The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2004)
Part V. REALITY AND IMAGINATION
Chapter 15. Teleporters and Time Machines
TRAVELING THROUGH SPACE AND TIME
Perhaps I just lacked imagination back in the 1960s, but what really struck me as unbelievable was the computer on board the Enterprise. My grade-school sensibilities granted poetic license to warp drive and to a universe populated by aliens fluent in English. But a machine that could—on demand—immediately display a picture of any historical figure who ever lived, give technical specifications for any piece of equipment ever built, or provide access to any book ever written? That strained my ability to suspend disbelief. In the late 1960s, this preteen was certain that there’d never be a way to gather, store, and give ready access to such a wealth of information. And yet, less than half a century later, I can sit here in my kitchen with laptop, wireless Internet connection, and voice recognition software and play Kirk, thumbing through a vast storehouse of knowledge—from the pivotal to the puerile—without lifting a finger. True, the speed and efficiency of computers depicted in the twenty-third-century world of Star Trek is still enviable, but it’s easy to envisage that when that era arrives, our technology will have exceeded the imagined expectations.
This example is but one of many that have made a cliché of science fiction’s ability to presage the future. But what of the most tantalizing of all plot devices—the one in which someone enters a chamber, flips a switch, and is transported to a faraway place or a different time? Is it possible we will one day break free from the meager spatial expanse and temporal epoch to which we have been so far confined and explore the farthest reaches of space and time? Or will this distinction between science fiction and reality remain forever sharply drawn? Having already been exposed to my childhood failure to anticipate the information revolution, you might question my ability to divine future technological breakthroughs. So, rather than speculating on the likelihood of what may be, in this chapter I’ll describe how far we’ve actually gone, in both theory and practice, toward realizing teleporters and time machines, and what it would take to go further and attain control over space and time.
Teleportation in a Quantum World
In conventional science fiction depictions, a teleporter (or, in Star Trek lingo, a transporter) scans an object to determine its detailed composition and sends the information to a distant location, where the object is reconstituted. Whether the object itself is “dematerialized,” its atoms and molecules being sent along with the blueprint for putting them back together, or whether atoms and molecules located at the receiving end are used to build an exact replica of the object, varies from one fictional incarnation to another. As we’ll see, the scientific approach to teleportation developed over the last decade is closer in spirit to the latter category, and this raises two essential questions. The first is a standard but thorny philosophical conundrum: When, if ever, should an exact replica be identified, called, considered, or treated as if it were the original? The second is the question of whether it’s possible, even in principle, to examine an object and determine its composition with complete accuracy so that we can draw up a perfect blueprint with which to reconstitute it.
In a universe governed by the laws of classical physics, the answer to the second question would be yes. In principle, the attributes of every particle making up an object—each particle’s identity, position, velocity, and so on—could be measured with total precision, transmitted to a distant location, and used as an instruction manual for recreating the object. Doing this for an object composed of more than just a handful of elementary particles would be laughably beyond reach, but in a classical universe, the obstacle would be complexity, not physics.
In a universe governed by the laws of quantum physics—our universe—the situation is far more subtle. We’ve learned that the act of measurement coaxes one of the myriad potential attributes of an object to snap out of the quantum haze and take on a definite value. When we observe a particle, for example, the definite features we see do not generally reflect the fuzzy quantum mixture of attributes it had a moment before we looked.1 Thus, if we want to replicate an object, we face a quantum Catch-22. To replicate we must observe, so we know what to replicate. But the act of observation causes change, so if we replicate what we see, we will not replicate what was there before we looked. This suggests that teleportation in a quantum universe is unattainable, not merely because of practical limitations arising from complexity, but because of fundamental limitations inherent in quantum physics. Nevertheless, as we’ll see in the next section, in the early 1990s an international team of physicists found an ingenious way to circumvent this conclusion.
As for the first question, regarding the relationship between replica and original, quantum physics gives an answer that’s both precise and encouraging. According to quantum mechanics, every electron in the universe is identical to every other, in that they all have exactly the same mass, exactly the same electric charge, exactly the same weak and strong nuclear force properties, and exactly the same total spin. Moreover, our well-tested quantum mechanical description says that these exhaust the attributes that an electron can possess; electrons are all identical with regard to these properties, and there are no other properties to consider. In the same sense, every up-quark is the same as every other, every down-quark is the same as every other, every photon is the same as every other, and so on for all other particle species. As recognized by quantum practitioners many decades ago, particles may be thought of as the smallest possible packets of a field (e.g., photons are the smallest packets of the electromagnetic field), and quantum physics shows that such smallest constituents of the same field are always identical. (Or, in the framework of string theory, particles of the same species have identical properties because they are identical vibrations of a single species of string.)
What can differ between two particles of the same species are the probabilities that they are located at various positions, the probabilities that their spins are pointing in particular directions, and the probabilities that they have particular velocities and energies. Or, as physicists say more succinctly, the two particles can be in different quantum states. But if two particles of the same species are in the same quantum state—except, possibly, for one particle having a high likelihood of being here while the other particle has a high likelihood of being over there—the laws of quantum mechanics ensure that they are indistinguishable, not just in practice but in principle. They are perfect twins. If someone were to exchange the particles’ positions (more precisely, exchange the two particles’ probabilities of being located at any given position), there’d be absolutely no way to tell.
Thus, if we imagine starting with a particle located here,40 and somehow put another particle of the same species into exactly the same quantum state (same probabilities for spin orientation, energy, and so on) at some distant location, the resulting particle would be indistinguishable from the original and the process would rightly be called quantum teleportation. Of course, were the original particle to survive the process intact, you might be tempted to call the process quantum cloning or, perhaps, quantum faxing. But as we’ll see, the scientific realization of these ideas does not preserve the original particle—it is unavoidably modified during the teleportation process—so we won’t be faced with this taxonomic dilemma.
A more pressing concern, and one that philosophers have considered closely in various forms, is whether what’s true for an individual particle is true for an agglomeration. If you were able to teleport from one location to another every single particle that makes up your DeLorean, ensuring that the quantum state of each, including its relationship to all others, was reproduced with 100% fidelity, would you have succeeded in teleporting the vehicle? Although we have no empirical evidence to guide us, the theoretical case in support of having teleported the car is strong. Atomic and molecular arrangements determine how an object looks and feels, sounds and smells, and even tastes, so the resulting vehicle should be identical to the original DeLorean—bumps, nicks, squeaky left wing-door, musty smell from the family dog, all of it—and the car should take a sharp turn and respond to flooring the gas pedal exactly as the original did. The question of whether the vehicle actually is the original or, instead, is an exact duplicate, is of no concern. If you’d asked United Quantum Van Lines to ship your car by boat from New York to London but, unbeknownst to you, they teleported it in the manner described, you could never know the difference—even in principle.
But what if the moving company did the same to your cat, or, having sated your appetite for airplane gastronomy, what if you decided on teleportation for your own transatlantic travel? Would the cat or person who steps out of the receiving chamber be the same as the one who stepped into the teleporter? Personally, I think so. Again, since we have no relevant data, the best that I or anyone can do is speculate. But to my way of thinking, a living being whose constituent atoms and molecules are in exactly the same quantum state as mine is me. Even if the “original” me still existed after the “copy” had been made, I (we) would say without hesitation that each was me. We’d be of the same mind—literally—in asserting that neither would have priority over the other. Thoughts, memories, emotions, and judgments have a physical basis in the human body’s atomic and molecular properties; an identical quantum state of these elementary constituents should entail an identical conscious being. As time went by, our experiences would cause us to differentiate, but I truly believe that henceforth there’d be two of me, not an original that was somehow “really” me and a copy that somehow wasn’t.
