Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)

by Lawrence M. Krauss

  C H A P T E R 1 2

  ALIENS FROM OTHER DIMENSIONS

  . . . the banality of existence has been so amply demonstrated, there is no need for us to discuss it any further here. The brilliant Cerebron, attack- ing the problem analytically, discovered three distinct kinds of dragon: the mythical, the chimeral, and the purely hypothetical. They were all, one might say, nonexistent, but each nonexisted in an entirely different way.

  —Stanislaw Lem, The Third Sally

  If physicists have been fickle in their intermittent love affair with extra dimensions, turning hot and cold as their whims and desires evolved, artists and writers have been much more faithful with their affections. Through good times and bad, a literary fascination with another world beyond the reach of our senses has held steadfast. There is an unbroken string of writing with this focus, stretching from Lewis Carroll’s Through the Looking Glass (1872) to C. S. Lewis’s The Lion, The Witch, and the Wardrobe (1950) and beyond. These books, written almost a century apart, were ostensibly created for children by austere British academics, but both reach out far more broadly to that primal yearning to answer with a resounding no, Peggy Lee’s plaintive cry: “Is that all there is?”

  Despite the gap in time and intentions of the writers (Carroll was, among other things, a satirist who poked fun at both authority and thenmodern mores, while C. S. Lewis wrote his tale as an allegory to promote his deep religious convictions), there is a remarkable similarity in their choice of dramatic method. Alice is transported through a looking glass to a new three-dimensional world that exists inside of the glass, but clearly not behind it. Lewis’s Lucy similarly enters a wardrobe, which again has a well-defined back when seen from the outside, but instead of encountering a wooden frame, she stumbles into the snowy night of that other threedimensional world, Narnia. From a mathematical perspective (and Carroll, at least, was a mathematician), what both young girls traverse is a mystical intersection between two completely separate three-dimensional worlds. To enter one is to disappear from the other . . . or at least in Alice’s case to disappear, once she turns the corner out of view of those peering into the mirror. And two separate and distinct three-dimensional worlds can intersect only if the underlying space is at least four-dimensional. As I have previously alluded, their experience is strangely reminiscent, if less terrifying perhaps, than little Christie’s experience in the Twilight Zone episode “Little Lost Girl.” Actually, this 1962 screenplay derived from an earlier short story by Richard Matheson that appeared in the science fiction magazine Amazing Stories in November 1953. The contemporaneous appearance of Matheson’s piece and Lewis’s allegory is perhaps not surprising, for just as the world of elementary particle physics was turning topsy-turvy during the 1940s and ’50s, so, too, did this period witness a resurgence of interest among writers, artists, and now filmmakers in a possible fourth spatial dimension. During this era and the decades that followed, the extradimensional imagination of artists and writers happily moved from the purely “mythical, chimerical, and hypothetical,” as per Stanislaw Lem’s fanciful science fiction story, to a sensibility that was more closely attuned to emerging scientific themes. What began as a rather unrealistic fascination with the mathematical properties of a purely hypothetical fourth spatial dimension through the 1940s and ’50s eventually progressed to topics like space and time travel, a host of possible new dimensions, and issues such as how information might leak in and out of our world.

  Perhaps the first and best known among the modern science fiction writers who helped rekindle popular fascination with a fourth dimension was Robert Heinlein. His classic short story “And He Built a Crooked House,” written in 1940 and published in the February 1941 issue of the science fiction monthly Astounding Science Fiction, tells the tale of an unfortunate California architect, Quintus Teal, who designs a revolutionary house based on a tesseract, which you will recall is a four-dimensional version of a cube. Teal has a brilliant idea to save space. If you could build a tesseract house, then its footprint in our three-dimensional world could be a simple cube. But, since the full 4D tesseract has eight 3D cubical faces (as a 3D ube has six 2D square faces, you will recall), one could have an eightroom house on land with only enough space for a single room. (I understand that in later editions of Superman comic books, his Fortress of Solitude had a similar design, for a similar reason.)

