by Thorne, Kip
In the movie, the time lapse between adjacent bedrooms is closer to a tenth of a second than a full second. By watching adjacent bedrooms carefully as the curtains in Murph’s bedroom window blow in the wind, you can estimate the time between bedrooms.
Of course each bedroom in the movie’s tesseract is Murph’s actual bedroom at a particular moment of time—the time labeled in black in Figure 29.13.
Cooper can move far faster than the flow of time in the bedroom extrusions, so he can easily travel through the tesseract complex to most any bedroom time that he wishes!
To travel most rapidly into the future of Murph-bedroom time, Cooper should move along a diagonal of his chamber in the direction of increasing blue, green, and brown time (rightward, upward, and inward)—that is, along the diagonal dashed violet line in Figure 29.13. Diagonals like this are devoid of extrusions; they are open channels along which Cooper can travel. In the movie we see him traveling along such an open diagonal channel to get from the bedroom time of the early ghostly book falls to the bedroom time of the wristwatch ticking (Figure 29.14).
Fig. 29.13. A portion of the lattice of bedrooms created by the intersections of the moving cross sections (the extrusions). The blue numbers identify specific bedrooms—an extension of the numbering system in previous figures. The black number on each bedroom indicates its amount of time to the future of bedroom 0. The dashed violet arrow is the direction in which Cooper can move most rapidly into the bedroom’s future.
Is Cooper really traveling forward and backward in time as he moves diagonally up and down through the complex? Forward and backward in the manner that Amelia Brand speculates bulk beings can when she says: “To Them time may be just another physical dimension. To Them the past might be a canyon they can climb into and the future a mountain they can climb up. But to us it’s not. Okay?”
What are the rules governing time travel in Interstellar?
Fig. 29.14. This is what Cooper sees as he travels rapidly into the future of Murph-bedroom time by soaring along a diagonal channel through the tesseract complex. The diagonal channel is in the picture’s upper center. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
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53 In Figure 29.7, Cooper has been turned over so he is facing the top of Murph’s head as in Figure 29.6. This suggests that in the wall images 2, 3, 4, and 5, Murph should also be turned over. However, having her upside down in four images and right side up in two would be confusing to a mass movie audience, so the wall images have not been inverted here or in the movie.
54 In the movie Murph’s bedroom is not a cube; its length, width, and height are 20, 15, and 10 feet, and Cooper’s chamber is three times larger in each dimension: 60, 45, and 30 feet. For simplicity, I idealize the bedrooms and chambers as cubes.
55 Chris and Paul call these chambers “voids” because they are regions through which no extrusions pass.
30
Messaging the Past
Communicating Rule Sets to a Movie Audience
Before Christopher Nolan became Interstellar’s director and rewrote the screenplay, his brother Jonah taught me about rule sets.
To maintain the desired level of suspense in a science-fiction movie, Jonah said, the audience must be told the rules of the game, the movie’s “rule set.” What do the laws of physics and the technology of the era allow, and what do they forbid? If the rules are not clear, then many in the audience will expect some miraculous event to save the heroine, out of the blue, and tension will fail to mount as it should.
Of course you can’t say to the audience, “Here is the rule set for this movie: . . .” It must be communicated in a subtle and natural way. And Chris is a master of this. He communicates his rule sets though the characters’ dialog. Next time you watch Interstellar (how can you resist watching it again?), look within the film for his tell-tale bits of rule-set dialog.
Christopher Nolan’s Rule Set for Time Travel
It turns out (see below) that backward time travel is governed by the laws of quantum gravity, which are terra almost incognita, so we physicists don’t know for sure what is allowed and what not.
Chris made two specific choices for allowed and forbidden time travel—his rule set:
Rule 1: Physical objects and fields with three space dimensions, such as people and light rays, cannot travel backward in time from one location in our brane to another, nor can information that they carry. The physical laws or the actual warping of spacetime prevent it. This is true whether the objects are forever lodged in our brane or journey through the bulk in a three-dimensional face of a tesseract, from one point in our brane to another. So, in particular, Cooper can never travel to his own past.
Rule 2: Gravitational forces can carry messages into our brane’s past.
In the movie, rule 1 generates mounting tension. Murph grows older and older as Cooper lingers near Gargantua. With no possibility to travel backward in time there’s a growing danger he’ll never return to her.