In fact, I’m willing to be a bit looser. Our physical composition goes through numerous transformations all the time—some minor, some drastic—but we remain the same person. From the Häagen-Dazs that inundates the bloodstream with fat and sugar, to the MRI that flips the spin axes of various atomic nuclei in the brain, to heart transplants and liposuction, to the trillion atoms in the average human body that are replaced every millionth of a second, we undergo constant change, yet our personal identity remains unaffected. So, even if a teleported being did not match my physical state with perfect accuracy, it could very well be fully indistinguishable from me. In my book, it could very well be me.
Certainly, if you believe that there is more to life, and conscious life in particular, than its physical makeup, your standards for successful teleportation will be more stringent than mine. This tricky issue—to what extent is our personal identity tied to our physical being?—has been debated for years in a variety of guises without being answered to everyone’s satisfaction. While I believe identity all resides in the physical, others disagree, and no one can claim to have the definitive answer.
But irrespective of your point of view on the hypothetical question of teleporting a living being, scientists have now established that, through the wonders of quantum mechanics, individual particles can be—and have been—teleported.
Let’s see how.
Quantum Entanglement and Quantum Teleportation
In 1997, a group of physicists led by Anton Zeilinger, then at the University of Innsbruck, and another group led by A. Francesco De Martini at the University of Rome,2 each carried out the first successful teleportation of a single photon. In both experiments, an initial photon in a particular quantum state was teleported a short distance across a laboratory, but there is every reason to expect that the procedures would have worked equally well over any distance. Each group used a technique based on theoretical insights reported in 1993 by a team of physicists—Charles Bennett of IBM’s Watson Research Center; Gilles Brassard, Claude Crepeau, and Richard Josza of the University of Montreal; the Israeli physicist Asher Peres; and William Wootters of Williams College—that rely on quantum entanglement (Chapter 4).
Remember, two entangled particles, say two photons, have a strange and intimate relationship. While each has only a certain probability of spinning one way or another, and while each, when measured, seems to “choose” randomly between the various possibilities, whatever “choice” one makes the other immediately makes too, regardless of their spatial separation. In Chapter 4, we explained that there is no way to use entangled particles to send a message from one location to another faster than the speed of light. If a succession of entangled photons were each measured at widely separated locations, the data collected at either detector would be a random sequence of results (with the overall frequency of spinning one way or another being consistent with the particles’ probability waves). The entanglement would become evident only on comparing the two lists of results, and seeing, remarkably, that they were identical. But that comparison requires some kind of ordinary, slower-than-light-speed communication. And since before the comparison no trace of the entanglement could be detected, no faster than light-speed signal could be sent.
Nevertheless, even though entanglement can’t be used for superluminal communication, one can’t help feeling that long-distance correlations between particles are so bizarre that they’ve got to be useful for something extraordinary. In 1993, Bennett and his collaborators discovered one such possibility. They showed that quantum entanglement could be used for quantum teleportation. You might not be able to send a message at a speed greater than that of light, but if you’ll settle for slower-than-light teleportation of a particle from here to there, entanglement’s the ticket.
The reasoning behind this conclusion, while mathematically straightforward, is cunning and ingenious. Here’s the flavor of how it goes.
Imagine I want to teleport a particular photon, one I’ll call Photon A, from my home in New York to my friend Nicholas in London. For simplicity, let’s see how I’d teleport the exact quantum state of the photon’s spin—that is, how I’d ensure that Nicholas would acquire a photon whose probabilities of spinning one way or another were identical to Photon A’s.
I can’t just measure the spin of Photon A, call Nicholas, and have him manipulate a photon on his end so its spin matches my observation; the result I find would be affected by the observation I make, and so would not reflect the true state of Photon A before I looked. So what can I do? Well, according to Bennett and colleagues, the first step is to ensure that Nicholas and I each have one of two additional photons, let’s call them Photons B and C, which are entangled. How we get these photons is not particularly important. Let’s just assume that Nicholas and I are certain that even though we are on opposite sides of the Atlantic, if I were to measure Photon B’s spin about any given axis, and he were to do the same for Photon C, we would find exactly the same result.
The next step, according to Bennett and coworkers, is not to directly measure Photon A—the photon I hope to teleport—since that turns out to be too drastic an intervention. Instead, I should measure a joint feature of Photon A and the entangled Photon B. For instance, quantum theory allows me to measure whether Photons A and B have the same spin about a vertical axis, without measuring their spins individually. Similarly, quantum theory allows me to measure whether Photons A and B have the same spin about a horizontal axis, without measuring their spins individually. With such a joint measurement, I do not learn Photon A’s spin, but I do learn how Photon A’s spin is related to Photon B’s. And that’s important information.
The distant Photon C is entangled with Photon B, so if I know how Photon A is related to Photon B, I can deduce how Photon A is related to Photon C. If I now phone this information to Nicholas, communicating how Photon A is spinning relative to his Photon C, he can determine how Photon C must be manipulated so that its quantum state will match Photon A’s. Once he carries out the necessary manipulation, the quantum state of the photon in his possession will be identical to that of Photon A, and that’s all we need to declare that Photon A has been successfully teleported. In the simplest case, for example, should my measurement reveal that Photon B’s spin is identical to Photon A’s, we would conclude that Photon C’s spin is also identical to Photon A’s, and without further ado, the teleportation would be complete. Photon C would be in the same quantum state as Photon A, as desired.
Well, almost. That’s the rough idea, but to explain quantum teleportation in manageable steps, I’ve so far left out an absolutely crucial element of the story, one I’ll now fill in. When I carry out the joint measurement on Photons A and B, I do indeed learn how the spin of Photon A is related to that of Photon B. But, as with all observations, the measurement itself affects the photons. Therefore, I do not learn how Photon A’s spin was related to Photon B’s before the measurement. Instead, I learn how they are related after they’ve both been disrupted by the act of measurement. So, at first sight, we seem to face the same quantum obstacle to replicating Photon A that I described at the outset: the unavoidable disruption caused by the measurement process. That’s where Photon C comes to the rescue. Because Photons B and C are entangled, the disruption I cause to Photon B in New York will also be reflected in the state of Photon C in London. That is the wondrous nature of quantum entanglement, as elaborated in Chapter 4. In fact, Bennett and his collaborators showed mathematically that through its entanglement with Photon B, the disruption caused by my measurement is imprinted on the distant Photon C.
And that’s fantastically interesting. Through my measurement, we are able to learn how Photon A’s spin is related to Photon B’s, but with the prickly problem that both photons were disrupted by my meddling. Through entanglement, however, Photon C is tied in to my measurement—even though it’s thousands of miles away—and this allows us to isolate the effect of the disruption and thereby have access to information ordinarily lost in the measurement process. If I now call Nicholas with the result of my measurement, he will learn how the spins of Photons A and B are related after the disruption, and, via Photon C, he will have access to the impact of the disruption itself. This allows Nicholas to use Photon C to, roughly speaking, subtract out the disruption caused by my measurement and thus skirt the obstacle to duplicating Photon A. In fact, as Bennett and collaborators show in detail, by at most a simple manipulation of Photon C’s spin (based on my phone call informing him how Photon A is spinning relative to Photon B) Nicholas will ensure that Photon C, as far as its spin goes, exactly replicates the quantum state of Photon A prior to my measurement. Moreover, although spin is only one characteristic of a photon, other features of Photon A’s quantum state (such as the probability that it has one energy or another) can be replicated similarly. Thus, by using this procedure, we could teleport Photon A from New York to London.3
As you can see, quantum teleportation involves two stages, each of which conveys critical and complementary information. First, we undertake a joint measurement on the photon we want to teleport with one member of an entangled pair of photons. The disruption associated with the measurement is imprinted on the distant partner of the entangled pair through the weirdness of quantum nonlocality. That’s Stage 1, the distinctly quantum part of the teleportation process. In Stage 2, the result of the measurement itself is communicated to the distant reception location by more standard means (telephone, fax, e-mail . . .) in what might be called the classical part of the teleportation process. In combination, Stage 1 and Stage 2 allow the exact quantum state of the photon we want to teleport to be reproduced by a straightforward operation (such as a rotation by a certain amount about particular axes) on the distant member of the entangled pair.
