I have written at length about the fictional fun one can have with wormholes in The Physics of Star Trek, so I will not repeat these discussions here. Suffice it to say that wormholes, if they actually were able to exist, would allow not only distant regions of space to be connected, but also distant regions of time . . . both past and future! But, they probably don’t exist, so don’t get too excited about their potential. Star Trek, in fact, has a long history of using the effects of gravity to achieve exotic results. In one of the series’s earliest episodes—and even before the physicist John Wheeler invented the term black hole to describe such gravitationally collapsed objects—its writers had the Enterprise travel too close to the gravitational field of a “black star,” and, as a result, the ship was thrown back in time.
While Star Trek has also had its share of wormholes and wormholeinduced travel, it is best known for its own faster-than-light travel mechanism, warp drive. While the very name suggests the warping of space, and I and others have discussed how, within the context of general relativity, faster-than-light travel is possible in principle (even though no information is ultimately transmitted faster than light, avoiding any contradiction with special relativity), it is interesting that in Star Trek lore warp drive is associated not with the dynamic warping of our own three-dimensional space, but rather with the possible existence of extra dimensions. Indeed, while black holes and wormholes are fascinating implications of the possibility of curved space, which in some ways can mimic various phenomena one might hope would result from the existence of extra dimensions, as I have emphasized already numerous times curved space itself neither implies nor requires the existence of any extra dimensions. Instead, black holes and wormholes demonstrate that even a seemingly pedestrian three-dimensional space can be far stranger than meets the eye.
Nevertheless, as I have just described, Star Trek does manage to mix up warped space and extra dimensions. In fact, at the heart of the Star Trek universe is an apparently infinite number of extra dimensions. In order to explain how the crew can communicate instantly with Starfleet when they are many hundreds if not thousands of light-years away, for example, the writers invoked “subspace” communication. Using this imaginary plot device, signals are transmitted into extra subspace dimensions, where almost instantly they can be beamed back into our three-dimensional space at a different location.
Star Trek’s use of subspace is characteristic of an explosion of interest beginning in the 1980s, especially in movies and television, in moving beyond merely a fourth dimension to the idea that many extra dimensions might exist, and moreover that periodically not only information but even material objects can leak from one dimension to another. Interestingly, the things that emerge from other possible dimensions are almost never benign. A classic Outer Limits episode from the 1960s involved an unfortunate alien inhabitant of another dimension who meant no harm but who was accidentally sucked into our space as a result of some wayward scientific experiments, causing a host of problems. By contrast, the horror film Poltergeist (1980) played off the long-held notion described earlier that somehow the spirit world inhabits other dimensions that at times intersect with our own. Inevitably, however, it seems that only evil spirits choose to cross the border. In one memorable scene during the movie, reminiscent of the discussion of the magical properties of motion in higher dimensions pondered by Edwin Abbott in the nineteenth century, a ball is thrown into a dark closet and reappears by falling from the ceiling in another location of the same house.
The notion of evil beings from other dimensions plays a large part in one of my personal favorite films, The Adventures of Buckaroo Banzai across the Eighth Dimension (1984), whose protagonist is not only a Nobel Prize–winning particle physicist but also a skilled neurosurgeon, rock musician, and Zen warrior. Its plot focuses on the mishaps that can occur when a rocket car that can go through matter by taking a short cut through the eighth dimension picks up unwanted alien hitchhikers.
At around this time in the 1980s Star Trek, too, began to fixate on multiple extra spatial dimensions and the aliens that could emerge from them. In one episode Commander Riker gets kidnapped by aliens from subspace dimensions and the ship is put in great danger until the responsible portal can be closed.
Star Trek also focused on another common science fiction theme, that of parallel universes. These involve other three-dimensional spaces, identical to our own, that somehow coexist with ours, but not necessarily within the context of a higher-dimensional space. For example, some writers have taken the many-worlds interpretation of quantum mechanics, which argues that while true quantum mechanical objects can exist in many different states simultaneously, each time we make a measurement of such an object, we immediately force it to exist on one of what can be an infinite number of parallel branches of the quantum mechanical “wavefunction” describing the objects. If one takes this notion literally, it suggests that we somehow define our reality by the observations we make, but that there could be an infinite other set of realities with different outcomes. While most physicists I know view the many-worlds interpretation as merely a mental crutch to help them deal with phenomena at the quantum level that simply have no sensible classical analogues, a number of writers have created stories using many worlds. In one Star Trek episode the Klingon Worf finds himself jumping between different branches of reality, in each of which all the other characters are slightly different. (Incidentally, the weird properties of quantum mechanics may have inspired artists as well as writers. More than one person I know has argued to me that Jackson Pollock’s abstract “drip” paintings are beautiful representations of the quantum fluctuations that populate the vacuum.)