Rule 2 gives Cooper hope. Hope that he can use gravity to transmit the quantum data backward in time to young Murph, so she can solve the Professor’s equation and figure out how to lift humanity off Earth.
How do these rules play out in Interstellar?
Messaging Murph
When falling into and through the tesseract, Cooper truly does travel backward relative to our brane’s time, from the era when Murph is an old woman to the era when she is ten years old. He does this in the sense that, looking at Murph in the tesseract bedrooms, he sees her ten years old. And he can move forward and backward relative to our brane’s time (the bedroom’s time) in the sense that he can look at Murph at various bedroom times by choosing which bedroom to look into. This does not violate rule 1 because Cooper has not reentered our brane. He remains outside it, in the tesseract’s three-dimensional channel, and he looks into Murph’s bedroom via light that travels forward in time from Murph to him.
But just as Cooper can’t reenter our brane in Murph’s ten-year-old era, so he can’t send light to her. That would violate rule 1. The light could bring her information from Cooper’s personal past, which is her future; information from the era when she is an old woman—backward-in-time information from one location in our brane to another. So there must be some sort of one-way spacetime barrier between ten-year-old Murph in her bedroom and Cooper in the tesseract, rather like a one-way mirror or a black-hole horizon. Light can travel from Murph to Cooper but not from Cooper to Murph.
In my scientist’s interpretation of Interstellar, the one-way barrier has a simple origin: Cooper, in the tesseract, is always in ten-year-old Murph’s future. Light can travel toward the future from Murph to him. It can’t travel to the past from him to Murph.
However, gravity can surmount that one-way barrier, Cooper discovers. Gravitational signals can go backward in time from Cooper to Murph. We first see this when Cooper desperately pushes books out of Murph’s bookcase. Figure 30.1 shows a still from that scene of the movie.
Fig. 30.1. Cooper pushes on the world tube of a book with his right hand. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
To explain this still, I must tell you a bit more about the bedroom extrusions, as Chris and Paul Franklin explained them to me. Let’s focus on the front blue extrusion in Figures 29.10 and 29.12, which I reproduce as Figure 30.2 with extraneous stuff removed. Recall that this extrusion is a set of vertical cross sections through Murph’s bedroom, traveling forward in bedroom time along the blue direction (rightward).
Fig. 30.2. The world tube of a book, within an extrusion of Murph’s bedroom. The book and its world tube are drawn much larger than they actually are. [My own hand sketch.]
Each object in the bedroom, for example each book, contributes to the bedroom’s extrusion. In fact, the book has
its own extrusion, which travels forward in time along the blue-arrow direction as part of the bedroom’s larger extrusion. We physicists call a variant of this extrusion the book’s “world tube.” And we call the extrusion of each particle of matter in the book the particle’s “world line.” So the book’s world tube is a bundle of world lines of all the particles that make up the book. Chris and Paul also use this language. The thin lines that you see in the movie, running along the extrusions, are world lines of particles of matter in Murph’s bedroom.
In Figure 30.1, Cooper slams his fist on the book’s world tube over and over again, creating a gravitational force, which travels backward in time to the moment in Murph’s bedroom that he is seeing and then pushes on the book’s world tube. The book’s tube responds by moving. The tube’s motion appears to Cooper as an instantaneous response to his pushes. And the motion becomes a wave traveling leftward down the tube (Figure 30.2).56 When the motion gets strong enough, the book falls out of the bookcase.
By the time Cooper has received the quantum data from TARS, he has mastered this means of communication. In the movie we see him pushing with his finger on the world tube of a watch’s second hand. His pushes produce a backward-in-time gravitational force, which makes the second-hand twitch in a Morse-encoded pattern that carries the quantum data. The tesseract stores the twitching pattern in the bulk so it repeats over and over again. When forty-year-old Murph returns to her bedroom three decades later, she finds the second hand still twitching, repeating over and over again the encoded quantum data that Cooper has struggled so hard to send her.
How does the backward-in-time gravitational force work? I’ll describe my physicist’s interpretation after I tell you what I know, or think I know, about backward time travel.
Time Travel Without a Bulk: What I Think I Know
In 1987, triggered by Carl Sagan (Chapter 14), I realized something amazing about wormholes. If wormholes are allowed by the laws of physics, then Einstein’s relativistic laws permit transforming them into time machines. The nicest example of this was discovered a year later by my close friend Igor Novikov, in Moscow, Russia. Igor’s example, Figure 30.3, shows that a wormhole’s transformation into a time machine might occur naturally, without the aid of intelligent beings.