Notice, as well, a couple of key features of quantum teleportation. Since Photon A’s original quantum state was disrupted by my measurement, Photon C in London is now the only one in that original state. There aren’t two copies of the original Photon A and so, rather than calling this quantum faxing, it is indeed more accurate to call this quantum teleportation.4 Furthermore, even though we teleported Photon A from New York to London—even though the photon in London becomes indistinguishable from the original photon we had in New York—we do not learn Photon A’s quantum state. The photon in London has exactly the same probability of spinning in one direction or another as Photon A did before my meddling, but we do not know what that probability is. In fact, that’s the trick underlying quantum teleportation. The disruption caused by measurement prevents us from determining Photon A’s quantum state, but in the approach described, we don’t need to know the photon’s quantumstate in order to teleport it. We need to know only an aspect of its quantum state—what we learn from the joint measurement with Photon B. Quantum entanglement with distant Photon C fills in the rest.
Implementing this strategy for quantum teleportation was no small feat. By the early 1990s, creating an entangled pair of photons was a standard procedure, but carrying out a joint measurement of two photons (the joint measurement on Photons A and B described above, technically called a Bell-state measurement) had never been attained. The achievement of both Zeilinger’s and De Martini’s groups was to invent ingenious experimental techniques for the joint measurement and to realize them in the laboratory.5 By 1997 they had achieved this goal, becoming the first groups to achieve the teleportation of a single particle.
Since you and I and a DeLorean and everything else are composed of many particles, the natural next step is to imagine applying quantum teleportation to such large collections of particles, allowing us to “beam” macroscopic objects from one place to another. But the leap from teleporting a single particle to teleporting a macroscopic collection of particles is staggering, and enormously far beyond what researchers can now accomplish and what many leaders in the field imagine achieving even in the distant future. But for kicks, here’s how Zeilinger fancifully dreams we might one day go about it.
Imagine I want to teleport my DeLorean from New York to London. Instead of providing Nicholas and me with one member each of an entangled pair of photons (what we needed to teleport a single photon), we must each have a chamber of particles containing enough protons, neutrons, electrons, and so on to build a DeLorean, with all the particles in my chamber being quantum entangled with all those in Nicholas’s chamber (see Figure 15.1). I also need a device that measures joint properties of all the particles making up my DeLorean with those particles flitting to and fro within my chamber (the analog of measuring joint features of Photons A and B). Through the entanglement of the particles in the two chambers, the impact of the joint measurements I carry out in New York will be imprinted on Nicholas’s chamber of particles in London (the analog of Photon C’s state reflecting the joint measurement of A and B). If I call Nicholas and communicate the results of my measurements (it’ll be an expensive call, as I’ll be giving Nicholas some 1030 results), the data will instruct him on how to manipulate the particles in his chamber (much as my earlier phone call instructed him on how to manipulate Photon C). When he finishes, each particle in his chamber will be in precisely the same quantum state as each particle in the DeLorean (before it was subjected to any measurements) and so, as in our earlier discussion, Nicholas will now have the DeLorean.41 Its teleportation from New York to London will be complete.
Figure 15.1 A fanciful approach to teleportation envisions having two chambers of quantum entangled particles at distant locations, and a means of carrying out appropriate joint measurements of the particles making up the object to be teleported with the particles in one of the chambers. The results of these measurements would then provide the necessary information to manipulate the particles in the second chamber to replicate the object, and complete the teleportation.
Note, though, that as of today, every step in this macroscopic version of quantum teleportation is fantasy. An object like a DeLorean has in excess of a billion billion billion particles. While experimenters are gaining facility with entangling more than a single pair of particles, they are extremely far from reaching numbers relevant for macroscopic entities.6 Setting up the two chambers of entangled particles is thus absurdly beyond current reach. Moreover, the joint measurement of two photons was, in itself, a difficult and impressive feat. Extending this to a joint measurement of billions and billions of particles is, as of today, unimaginable. From our current vantage point, a dispassionate assessment would conclude that teleporting a macroscopic object, at least in the manner so far employed for a single particle, is eons—if not an eternity—away.
But, as the one constant in science and technology is the transcendence of naysaying prophesies, I’ll simply note the obvious: teleportation of macroscopic bodies looks unlikely. Yet, who knows? Forty years ago, the Enterprise’s computer looked pretty unlikely too.7
The Puzzles of Time Travel
There’s no denying that life would be different if teleporting macroscopic objects were as easy as calling FedEx or hopping on a subway. Impractical or impossible journeys would become available, and the concept of travel through space would be revolutionized to that rare degree at which a leap in convenience and practicality marks a fundamental shift in worldview.
Even so, teleportation’s impact on our sense of the universe would pale in comparison to the upheaval wrought by achieving volitional travel through time. Everyone knows that with enough effort and dedication we can, at least in principle, get from here to there. Although there are technological limitations on our travels through space, within those constraints our travels are guided by choice and whim. But to get from now to then? Our experiences overwhelmingly attest to there being at most one route: we must wait it out—second must follow second as tick by tock now methodically gives way to then. And this assumes that “then” is later than “now.” If then precedes now, experience dictates that there is no route at all; traveling to the past seems not to be an option. Unlike travels through space, travels through time appear to be anything but a matter of choice and whim. When it comes to time, we get dragged along in one direction, whether we like it or not.
Were we able to navigate time as easily as we navigate space, our worldview would not just change, it would undergo the single most dramatic shift in the history of our species. In light of such undeniable impact, I am often struck by how few people realize that the theoretical underpinnings for one kind of time travel—time travel to the future— have been in place since early last century.
When Einstein discovered the nature of special relativistic spacetime, he laid out a blueprint for fast-forwarding to the future. If you want to see what’s happening on planet earth 1,000, or 10,000, or 10 million years in the future, the laws of Einsteinian physics tell you how to go about it. You build a vehicle whose speed can reach, say 99.9999999996 percent of light speed. At full throttle, you head off into deep space for a day, or ten days, or a little over twenty-seven years according to your ship’s clock, then abruptly turn around and head back to earth, again at full throttle. On your return, 1,000, or 10,000, or 10 million years of earth time will have elapsed. This is an undisputed and experimentally verified prediction of special relativity; it is an example of the slowing of time with the increasing of speed described in Chapter 3.8 Of course, since vehicles of such speed are beyond what we can build, no one has tested these predictions literally. But as we discussed earlier, researchers have confirmed the predicted slowing of time for a commercial airliner, traveling at a small fraction of light speed, as well as that of elementary particles like muons racing through accelerators at very nearly the speed of light (stationary muons decay into other particles in about two millionths of a second, but the faster they travel the slower their internal clock’s tick, and so the longer the muons appear to live). There is every reason to believe, and no reason not to believe, that special relativity is correct, and its strategy for reaching the future would work as predicted. Technology, not physics, keeps each of us tethered to this epoch.42
Thornier issues arise, though, when we think about the other kind of time travel, travel to the past. No doubt you are familiar with some of these. For example, there’s the standard scenario in which you travel to the past and prevent your own birth. In many fictional descriptions this is achieved with violence; however, any less drastic but equally effective intervention—such as preventing your parents from meeting—would do just as well. The paradox is clear: if you were never born, how did you come to be, and, in particular, how did you travel to the past and keep your parents from meeting? To travel to the past and keep your parents apart, you had to have been born; but if you were born, traveled to the past, and kept your parents apart, you wouldn’t have been born. We run headlong into a logical impasse.