Up until the 1980s, the many extra dimensions proposed by science fiction and spiritual literature were essentially completely divorced from anything being considered by the scientific community. As late as 1981, for example, the idea that somehow the nature of particles and fields at the smallest scales might somehow be related to extra dimensions appeared in a story written by Craig Harrison and, in 1986, turned into a movie called Quiet Earth. In it, a scientist produces a fundamental change in the basic structure of matter in his laboratory, but as a result he transports almost all of the human populace to another dimension.
The nature of the confluence of extra-dimensional speculations in science and science fiction began to change, however, as notions that started to arise in elementary particle physics made their way into popular culture.
As we shall see, it was precisely the study of elementary particle physics that caused physicists to reconsider, at about the same time as Harrison’s story was published, the existence of five, six, and even twenty-six dimensional spaces. And by the 1990s, after various popular accounts of the emerging research interest in the possibility of extra dimensions had appeared, one finds numerous science fiction stories—for example, “Eula Makes up Her Mind,” which was featured in a recent science fiction anthology competition that I happened to judge—in which the extra dimensions of string theory play a key role. In a recent New York play the heroine somehow uses lessons from string theory in twenty-six dimensions to help her sort out her confusing love life!
As the latter example makes clear, in spite of the cross-pollination of ideas, there nevertheless remains a certain cognitive dissonance between explorations in physics and the literary allusions. I imagine that this is inevitable, and that one need not bemoan it. One of the purposes of science is to inspire people to pose questions about the universe, and if the inspiration that results is often off the mark, the effort should still be welcomed—that is, as long as people don’t confuse art and reality too strongly.
Consider, after all, that from the time of Klein in the 1920s to the resurgence of interest in the topic in the 1980s and ’90s, physicists were concentrating on microscopically tiny extra dimensions, so small that nothing of real interest on human scales could transpire within them or emerge from them. As I wrote in The Physics of Star Trek, while extra di
mensions might exist, if they did, they were thought to be far too small for aliens to abduct us into them.
But, once again, life is appearing to imitate art, and to some extent science is playing catch-up. As I shall describe, possibly infinitely large extra dimensions and even parallel universes that might house everything from stars and planets to aliens have become topics that physicists now actually discuss seriously. The story of how we got to this strange place will occupy us for the rest of this book. Whether or not the current speculations about large, or even small, extra dimensions are any more firmly grounded in reality than the extra dimensions imagined by More in 1671 to house spirits or those imagined by the Star Trek writers from which hostile aliens might emerge, or whether instead they resemble the fictional Cerebron’s analytical discovery of three different kinds of dragon—the mythical, the chimeral, and the purely hypothetical—is, of course, the million-dollar question.
C H A P T E R 1 3
AN ENTANGLED KNOT
My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect in the Unseen residing.
And think doth like a convict sit,
With marlinspike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying.
—James Clerk Maxwell
While the 1960s proved to be a period of discovery and confusion in elementary particle physics, as I have described, the 1970s were one of exultation, vindication, and ultimately, hubris. We began the decade mired in confusion about the quantum mechanical nature of every known force except for electromagnetism, and we completed it with a beautiful and perfectly accurate microscopic formulation of three of the four known forces in nature, with the hope of one day joining them into a single Grand Unified Theory (GUT).
It is within this historical framework that we should view the developments that have taken place since the 1970s. While the dual string theories of the late 1960s caused some physicists to take what so far appears to have been a dead-end detour to explore how microscopic extra dimensions might explain the physics of strongly interacting particles, the subsequent remarkable advances of the 1970s ultimately emboldened physicists to attempt to address the “really big” questions. Just as Einstein’s great success gave him the hubris, and stamina, to devote the final thirty years of his life to an (ultimately futile) effort to produce a unified theory of all interactions, so, too, in the 1980s did physicists begin to reexamine ideas ranging from the Kaluza–Klein higher-dimensional framework to the mathematical miracles of the dual string model in an effort to once again attempt to reach Einstein’s elusive goal of a unified theory.
Like all grand and ambitious campaigns, perhaps, this one began via a series of independent and sometimes serendipitous developments on seemingly unrelated fronts. These all converged in the mid-1980s in an explosion of excitement and activity that has transformed much of the focus of fundamental physics ever since.
In 1971 a young Dutch physicist, Gerardus ’tHooft, working on his PhD with his professor, Martinus Veltman, made one of those rare discoveries that changed the way physicists thought about fundamental physics. When Veltman had first met young ’tHooft, he told him to read the classic 1954 paper by Yang and Mills that proposed the now-famous Yang-Mills theories—the generalizations of electromagnetism that I wrote about earlier. While at the time the formalism proposed by Yang and Mills was essentially purely mathematical—there were no systems in nature that it could clearly describe—its elegance had raised the interest of several key theoretical physicists. One was the Nobel laureate Julian Schwinger, who around 1959 advised his graduate student Sheldon Glashow to consider how one might use these ideas to study the weak interactions, which ultimately led to Glashow’s 1961 paper for which he would win the Nobel prize. Another was Veltman, who was convinced that the symmetry associated with the Yang-Mills theories was too beautiful to not be applicable to nature.