  Of course, not having access to four dimensions, Teal does the next best thing: He builds an unfolded tesseract. Again, just as you could unfold a cube by cutting along its edges to lay out on a piece of paper the six squares that make it up, say as follows,

  so too, you could imagine unfolding a tesseract and projecting onto a three-dimensional space the eight cubes that form its surface:

  This projection, which is also called a “net,” was Teal’s construction—that is, until an earthquake accidentally causes the structure to fold back up into its four-dimensional form, nearly trapping Teal and the new owners in another three-dimensional space forever removed from our own. Heinlein’s fascination with hypercubes was not novel. Charles Hinton’s fixation with four dimensions caused him to imagine and present a host of ways of visualizing four-dimensional objects such as tesseracts (or hypercubes, as they are also known) in all of his many writings at the turn of the last century. In the 1920s short stories continued to focus on the fourth dimension as a way to move in and out of interesting threedimensional spaces. Both Richard Hughes’s humorous “The Vanishing Man” (1926) and Miles Breuer’s “The Appendix and the Spectacles” (1928) focus on the opportunities and problems that result from the fact that moving into a fourth spatial dimension would allow one to visit and explore the insides of objects, including human beings, without ever having to actually travel through their outer surfaces. But I suspect it was Heinlein’s work (in particular “Crooked House”) and later writing (such as Madeline L’Engle’s children’s classic A Wrinkle in Time, in which a tesseract is used as a portal to reach faraway distances and times in a folded space) that brought the idea to popular attention, and made the term tesseract a familiar one in popular culture. (Heinlein continued his fascination with a fourth dimension up through his 1963 story “Glory Road,” which involved a hyperdimensional packing case that was bigger inside than outside.)

  Coincidentally, at almost the same time as Heinlein’s and Matheson’s work was permeating popular culture, one of the twentieth century’s most prolific and imaginative artists, Salvador Dali, who had moved well beyond cubism to help spearhead surrealism, produced his classic painting, Crucifixion, Corpus Hypercubus, which reproduces the tesseract net I displayed earlier.

  While modern art has itself moved well beyond surrealism, so that concern with the three-dimensional notion of form has been replaced by such interests as color—or in the most extreme forms of conceptual art, no form at all—the inclusion in 1954 of a tesseract as a surrealist object of interest is part of a pattern in popular culture that I find particularly intriguing. Recall that, at the turn of the century, before, during, and immediately after the introduction of Einstein’s work, fascination with a fourth spatial dimension existed entirely independently of special relativity. Yet almost a half-century after Einstein’s revolutionary theories, the notion that the fourth dimension of that theory was not a spatial dimension still had not fully filtered down to the popular level. Or alternatively, even if it had, the recognition of our existence within a four-dimensional space-time continued to inspire at least a hope that other spatial dimensions might actually exist. In particular, in both Matheson’s story and Heinlein’s, and in much other contemporaneous writing—such as Mark Clifton’s charming short story “Star Bright” (1952) about a brilliant young girl (evolved in mental powers well beyond those of her father) who starts studying about mobius strips, Klein bottles, and tesseracts, and ultimately wills herself to step into a fourth dimension—the protagonists assume that a fourth dimension actually exists, and is common knowledge. In both “Little Lost Girl” and “Star
Bright” it was implied that such a fourth dimension was a genuine concern of the physics of that period. The bewildered father in “Star Bright” exclaims: “The Moebius Strip, the Klein Bottle, the unnamed twisted cube—Einsteinian Physics. Yes, it was possible.” And the physicist Bill in “Little Lost Girl” talks to the terrified couple about a portal to the fourth dimension as if it were something that everyone should be familiar with, although he does add a cautionary note: “I’m not an expert in this. . . . Who is?”