A similar paradox, suggested by the Oxford philosopher Michael Dummett and highlighted by his colleague David Deutsch, teases the brain in a slightly different, perhaps even more baffling way. Here’s one version. Imagine I build a time machine and travel ten years into the future. After a quick lunch at Tofu-4-U (the chain that overtook McDonald’s after the great mad-cow pandemic put a dent in the public enthusiasm for cheeseburgers), I find the nearest Internet café and get online to see what advances have been made in string theory. And do I get a splendid surprise. I read that all open issues in string theory have been resolved. The theory has been completely worked out and successfully used to explain all known particle properties. Incontrovertible evidence for the extra dimensions has been found, and the theory’s predictions of supersymmetric partner particles—their masses, electric charges, and so on— have just been confirmed, spot on, by the Large Hadron Collider. There is no longer any doubt: string theory is the unified theory of the universe.
When I dig a little deeper to see who is responsible for these great advances, I get an even bigger surprise. The breakthrough paper was written a year earlier by none other than Rita Greene. My mother. I’m shocked. No disrespect intended: my mother is a wonderful person, but she’s not a scientist, can’t understand why anybody would be a scientist, and, for example, read only a few pages of The Elegant Universe before putting it down, saying it gave her a headache. So how in the world could she have written the key paper in string theory? Well, I read her paper online, am blown away by the simple yet deeply insightful reasoning, and see at the end that she’s thanked me for years of intense instruction in mathematics and physics after a Tony Robbins seminar persuaded her to overcome her fears and pursue her inner physicist. Yikes, I think. She’d just enrolled in that seminar when I embarked on my trip to the future. I’d better head back to my own time to begin the instruction.
Well, I go back in time and begin to tutor my mother in string theory. But it’s not going well. A year goes by. Then two. And although she’s trying hard, she’s just not getting it. I’m starting to worry. We stay at it for another couple of years, but progress is minimal. Now I’m really worried. There is not much time left before her paper is supposed to appear. How is she going to write it? Finally, I make the big decision. When I read her paper in the future, it left such an impression on me that I remember it clear as day. And so, instead of having her discover it on her own—something that’s looking less and less likely—I tell her what to write, making sure she includes everything exactly as I remember reading it. She releases the paper, and in short order it sets the physics world on fire. All that I read about during my time in the future comes to pass.
Now here’s the puzzling issue. Who should get the credit for my mother’s groundbreaking paper? I certainly shouldn’t. I learned of the results by reading them in her paper. Yet how can my mother take credit, when she wrote only what I told her to? Of course, the issue here is not really one of credit—it’s the issue of where the new knowledge, new insights, and new understanding presented in my mother’s paper came from. To what can I point and say, “This person or this computer came up with the new results”? I didn’t have the insights, nor did my mother, there wasn’t anyone else involved, and we didn’t use a computer. Nevertheless, somehow these brilliant results are all in her paper. Apparently, in a world that allows time travel both to the future and to the past, knowledge can materialize out of thin air. Although not quite as paradoxical as preventing your own birth, this is positively weird.
What should we make of such paradox and weirdness? Should we conclude that while time travel to the future is allowed by the laws of physics, any attempt to return to the past must fail? Some have certainly thought so. But, as we’ll now see, there are ways around the tricky issues we’ve come upon. This doesn’t mean that travel to the past is possible— that’s a separate issue we’ll consider shortly—but it does show that travel back in time can’t be ruled out merely by invoking the puzzles we’ve just discussed.
Rethinking the Puzzles
Recall that in Chapter 5 we discussed the flow of time, from the perspective of classical physics, and came upon an image that differs substantially from our intuitive picture. Careful thought led us to envision spacetime as a block of ice with every moment forever frozen in place, as opposed to the familiar image of time as a river sweeping us forward from one moment to the next. These frozen moments are grouped into nows—into events that happen at the same time—in different ways by observers in different states of motion. And to accommodate this flexibility of slicing the spacetime block into different notions of now, we also invoked an equivalent metaphor in which spacetime is viewed as a loaf of bread that can be sliced at different angles.
But regardless of the metaphor, Chapter 5’s lesson is that moments— the events making up the spacetime loaf—just are. They are timeless. Each moment—each event or happening—exists, just as each point in space exists. Moments don’t momentarily come to life when illuminated by the “spotlight” of an observer’s present; that image aligns well with our intuition but fails to stand up to logical analysis. Instead, once illuminated, always illuminated. Moments don’t change. Moments are. Being illuminated is simply one of the many unchanging features that constitute a moment. This is particularly evident from the insightful though imaginary perspective of Figure 5.1, in which all events making up the history of the universe are on view; they are all there, static and unchanging. Different observers don’t agree on which of the events happen at the same time—they time-slice the spacetime loaf at different angles—but the total loaf and its constituent events are universal, literally.
Quantum mechanics offers certain modifications to this classical perspective on time. For example, we saw in Chapter 12 that on extremely short scales, space and spacetime become unavoidably wavy and bumpy. But (Chapter 7), a full assessment of quantum mechanics and time requires a resolution of the quantum measurement problem. One of the proposals for doing so, the Many Worlds interpretation, is particularly relevant for coping with paradoxes arising from time travel, and we will take that up in the next section. But in this section, let’s stay classical and bring the block-of-ice/loaf-of-bread depiction of spacetime to bear on these puzzles.
Take the paradoxical example of your having gone back in time and having prevented your parents from meeting. Intuitively, we all know what that’s supposed to mean. Before you time-traveled to the past, your parents had met—say, at the stroke of midnight, December 31, 1965,43 at a New Year’s party—and, in due course, your mother gave birth to you. Then, many years later, you decided to travel to the past—back to December 31, 1965—and once there, you changed things; in particular, you kept your parents apart, preventing your own conception and birth. But let’s now counter this intuitive description with the more fully reasoned spacetime-loaf depiction of time.
At its core, the intuitive description fails to make sense because it assumes moments can change. The intuitive picture envisions the stroke of midnight, December 31, 1965 (using standard earthling time-slicing), as “initially” being the moment of your parents meeting, but envisions further that your interference “subsequently” changes things so that at the stroke of midnight, December 31, 1965, your parents are miles, if not continents, apart. The problem with this recounting of events, though, is that moments don’t change; as we’ve seen, they just are. The spacetime loaf exists, fixed and unchanging. There is no meaning to a moment’s “initially” being one way and “subsequently” being another way.
If you time-traveled back to December 31, 1965, then you were there, you were always there, you will always be there, you were never not there. December 31, 1965, did not happen twice, with your missing the debut but attending the encore. From the timeless perspective of Figure 5.1, you exist—static and unchanging—at various locations in the spacetime loaf. If today you set the dials on your time machine to send you to 11:50 p.m., December 31, 1965, then this latter moment will be among the locations in the spacetime loaf at which you can be found. But your presence on New Year’s Eve, 1965, will be an eternal and immutable feature of spacetime.