The problem with these theories was that if one tried to use them to describe physical phenomena, such as those associated with the weak interactions, then mathematical infinities appeared to result, which were not too different than those that caused physicists working on the strong interaction to first resort to the study of dual string models. Indeed, the model proposed by Glashow, and independently by Weinberg and Salam in 1967, appeared to suffer from just such infinities, so it is interesting to note that from the period 1961 to 1971 the papers that ultimately unified the weak and electromagnetic interactions were cited in the literature by physicists less than a dozen times.
However, ’tHooft, working under Veltman’s guidance, discovered in 1971 that the infinities that appeared to plague the electroweak model of Glashow, Weinberg, and Salam could cleverly be removed so that the theories made mathematical sense and their predictions could be compared with experiment to arbitrarily high precision—if one had sufficient energy to do the calculations. Within two years it was understood that both the strong and weak interactions were described by Yang-Mills “nonabelian gauge theories.” Three of the four forces in nature were now understood as full quantum theories. All that remained to conquer was gravity!
In the twenty years or so following Yang and Mills’s work, a handful of physicists had explored the possibility that one might extend the work of Kaluza and Klein in unifying electromagnetism and gravity to the possibility of unifying gravity and Yang-Mills theories. The rationale for this was not evident, except that it was an interesting mathematical problem. It was immediately clear that these theories, which you may recall involve more than one “photonlike” force carrier, would require a generalization to more than five dimensions. Remember that Kaluza and Klein had been able to reproduce the force of electromagnetism in four dimensions by making the photon field a part of a five-dimensional gravitational field, with the one extra dimension invisible to us.
By 1975 or so the problem had finally been worked out by various physicists, with a complete derivation by Peter Freund and collaborator Y. M. Cho. The result was what one might expect: Namely, as one could incorporate one photon by having a gravitational field in one extra (i.e., a fifth) dimension, so one could accommodate more than one “photonlike”
field, as occurs in Yang-Mills theories, by adding one extra dimension for each field, and having general relativity operate in the full multidimensional space. This model, however, did not attract much, if any, attention, for a variety of reasons. Most important was the fact that unlike the Kaluza-Klein theory, a complete solution of whose equations allows three “large” and relatively flat spatial dimensions along with a compactified and thus “small” fourth spatial dimension, it turned out that the solutions of the higher-dimensional theories were not so simple.
Since the world we happen to live in is manifestly both large and threedimensional, one might expect that the fact that these higher-dimensional unification models did not predict such a universe would kill any interest in them whatsoever. However, as I have pointed out in another context, putting aside some mathematical ideas is like trying to put the toothpaste back in the tube after you have squirted it out. Once they are out there, they tend to take on lives of their own.
Indeed, within a year, it was recognized that if one added additional particles and forces beyond those associated with gravity in the higherdimensional framework, one could produce the desired compactification to a large, flat, three-dimensional space and smaller extra compact dimensions. Of course, in so doing one was deviating from the spirit of Kaluza and Klein, who hoped that all the forces in nature might arise from a single gravitational field in higher dimensions. Once additional particles and fields are introduced in these extra dimensions, much of the beauty and economy of the proposal would at first seem to fade. But beauty is in the eye of the beholder, and it would turn out that there were other, equally mathematically elegant reasons to consider such additions. For the moment though
, let us return to the spirit of Kaluza and Klein and ask, if the mathematical Yang–Mills symmetries associated with the known forces in nature were to result from the geometric properties of some underlying extra-dimensional space, how many extra dimensions would we need to accommodate all the known forces? The answer turns out to be seven, leading to a total of eleven space-time dimensions. Thus, at the very least, the physics of the past fifty years tells us that if extra dimensions are to be the key to understanding all of the known forces in nature, there have to be a lot of them!
Eleven dimensions may seem like a lot to accommodate, but there are some good things associated with doing so. First, it is fewer than twentysix dimensions, which is what the dual string models naively seemed to require. At the same time, it turned out that there was an independent reason to consider spaces as large as eleven dimensions in physics, coming from a consideration of the differences between the nature of matter and the matter of nature. When we classify all the forces in nature, one fact stands out clearly: All of these forces appear to result via the exchange of virtual particles called “bosons.” Recall that in quantum mechanics various properties of elementary objects, such as energy and momentum, can take on only various discrete “quantized” values. Bosons are elementary particles whose quantum angular momentum, or “spin” as we call it, comes in integer multiples of some basic fundamental value. However, when we look at matter, there is no such restriction. The basic particles that make up matter—electrons and quarks—all have spin values that are half-integer multiples of that fundamental value, and are called “fermions.” Composite objects, made up of combinations of quarks, can have either half-integer or integer spin.
Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Page 17