed an early version of a question to which he would repeatedly return in his writings: when a quantum computer carries out a calculation that requires two “processor days” of computation in less than a day, “where was it computed?”12 Now that we actually have quantum computers, the question assumes even greater significance; but most of the people who work with such machines ignore it, happy that their computers work FAPP. But the question cannot be swept under the rug, and before going on to the practicalities of quantum computing in the twenty-first century I shall summarize thinking about the quantum multiverse today.
A MEASURE OF UNIVERSES
It's worth repeating that the important point to take away from all this is that even within the modern version of the Many Worlds Interpretation, interference, such as in the experiment with two holes, does not involve any “splitting” and “recombining” of the Universe(s). Rather, this kind of experiment allows interference between nearby parallel worlds to become obvious. “Nearby” in this sense means “similar.” Another important point is that it is meaningful to talk about fractions of infinity. Although half of infinity is still infinity, it does make mathematical sense to talk about 50:50 probabilities (as in the experiment with two holes, or a photon hitting a half-silvered mirror) in terms of half of the universes following one history and half following the alternative history.
Mathematicians study infinity in terms of infinite sets. In this context, an infinite set has the property that some part of the set has as many components (elements) as the whole set. The so-called natural numbers, or integers, provide an example. Counting 1, 2, 3 and so on, there is always one number bigger than the last number counted. But if we write numbers down in two columns alongside each other, starting with 1 in one column and 2 (or any other number bigger than 1) in the other, we get pairs, 1-2, 2-3, 3-4 and so on. Clearly, the second column has as many elements as the first column—there is a one-to-one correspondence. But the second set is also a subset of the whole set, because it does not contain the number 1. So the whole set is infinite.
Any infinity that can be placed in a one-to-one correspondence with the set of natural numbers is called a countable infinity. The set of “all the natural numbers except 1” is itself an example of a countable infinity. There are other kinds of infinity, which are larger than countable infinities and are called uncountable infinities. An example is the set of all possible decimal numbers (known to mathematicians as “real” numbers). We can see this by assigning decimal numbers in the range from 0 to 1 to the integers, so that, for example, 1 is paired with 0.12345…, 2 is paired with 0.23456…, 3 is paired with 0.34567…and so on.13 Now, make a new decimal number by making the first digit anything except the first digit of the first number (that is, not 1), the second digit anything except the second digit of the second number (not 3), the third digit anything except the third digit of the third number (not 5) and so on. This new decimal number will differ from the decimal number assigned to the natural number 1 in the first digit, from the number assigned to 2 in the second digit, from the number assigned to 3 in the third digit, and so on. So it does not correspond to any of the numbers that are paired with the natural numbers. And this is true for an uncountably large infinity of real numbers.
Unfortunately, as far as we can tell the Multiverse consists of an uncountably infinite set of universes. That includes, as I have discussed in my book In Search of the Multiverse, such exotic possibilities as universes in which the laws of physics are different from those in our Universe. But, happily, if we restrict ourselves to the set of all universes in which the laws of physics are the same as in our Universe (itself an uncountably large infinite set) it is meaningful to talk in terms of, say, “half the universes” doing one thing and “half the universes” doing something else, even though each half is itself infinite. This is because the phenomenon of quantum interference involves interactions between universes—internal interactions within the Multiverse, making the Multiverse itself a single entity—that make such talk in terms of proportions or ratios meaningful. This way of measuring infinities is known, logically enough, as a “measure.” Deutsch has described the Multiverse as the set of all such universes evolving together, like a machine in which cogwheels are interconnected so that you cannot move one without moving the rest.
So when we talk about the cat in the box, we should not be thinking of a single cat in a single box, or even two cats in two boxes in two parallel worlds, but an uncountably infinite number of cats in an uncountably infinite number of boxes. In half of those parallel universes the cat dies, and in the other half it lives. For more subtle situations where there are different possible outcomes with different probabilities, it is meaningful to say that, for example, in 25 percent of the universes one history develops, in 60 percent an alternative history develops, and in 15 percent a third history develops. And that is why, in situations such as radioactive decay, in any one universe the outcome is entirely random (that is, it obeys the laws of probability) from the point of view of an observer in that universe.
There's another aspect of the infinite Multiverse that is worth mentioning, even though it is not directly relevant to the story of quantum computation. In Deutsch's words, “all fiction that does not violate the laws of physics is fact.” So all of Jane Austen's stories recount real events in parallel realities to our own; but The Lord of the Rings does not. And in an infinite number of universes there are writers busily producing what they regard as a fictional tale about a quantum physicist called David Deutsch who wrote a landmark paper about the concept of a universal quantum computer.
The connection between the Multiverse and the quantum computer is made explicit by Deutsch using a concept known as “fungibility,” taken from the lexicon of legal language. In law, two objects are deemed to be fungible if they are identical FAPP. The usual example is a banknote. If I borrow a £10 note from you and promise to pay it back on Friday, you do not expect me to give you back the same £10 note; any £10 note will do. All (genuine) £10 notes are fungible in law. But if I borrow your car for the afternoon to visit my cousin, you expect me
to give you the same car back in the evening; cars are not fungible. Elaborating the financial theme slightly, my wife and I have a joint bank account. Half the money is mine, and half is hers. But there is no sense in which there are two piles of money in the bank, labeled “his” and “hers”—and there wouldn't be even if the money was literally “in the bank” and not merely an electronic record inside a computer. Deutsch argues that universes with identical histories are literally and physically fungible. This goes beyond the concept of parallel universes—which implies running side by side, somehow separated in space, or superspace, or whatever you want to call it. Two or more fungible universes become differentiated when forced to by quantum phenomena, such as the experiment with two holes, leading to the diversity of universes within the Multiverse, but in accordance with the laws of probability, as discussed above. These universes can briefly interfere with one another as this process occurs. But quantum interference is suppressed by entanglement, so the larger and more complex an object is, the less it will be affected by interference. Which is why we have to set up careful experiments (like the one with half-silvered mirrors) to see interference at work, and why there are such large practical problems involved in building quantum computers, where entanglement has to be avoided except in special places. A universe like ours, suggests Deutsch, is really made up of a bundle of “coarse-grained” histories differing from each other only in sub-microscopic detail, but affecting each other through interference. Each such bundle of coarse-grained histories “somewhat resembles the universe of classical physics.” And these coarse-grained universes really do fit the description of parallel universes familiar from science fiction.