This realization still leads us to some quirky conclusions, but it avoids paradox. For example, you would appear in the spacetime loaf at 11:50 p.m., December 31, 1965, but before that moment there would be no record of your existence. This is strange, but not paradoxical. If a guy saw you pop in at 11:50 p.m. and asked you, with fear in his eyes, where you came from, you could calmly answer, “The future.” In this scenario, at least so far, we are not caught in a logical impasse. Where things get more interesting, of course, is if you then try to carry out your mission and keep your parents from meeting. What happens? Well, carefully maintaining the “spacetime block” perspective, we inescapably conclude that you can’t succeed. No matter what you do on that fateful New Year’s Eve, you’ll fail. Keeping your parents apart—while seeming to be within the realm of things you can do—actually amounts to logical gobbledygook. Your parents met at the stroke of midnight. You were there. And you will “always” be there. Each moment just is; it doesn’t change. Applying the concept of change to a moment makes as much sense as subjecting a rock to psychoanalysis. Your parents met at the stroke of midnight, December 31, 1965, and nothing can change that because their meeting is an immutable, unchangeable event, eternally occupying its spot in spacetime.
In fact, now that you think about it, you remember that sometime in your teens, when you asked your dad what it was like to propose to your mother, he told you that he hadn’t planned to propose at all. He had barely met your mother before asking the big question. But about ten minutes before midnight at a New Year’s party, he got so freaked by seeing a man pop in from nowhere—a man who claimed to be from the future— that when he met your mother he decided to propose, right on the spot.
The point is that the complete and unchanging set of events in spacetime necessarily fits together into a coherent, self-consistent whole. The universe makes sense. If you time-travel back to December 31, 1965, you are actually fulfilling your own destiny. In the spacetime loaf, there is someone present at 11:50 p.m. on December 31, 1965, who is not there at any earlier time. From the imaginary, outside perspective of Figure 5.1, we would be able to see this directly; we would also see, undeniably, that the person is you at your current age. For these events, situated decades ago, to make sense, you must time-travel back to 1965. What’s more, from our outside perspective we can see your father asking you a question just after 11:50 p.m. on December 31, 1965, looking frightened, rushing away, and meeting your mother at midnight; a little further along the loaf, we can see your parents’ wedding, your birth, your ensuing childhood, and, later on, your stepping into the time machine. If time travel to the past were possible, we could no longer explain events at one time solely in terms of events at earlier times (from any given perspective); but the totality of events would necessarily constitute a sensible, coherent, noncontradictory story.
As emphasized in the last section, this doesn’t, by any stretch of the imagination, signify that time travel to the past is possible. But it does suggest strongly that the purported paradoxes, such as preventing your own birth, are themselves born of logical flaws. If you time-travel to the past, you can’t change it any more than you can change the value of pi. If you travel to the past, you are, will be, and always were part of the past, the very same past that leads to your traveling to it.
From the outside perspective of Figure 5.1, this explanation is both tight and coherent. Surveying the totality of events in the spacetime loaf, we see that they interlock with the rigid economy of a cosmic crossword puzzle. Yet, from your perspective on December 31, 1965, things are still puzzling. I declared above that even though you may be determined to keep your parents from meeting, you can’t succeed in the classical approach to this problem. You can watch them meet. You can even facilitate their meeting, perhaps inadvertently as in the story I’ve told. You can travel back in time repeatedly, so there are many of you present, each intent on preventing your parents’ union. But to succeed in preventing your parents from meeting would be to change something with respect to which the concept of change is meaningless.
But, even with the insight of these abstract observations, we can’t help asking: What stops you from succeeding? If you are standing at the party at 11:50 p.m. and see your young mother, what stops you from whisking her away? Or, if you see your young father, what stops you from—oh, what the heck, let’s just say it—shooting him? Don’t you have free will? Here is where, some suspect, quantum mechanics may enter the story.
Free Will, Many Worlds, and Time Travel
Free will is a tricky issue, even absent the complicating factor of time travel. The laws of classical physics are deterministic. As we saw earlier, if you were to know precisely how things are now (the position and velocity of every particle in the universe), the laws of classical physics would tell you exactly how things were or would be at any other moment you specified. The equations are indifferent to the supposed freedom of human will. Some have taken this to mean that in a classical universe, free will would be an illusion. You are made of a collection of particles, so if the laws of classical physics could determine everything about your particles at any moment—where they’d be, how they’d be moving and so on—your willful ability to determine your own actions would appear fully compromised. This reasoning convinces me, but those who believe we are more than the sum of our particles may disagree.
Anyway, the relevance of these observations is limited, since ours is a quantum, not a classical, universe. In quantum physics, real-world physics, there are resemblances to this classical perspective; there are also potentially pivotal differences. As you read in Chapter 7, if you know the quantum wavefunction right now for every particle in the universe, Schrödinger’s equation tells you how the wavefunction was or will be at any other moment you specify. This component of quantum physics is fully deterministic, just as in classical physics. However, the act of observation complicates the quantum mechanical story and, as we’ve seen, heated debate over the quantum measurement problem still rages. If physicists one day conclude that Schrödinger’s equation is all there is to quantum mechanics, then quantum physics, in its entirety, would be every bit as deterministic as classical physics. As with classical determinism, some would say this means free will is an illusion; others would not. But if we’re currently missing part of the quantum story—if the passage from probabilities to definite outcomes requires something beyond the standard quantum framework—it’s at least possible that free will might find a concrete realization within physical law. We might one day find, as some physicists have speculated, that the act of conscious observation is an integral element of quantum mechanics, being the catalyst that coaxes one outcome from the quantum haze to be realized.9 Personally, I find this extremely unlikely, but I know of no way to rule it out.
The upshot is that the status of free will and its role within fundamental physical law remain unresolved. So let’s consider both possibilities, free will that’s illusory and free will that’s real.
If free will is an illusion, and if time travel to the past is possible, then your inability to prevent your parents from meeting poses no puzzle. Although you feel as if you have control over your actions, the laws of physics are really pulling the strings. When you go to whisk away your mother or shoot your father, the laws of physics get in the way. The time machine lands you on the wrong side of town, and you arrive after your parents have met; or you try to pull the trigger and the gun jams; or you do pull the trigger, but you miss the target and instead knock off your father’s only competitor for your mother’s hand, clearing the way for their union; or, perhaps, when you step out of the time machine you no longer have the desire to prevent your parents from meeting. Regardless of your intention when you enter the time machine, your actions when you exit are part of spacetime’s consistent story. The laws of physics trump all attempts to thwart logic. Everything you do fits in perfectly. It always has and always will. You can’t change the unchangeable.
If free will is not an illusion, and if time travel to the past is possible, quantum physics gives alternative suggestions for what might happen, and is distinctly different from the formulation based on classical physics. One particularly compelling proposal, championed by Deutsch, makes use of the Many Worlds interpretation of quantum mechanics. Remember from Chapter 7 that in the Many Worlds framework, every potential outcome embodied in a quantum wavefunction—a particle’s spinning this way or that, another particle’s being here or there—is realized in its own separate, parallel universe. The universe we’re aware of at any given moment is but one of an infinite number in which every possible evolution allowed by quantum physics is separately realized. In this framework, it’s tempting to suggest that the freedom we feel to make this or that choice reflects the possibility we have to enter this or that parallel universe in a subsequent moment. Of course, since infinitely many copies of you and me are sprinkled across the parallel universes, the concepts of personal identity and free will need to be interpreted in this broadened context.
