The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

  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 writ
ten in 1937 by the Scottish physicist W. J. van Stockum 11 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."