  By the 1960s, however, one finds a growing and more realistic use of the intimate connection between space and time exposed by special and general relativity. Perhaps this was driven in part by the new opportunities for creative expression as special effects in movies began to blossom in the 1950s and ’60s, and as television emerged as a key medium. With new graphic opportunities came new stories that exploited them. I suspect that one of the strongest driving forces, however, was the new popular fascination that began, following the 1957 launch of Sputnik, with the opportunities it promised of space travel. Once attention was focused on the apparently infinite expanse of space, it was natural for scientists, and for writers and filmmakers, to speculate both about ways that one might traverse vast distances and about the large-scale nature of space itself. Stories began to proliferate in which not only does time travel become possible via transport into a fourth dimension, but also a curved space, including a curved fourth dimension, can provide spatial transport to otherwise inaccessibly distant locations. The famous 1963 French science fiction novel by Pierre Boulle, Monkey Planet, became an even more famous American film, Planet of the Apes, filmed in 1968. In the cinematic version, an astronaut who has gone on a long voyage to a distant planet later discovers that he has merely traveled in time but not in space.

  Planet of the Apes makes a vague inference that somehow the long time lapse on Earth might be related to the remarkable fact, arising from special relativity, that objects moving near the speed of light relative to observers watching them have clocks that appear to be running slowly relative to the observer’s clocks. This connection between space and time in relativity implies that in principle, if one was traveling at speeds close to light speed one could cross the galaxy in a single human lifetime, even if observers on the ground would measure the time elapsed for such a voyage to be many thousands of years. This fact, which (again, in principle) allows human interstellar travel without exceeding the speed of light, has become a staple of science fiction writing about space travel over the years. Indeed, as I have noted in The Physics of Star Trek, even the Star Trek writers took this fact into account, inventing a Federation “impulse drive” Speed Limit of less than half the speed of light for extended periods, so that Federation ships would not get out of time synch with their home bases.

  All these applications of relativity to hypothetical space travel, in fact, involve “sub–light-speed” travel. Indeed, since special relativity suggests that travel at the speed of light is an absolute limit, there appears to be no room for anything else. However, the imaginations of writers and of scientists have offered up hopeful alternatives, of varying degrees of credibility. Almost all of these have been centered on the fact that once one allows for space itself to be dynamic—curving, expanding, or contracting in the presence of mass and energy—faster-than-light travel may be feasible. For scientists, it has been the possible dynamic evolution of space that offers the most potential. For writers, however, the curvature of space, which as I have noted is suggestive (although incorrectly so) of an embedding of our own space in a space of higher dimensions, seems to have been the primary motivating force.The prolific Australian (British-born) science fiction writer A. Bertram Chandler was fascinated with faster-than-light travel as well as alternate realities and extra dimensions. In his story “Catch the Star Winds” (1969) he combined both ideas in a single work. The crew of the Flying Cloud manipulate space and time to travel faster than light and back in time, but in so doing they get hurtled into alternate dimensions from which return is impossible.

  Chandler’s stories may be far removed from any realistic science, but by the 1960s, physics had in fact produced some theoretical constructs associated with curved space whose properties are reminiscent of the fourdimensional objects that had earlier so fascinated Heinlein: namely, black holes and ultimately even more exotic objects called wormholes. Black holes are remarkable not merely because they are so exotic—configurations of matter and energy so dense that the escape velocity from their surface exceeds even the speed of light—but because classically, at least, anything that falls inside one is doomed to encounter a “singularity” at their origin: A place of infinite density where the concept of space itself breaks down. Within the context of general relativity, it seems that nothing can stop the ultimate gravitational collapse of a black hole, so that the material making it up gets compressed until it achieves infinite density, at least if one follows the classical trajectories indefinitely. However, we expect that general relativity probably gets modified at small scales and high densities, where the laws of quantum mechanics hold sway.

  Interestingly, however, even the classical geometry of black holes carries with it certain exotic possibilities. In particular, mathematically at least, the region inside what is called the event horizon of a black hole—the volume out of which nothing that falls in can escape—does not just extend down to the singularity, but crosses it, and connects it to another mirror image of all of space outside the event horizon. Is this just an artifact of the mathematics of classical general relativity, or could black holes act as portals to another causally disconnected universe? Both scientists and writers have speculated about this, although if one had to pass through the singularity to get there, one probably wouldn’t look too healthy coming out—rather more like meat after it has been through a grinder.