As far as time travel and the potential paradoxes go, the Many Worlds interpretation suggests a novel resolution. When you travel to 11:50 p.m. on December 31, 1965, pull out your weapon, aim at your father, and pull the trigger, the gun works and you hit the intended target. But since this is not what happened in the universe from which you embarked on your time travel odyssey, your journey must not only have been through time, it must have been also from one parallel universe to another. The parallel universe in which you now find yourself is one in which your parents never did meet—a universe which the Many Worlds interpretation assures us is out there (since every possible universe consistent with the laws of quantum physics is out there). And so, in this approach, we face no logical paradox, because there are various versions of a given moment, each situated in a different parallel universe; in the Many Worlds interpretations, it’s as if there are infinitely many spacetime loaves, not just one. In the universe of origination, your parents met on December 31, 1965, you were born, you grew up, you held a grudge against your father, you became fascinated with time travel, and you embarked on a journey to December 31, 1965. In the universe in which you arrive, your father is killed on December 31, 1965, before meeting your mother, by a gunman claiming to be his son from the future. A version of you is never born in this universe, but that’s okay, since the you who pulled the trigger does have parents. It’s just that they happen to live in a different parallel universe. Whether anyone in this universe believes your story or, instead, views you as delusional, I can’t say. But what’s clear is that in each universe—the one you left and the one you entered—we avoid self-contradictory circumstances.
What’s more, even in this broadened context, your time travel expedition doesn’t change the past. In the universe you left, that’s manifest, since you never visit its past. In the universe you enter, your presence at 11:50 p.m. on December 31, 1965, does not change that moment: in that universe you were, and always will be, present at that moment. Again, in the Many Worlds interpretation, every physically consistent sequence of events happens in one of the parallel universes. The universe you enter is one in which the murderous actions you choose to undertake are realized. Your presence on December 31, 1965, and all the mayhem you create, are part of the unchangeable fabric of that universe’s reality.
The Many Worlds interpretation offers a similar resolution to the issue of knowledge seemingly materializing from nowhere, as in the scenario of my mother’s writing a decisive paper in string theory. According to the Many Worlds interpretation, in one of the myriad parallel universes my mother does develop quickly into a string theory expert, and on her own discovers all that I read in her paper. When I undertake my excursion to the future, my time machine takes me to that universe. The results I read in my mother’s paper while I’m there were indeed discovered by the version of my mother in that world. Then, when I travel back in time, I enter a different one of the parallel universes, one in which my mother has difficulty understanding physics. After years of trying to teach her, I give up and finally tell her what to write in the paper. But in this scenario there is no puzzle regarding who is responsible for the breakthroughs. The discoverer is the version of my mother in the universe in which she’s a physics whiz. All that’s happened as a result of my various time travels is that her discoveries are communicated to a version of herself in another parallel universe. Assuming you find parallel universes easier to swallow than authorless discoveries—a debatable proposition—this provides a less baffling explanation of the interplay of knowledge and time travel.
None of the proposals we’ve discussed in this or the previous section are necessarily the resolution to the puzzles and paradoxes of time travel. Instead, these proposals are meant to show that puzzles and paradoxes do not rule out time travel to the past since, with our current state of understanding, physics provides possible avenues for end runs around the problems. But failing to rule something out is a far cry from declaring it possible. So we are now led to ask the main question:
Is Time Travel to the Past Possible?
Most sober physicists would answer no. I would say no. But unlike the definitive no you’d get if you asked whether special relativity allows a massive object to accelerate up to and then exceed the speed of light, or whether Maxwell’s theory allows a particle with one unit of electric charge to disintegrate into particles with two units of electric charge, this is a qualified no.
The fact is, no one has shown that the laws of physics absolutely rule out past-directed time travel. To the contrary, some physicists have even laid out hypothetical instructions for how a civilization with unlimited technological prowess, operating fully within the known laws of physics, might go about building a time machine (when we speak of time machines, we will always mean something that is able to travel both to the future and to the past). The proposals bear no resemblance to the spinning gizmo described by H. G. Wells or Doc Brown’s souped-up DeLorean. And the design elements all brush right up against the limits of known physics, leading many researchers to suspect that with subsequent refinements in our grasp of nature’s laws, existing and future proposals for time machines will be deemed beyond the bounds of what’s physically possible. But as of today, this suspicion is based on gut feeling and circumstantial evidence, not solid proof.
Einstein himself, during the decade of intense research leading to the publication of his general theory of relativity, pondered the question of travel to the past.10 Frankly, it would have been strange if he hadn’t. As his radical reworkings of space and time discarded long-accepted dogma, an ever-present question was how far the upheaval would go. Which features, if any, of familiar, everyday, intuitive time would survive? Einstein never wrote much on the issue of time travel because, by his own account, he never made much progress. But in the decades following the release of his paper on general relativity, slowly but surely, other physicists did.
Among the earliest general relativity papers with relevance for time machines were those written in 1937 by the Scottish physicist W. J. van Stockum11 and in 1949 by a colleague of Einstein’s at the Institute for Advanced Study, Kurt Gödel. Van Stockum studied a hypothetical problem in general relativity in which a very dense and infinitely long cylinder is set into spinning motion about its (infinitely) long axis. Although an infinite cylinder is physically unrealistic, van Stockum’s analysis led to an interesting revelation. As we saw in Chapter 14, massive spinning objects drag space into a whirlpool-like swirl. In this case, the swirl is so significant that, mathematical analysis shows, not only space but also time would get caught up in the whirlpool. Roughly speaking, the spinning twists the time direction on its side, so that circular motion around the cylinder takes you to the past. If your rocket ship encircles the cylinder, you can return to your starting point in space before you embark on your journey. Certainly, no one can build an infinitely long spinning cylinder, but this work was an early hint that general relativity might not prohibit time travel to the past.
Gödel’s paper also investigated a situation involving rotational motion. But rather than focusing on an object rotating within space, Gödel studied what happens if all of space undergoes rotational motion. Mach would have thought this meaningless. If the whole universe is rotating, then there’s nothing with respect to which the purported rotation is happening. Mach would conclude, a rotating universe and a stationary universe are one and the same. But this is another example in which general relativity fails to fully conform to Mach’s relational conception of space. According to general relativity, it does make sense to speak of the entire universe’s rotating, and with this possibility come simple observational consequences. For example, if you fire a laser beam in a rotating universe, general relativity shows that it will appear to travel along a spiral path rather than a straight line (somewhat like the path you’d see a slow-moving bullet follow if you fired a toy gun upward while riding a merry-go-round). The surprising feature of Gödel’s analysis was his realization that if your rocket ship were to follow appropriate trajectories in a spinning universe, you could also return to your place of origin in space before the time of your departure. A rotating universe would thus itself be a time machine.
Einstein congratulated Gödel on his discovery, but suggested that further investigation might show that solutions to the equations of general relativity permitting travel to the past run afoul of other essential physical requirements, making them no more than mathematical curiosities. As far as Gödel’s solution goes, increasingly precise observations have minimized the direct relevance of his work by establishing that our universe is not rotating. But van Stockum and Gödel had let the genie out of the bottle; within a couple of decades, yet more solutions to Einstein’s equations permitting time travel to the past were found.
In recent decades, interest in hypothetical time machine designs has revived. In the 1970s, Frank Tipler reanalyzed and refined van Stockum’s solution, and in 1991, Richard Gott of Princeton University discovered another method for building a time machine making use of so-called cosmic strings (hypothetical, infinitely long, filamentary remnants of phase transitions in the early universe). These are all important contributions, but the proposal that’s simplest to describe, using concepts we’ve developed in previous chapters, was found by Kip Thorne and his students at the California Institute of Technology. It makes use of wormholes.
Blueprint for a Wormhole Time Machine
I’ll first lay out the basic strategy for constructing Thorne’s wormhole time machine, and in the next section I’ll discuss the challenges faced by any contractor Thorne might hire to execute the plans.
A wormhole is a hypothetical tunnel through space. A more familiar kind of tunnel, such as one that’s been bored through the side of a mountain, provides a shortcut from one location to another. Wormholes serve a similar function, but they differ from conventional tunnels in one important respect. Whereas conventional tunnels provide a new route through existing space—the mountain and the space it occupies exist before a tunnel is constructed—a wormhole provides a tunnel from one point in space to another along a new, previously nonexistent tube of space. Were you to remove the tunnel through the mountain, the space it occupied would still exist. Were you to remove a wormhole, the space it occupied would vanish.
Figure 15.2a illustrates a wormhole connecting the Kwik-E-Mart and the Springfield Nuclear Power Plant, but the drawing is misleading because the wormhole appears to stretch across Springfield airspace. More accurately, the wormhole should be thought of as a new region of space that interfaces with ordinary, familiar space only at its ends—its mouths. If while walking along the streets of Springfield, you scoured the skyline in search of the wormhole, you’d see nothing. The only way to see it would be to hop on over to the Kwik-E-Mart, where you would find an opening in ordinary space—one wormhole mouth. Looking through the opening, you’d see the inside of the power plant, the location of the second mouth, as in Figure 15.2b. Another misleading feature of Figure 15.2a is that the wormhole doesn’t appear to be a shortcut. We can fix this by modifying the illustration as in Figure 15.3. As you can see, the usual route from the power plant to the Kwik-E-Mart is indeed longer than the wormhole’s new spatial passage. The contortions in Figure 15.3 reflect the difficulties in drawing general relativistic geometry on a page, but the figure does give an intuitive sense of the new connection a wormhole would provide.
Figure 15.2 (a) A wormhole extending from the Kwik-E-Mart to the nuclear power plant. (b) The view through the wormhole, looking from the mouth at the Kwik-E-Mart and into the mouth in the power plant.
Figure 15.3 Geometry which more clearly shows that the wormhole is a shortcut. (Wormhole mouths are really inside Kwik-E-Mart and the nuclear power plant, although that is difficult to show in this representation.)
No one knows whether wormholes exist, but many decades ago physicists established that they are allowed by the mathematics of general relativity and so are fair game for theoretical study. In the 1950s, John Wheeler and his coworkers were among the earliest researchers to investigate wormholes, and they discovered many of their fundamental mathematical properties. More recently, though, Thorne and his collaborators revealed the full richness of wormholes by realizing that not only can they provide shortcuts through space, they can also provide shortcuts through time.
Here’s the idea. Imagine that Bart and Lisa are standing at opposite ends of Springfield’s wormhole—Bart at the power plant, Lisa at the Kwik-E-Mart—idly chatting with each other about what to get Homer for his birthday, when Bart decides to take a short transgalactic jaunt (to get Homer some of his favorite Andromedean fish fingers). Lisa doesn’t feel up for the ride but, as she’s always wanted to see Andromeda, she persuades Bart to load his wormhole mouth on his ship and take it along, so she can have a look. You might expect this to mean that Bart will have to keep stretching the wormhole longer as his journey progresses, but that assumes the wormhole connects the Kwik-E-Mart and Bart’s ship through ordinary space. It doesn’t. And, as illustrated in Figure 15.4, through the wonders of general relativistic geometry, the wormhole’s length can remain fixed throughout the entire voyage. This is a key point. Even though Bart rockets off to Andromeda, his distance to Lisa through the wormhole does not change. This makes manifest the wormhole’s role as a shortcut through space.
For definiteness, let’s say that Bart heads off at 99.999999999999999999 percent of light speed and travels four hours outbound to Andromeda, all the while continuing to chat with Lisa through the wormhole, just as they’d been doing before the flight. When
Figure 15.4 (a) A wormhole connecting the Kwik-E-Mart and the nuclear power plant. (b) The lower wormhole opening transported (from the nuclear power plant) to outer space (on spaceship, not shown). The wormhole length remains fixed. (c) The wormhole opening arrives at the Andromeda galaxy; the other opening is still at the Kwik-E-Mart. The length of the wormhole is unchanged throughout the entire voyage.
the ship reaches Andromeda, Lisa tells Bart to pipe down so she can take in the view without disturbance. She’s exasperated by his insistence on quickly grabbing the takeout at the Fish Finger Flythrough and heading back to Springfield, but agrees to keep on chatting until he returns. Four hours and a few dozen rounds of tic-tac-toe later, Bart safely sets his ship down on the lawn of Springfield High.
When he looks out the ship window, though, Bart gets a bit of a shock. The buildings look completely different, and the scoreboard floating high above the rollerball stadium gives a date some 6 million years after his departure. “Dude!?!” he says to himself, but a moment later it all becomes clear. Special relativity, he remembers from a heart-to-heart he’d recently had with Sideshow Bob, ensures that the faster you travel the slower your clock ticks. If you travel out into space at high speed and then return, only a few hours might have elapsed aboard your ship while thousands or millions of years, if not more, will have elapsed according to someone stationary. With a quick calculation, Bart confirms that at the speed he was traveling, eight hours elapsed on the ship would mean 6 million years elapsed on earth. The date on the scoreboard is right; Bart realizes he has traveled far into earth’s future.
“. . . Bart! Hello, Bart!” Lisa yells through the wormhole. “Have you been listening to me? Step on it. I want to get home in time for dinner.” Bart looks into his wormhole mouth and tells Lisa he’s already landed on the lawn of Springfield High. Looking more closely through the wormhole, Lisa sees that Bart is telling the truth, but looking out of the Kwik-E-MART toward Springfield High, she doesn’t see his ship on the lawn. “I don’t get it,” she says.
“Actually, it makes perfect sense,” Bart proudly answers. “I’ve landed at Springfield High, but 6 million years into the future. You can’t see me by looking out the Kwik-E-Mart window, because you’re looking at the right place, but you’re not looking at the right time. You’re looking 6 million years too early.”
“Oh, right, that time-dilation thing of special relativity,” Lisa agrees. “Cool. Anyway, I want to get home in time for dinner, so climb through the wormhole, because we’ve got to hurry.” “Okay,” Bart says, crawling through the wormhole. He buys a Butterfinger from Apu, and he and Lisa head home.
Notice that although Bart’s passage through the wormhole took him but a moment, it transported him 6 million years back in time. He and his ship and the wormhole mouth had landed far into earth’s future. Had he gotten out, spoken with people, and checked the newspaper, everything would have confirmed this. Yet, when he passed through the wormhole and rejoined Lisa, he found himself back in the present. The same holds true for anyone else who might follow Bart through the wormhole mouth: he would also travel 6 million years back in time. Similarly, anyone who climbs into the wormhole mouth at the Kwik-E-Mart, and out of the mouth Bart left in his ship, would travel 6 million years into the future. The important point is that Bart did not just take one of the wormhole mouths on a journey through space. His journey also transported the wormhole mouth through time. Bart’s voyage took him and the wormhole’smouth into earth’s future. In short, Bart transformed a tunnel through space into a tunnel through time; he turned a wormhole into a time machine.