  This practical issue aside, there was a compelling reason for some physicists, in particular Stephen Hawking, to have espoused the possibility that black holes are portals. When things fall through the event horizon into a black hole, one loses all subsequent information about them. Hawking showed in 1972 that when one incorporates the laws of quantum mechanics near the event horizon, black holes can actually radiate away energy, and in the process may ultimately shrink and disappear. However, it appeared mathematically that the radiation that emerged from the black hole would contain no information at all about what had fallen into it. This is a big problem, because quantum mechanics requires that this information should be recoverable, at least in principle, if not in actual practice. If Hawking radiation really violates this principle, then quantum mechanics is definitively incompatible with gravity. Indeed, the so-called information loss paradox has been one of the central problems driving theoretical physicists to attempt to go beyond general relativity for a new theory that might be explicitly compatible with quantum mechanics. Now, if it were really true that the information that fell down a black hole was lost to our universe, one might naturally ask where this information disappeared to. One possibility, which is the one Hawking raised, is that it would vanish down through the singularity to emerge in another universe.

  Recently, however—indeed, as this book was being written—Hawking has revised his opinion. He now claims to have done a calculation that suggests that the Hawking radiation that comes out of a black hole actually does carry all the information that fell into it. If this is true, then it is a profoundly important result, as I shall later discuss, because it suggests that no significant modifications of general relativity may be necessary to resolve the information loss paradox. And, as Hawking himself has pointed out, this would also remove the prime motivation for considering black holes as portals, a fact he acknowledged with an apology: “I’m sorry to disappoint science-fiction fans.”

  Whether or not black holes can function as portals to another universe, the notion that there could be a potentially infinite space inside of objects that appear from the outside to have a finite size, extending
Heinlein’s “Crooked House” concept to its extreme, is actually not crazy at all. Indeed, we may be experiencing precisely this phenomenon in the universe in which we live. As I have discussed, our universe appears to be accelerating in its expansion, and if this acceleration is left unchecked, almost everything that astronomers can now see will recede from view, expanding infinitely far away in the infinite future. However, as Alan Guth—who in 1980 first recognized the likelihood and potential significance of periods of acceleration during the history of the universe—has demonstrated, an initially finite region of the universe that is inflating on the inside, can actually appear to be contracting when seen from the outside!

  As the universe cools, certain regions can get stuck in a state that is not the true lowest-energy configuration of matter and energy, just as when one cools water down while stirring it, it can remain a liquid well below freezing. In particle physics such regions are called false vacua. Guth realized that a bubble of false vacuum amidst a sea of true vacuum would look very different when seen from the inside versus from the outside. Viewed from inside, the region would appear to be inflating, expanding with a constant rate of acceleration. From outside, the bubble would in fact appear to be decreasing in size, and would eventually disappear from view. Where would everything in the bubble end up? In a different, causally disconnected, and otherwise infinite universe!

  This is only one of several ways that the exotic physics of curved space associated with general relativity can allow seemingly impossible things to happen. A more familiar example, perhaps, and one borrowed by Carl Sagan from physics (via his friend Kip Thorne) in his 1985 novel and then movie, Contact, involves wormholes. Wormholes are literally shortcuts through a curved space, much as a tunnel under a mountain saves you the travel time that would be required to cross over it. Two otherwise distant regions of space might in principle be connected via a three-dimensional wormhole if one amassed enough mass and energy at either of its mouths to produce huge local curvatures of space. However unlike a tunnel (which connects two points separated by the same linear distance apart whether or not the tunnel is there to connect them in this way), a wormhole literally changes the nature of space connecting them. Before it is created there is literally no sense in which the two points might otherwise be considered close to each other.