A rough way to visualize what’s going on is depicted in Figure 15.5. In Figure 15.5a we see a wormhole connecting one spatial location with another, with the wormhole configuration drawn so as to emphasize that it lies outside of ordinary space. In Figure 15.5b, we show the time evolution of this wormhole, assuming both its mouths are kept stationary. (The time slices are those of a stationary observer.) In Figure 15.5c, we show what happens when one wormhole mouth is loaded onto a spaceship and taken on a round-trip journey. Time for the moving mouth, just like time on a moving clock, slows down, so that the moving mouth is transported to the future. (If an hour elapses on a moving clock but a thousand years elapse on stationary clocks, the moving clock will have jumped into the stationary clocks’ future.) Thus, instead of the stationary wormhole mouth’s connecting, via the wormhole tunnel, to a mouth on the same time slice, it connects to a mouth on a future time slice, as in Figure 15.5c. Unless the wormhole mouths are moved further, the time difference between them will remain locked in. At any moment, should you enter one mouth and exit the other, you will have become a time traveler.
Building a Wormhole Time Machine
One blueprint for building a time machine is now clear. Step 1: find or create a wormhole wide enough for you, or anything you want to send through time, to pass. Step 2: establish a time difference between the wormhole mouths—say, by moving one relative to the other. That’s it. In principle.
Figure 15.5 (a) A wormhole, created at some moment in time, connects one location in space with another. (b) If the wormhole mouths do not move relative to one another, they “pass” through time at the same rate, so the tunnel connects the two regions at the same time. (c) If one wormhole mouth is taken on a round-trip journey (not shown), less time will elapse for that mouth, and hence the tunnel will connect the two regions of space at different moments of time. The wormhole has become a time machine.
How about in practice? Well, as I mentioned at the outset, no one knows whether wormholes even exist. Some physicists have suggested that tiny wormholes might be plentiful in the microscopic makeup of the spatial fabric, being continually produced by quantum fluctuations of the gravitational field. If so, the challenge would be to enlarge one to macroscopic size. Proposals have been made for how this might be done, but they’re barely beyond theoretical flights of fancy. Other physicists have envisioned the creation of large wormholes as an engineering project in applied general relativity. We know that space responds to the distribution of matter and energy, so with sufficient control over matter and energy, we might cause a region of space to spawn a wormhole. This approach presents an additional complication, because just as we must tear open the side of a mountain to attach the mouth of a tunnel, we must tear open the fabric of space to attach the mouth of a wormhole.12 No one knows whether such tears in space are allowed by the laws of physics. Work with which I’ve been involved in string theory (see this page) has shown that certain kinds of spatial tears are possible, but so far we have no idea whether these rips might be relevant to the creation of wormholes. The bottom line is that intentional acquisition of a macroscopic wormhole is a fantasy that, at best, is a very long way from being realized.
Morever, even if we somehow managed to get our hands on a macroscopic wormhole, we wouldn’t be done; we’d still face a couple of significant obstacles. First, in the 1960s, Wheeler and Robert Fuller showed, using the equations of general relativity, that wormholes are unstable. Their walls tend to collapse inward in a fraction of a second, which eliminates their utility for any kind of travel. More recently, though, physicists (including Thorne and Morris, and also Matt Visser) have found a potential way around the collapse problem. If the wormhole is not empty, but instead contains material—so-called exotic matter—that can exert an outward push on its walls, then it might be possible to keep the wormhole open and stable. Although similar in its effect to a cosmological constant, exotic matter would generate outward-pushing repulsive gravity by virtue of having negative energy (not just the negative pressure characteristic of a cosmological constant13). Under highly specialized conditions, quantum mechanics allows for negative energy,14 but it would be a monumental challenge to generate enough exotic matter to hold a macroscopic wormhole open. (For example, Visser has calculated that the amount of negative energy needed to keep open a one-meter-wide wormhole is roughly equal in magnitude to the total energy produced by the sun over about 10 billion years.15)
Second, even if we somehow found or created a macroscopic wormhole, and even if we somehow were able to buttress its walls against immediate collapse, and even if we were able to induce a time difference between the wormhole mouths (say, by flying one mouth around at high speed), there would remain another hurdle to acquiring a time machine. A number of physicists, including Stephen Hawking, have raised the possibility that vacuum fluctuations—the jitters arising from the quantum uncertainty experienced by all fields, even in empty space, discussed in Chapter 12—might destroy a wormhole just as it was getting into position to be a time machine. The reason is that, just at the moment when time travel through the wormhole becomes possible, a devastating feedback mechanism, somewhat like the screeching noise generated when microphone and speaker levels in a sound system are not adjusted appropriately, may come into play. Vacuum fluctuations from the future can travel through the wormhole to the past, where they can then travel through ordinary space and time to the future, enter the wormhole, and travel back to the past again, creating an endless cycle through the wormhole and filling it with ever-increasing energy. Presumably, such an intense energy buildup would destroy the wormhole. Theoretical research suggests this as a real possibility, but the necessary calculations strain our current understanding of general relativity and quantum mechanics in curved spacetime, so there is no conclusive proof.
The challenges to building a wormhole time machine are clearly immense. But the final word won’t be given until our facility with quantum mechanics and gravity is refined further, perhaps through advances in superstring theory. Although at an intuitive level physicists generally agree that time travel to the past is impossible, as of today the question has yet to be fully closed.
In thinking about time travel, Hawking has raised an interesting point. Why, he asks, if time travel is possible, haven’t we been inundated with visitors from the future? Well, you might answer, maybe we have. And you might go further and say we’ve put so many time travelers in locked wards that most of the others don’t dare identify themselves. Of course, Hawking is half joking, and so am I, but he does raise a serious question. If you believe, as I do, that we have not been visited from the future, is that tantamount to believing time travel impossible? Surely, if people succeed in building time machines in the future, some historian is bound to get a grant to study, up close and personal, the building of the first atomic bomb, or the first voyage to the moon, or the first foray into reality television. So, if we believe no one has visited us from the future, perhaps we are implicitly saying that we believe no such time machine will ever be built.
Actually, though, this is not a necessary conclusion. The time machines that have thus far been proposed do not allow travel to a time prior to the construction of the first time machine itself. For the wormhole time machine, this is easy to see by examining Figure 15.5. Although there is a time difference between the wormhole mouths, and although that difference allows travel forward and backward in time, you can’t reach a time before the time difference was established. The wormhole itself does not exist on the far left of the spacetime loaf, so there is no way you can use it to get there. Thus, if the first time machine is built, say, 10,000 years from now, that moment will no doubt attract many time-traveling tourists, but all previous times, such as ours, will remain inaccessible.
I find it curious and compelling that our current understanding of nature’s laws not only suggests how to avoid the seeming paradoxes of time travel but also offers proposals for how time travel might actually be accomplished. Don’t get me wrong: I count myself among the sober physicists who feel intuitively that we will one day rule out time travel to the past. But until there’s definitive proof, I think it justified and appropriate to keep an open mind. At the very least, researchers focusing on these issues are substantially deepening our understanding of space and time in extreme circumstances. At the very best, they may be taking the first critical steps toward integrating us into the spacetime superhighway. After all, every moment that goes by without our having succeeded in building a time machine is a moment that will be forever beyond our reach and the reach of all who follow.