In Figure 30.3, the bottom mouth of the wormhole is in orbit around a black hole and the upper mouth is far from the black hole. Because of the black hole’s intense gravitational pull, Einstein’s law of time warps dictates that time flow more slowly at the lower mouth than at the upper mouth. More slowly, that is, when compared along the path of gravity’s intense pull: the dashed purple path through the external universe. I presume, for concreteness, that this has produced a one-hour lag so when compared through the external universe, the bottom clock shown in the figure is one hour behind the top clock. And this time lag is continuing to grow.
Fig. 30.3. Wormhole as a time machine.
Since there is only a tiny gravitational pull inside the wormhole, Einstein’s law of time warps dictates that, as seen through the wormhole, time flows at essentially the same rate in the upper mouth as in the lower mouth. So there is no time lag when the clocks are compared through the wormhole. They are synchronized.
Suppose, further, for concreteness, that the distance from mouth to mouth in the external universe is short enough that you can traverse it in five minutes as measured by the clocks, and you can travel through the wormhole in one minute. Then this wormhole has already become a time machine. You leave the upper mouth at time 2:00 as measured by the clock there, and travel through the external universe to the lower mouth, arriving at 2:05 upper clock time and 1:05 lower clock time. You then make a one-minute trip upward through the wormhole, from lower mouth to upper. Since the clocks. are synchronized through the wormhole, you reach the upper mouth at time 1:06 as seen by both clocks. You arrive back at your starting point fifty-four minutes before your 2:00 departure, and you meet your younger self.
Some days earlier, when the time difference was much less, the wormhole was not yet a time machine. It became a time machine at the first moment when something, moving at the highest possible speed, the speed of light, was able to travel along your route and arrive back at the top mouth at the very moment it started out.
If that something is a particle of light (a photon), for example, then we began with one photon and we now have two, at the starting place and time. After those two make the trip, we have four at that same place and time, then eight, then sixteen, . . . ! There is a growing crescendo of energy coursing through the wormhole, perhaps enough that the energy’s gravity destroys the wormhole at the very moment it is becoming a time machine.
It would seem easy to prevent this. Just shield the wormhole from photons. However, there is something you cannot shield out: quantum fluctuations of light with ultrahigh frequency—fluctuations that inevitably exist, according to the quantum laws (Chapter 26). In 1990, Sung-Won Kim (a postdoctoral student in my research group) and I used the quantum laws to compute the fate of such fluctuations. We found a growing explosion (Figure 30.4). We thought, at first, that the explosion was too weak to destroy the wormhole. The wormhole would become a time machine despite the explosion, we thought. Stephen Hawking convinced us otherwise. The fate of the explosion is controlled by the laws of quantum gravity, he convinced us. Only when those laws are well understood will we know for sure whether backward time travel is possible.
Stephen, however, was so convinced that the ultimate answer will be no time machines, that he codified this in what he calls his “chronology protection conjecture”: The laws of physics will always prevent backward time travel, thereby “keeping the universe safe for historians.”
Fig. 30.4. Quantum fluctuations of light, traveling along the red path, build up into a crescendo explosion at the moment the wormhole is becoming a time machine.
Many researchers have struggled, over the past twenty years, to prove or disprove Hawking’s chronology protection conjecture. The bottom line today, I think, remains the same as in the early 1990s, when he and I were debating the issue: Only the laws of quantum gravity know for sure.
Time Travel with a Bulk
All this research and conclusions—educated guesses—are based on the laws of physics that prevail if there is no bulk with a large fifth dimension. What happens to time travel if a large bulk does exist, as in Interstellar?
We physicists find Einstein’s relativistic laws so compelling that we suspect they hold in the bulk as well as in our brane. So Lisa Randall, Raman Sundrum, and others have extended his laws into the five-dimensional bulk by one simple step: adding a new dimension to space. That extension proceeds mathematically in a straightforward and beautiful manner, which makes us physicists think we may be on the right track. In my interpretation of the movie, Professor Brand uses this extension as a foundation for his equation and for his struggle to understand gravitational anomalies (Chapter 25).
If this speculative extension is correct, then time behaves fundamentally the same in the bulk as in our brane. In particular, objects and signals in the bulk, like those in our brane, can only move in one direction through locally measured time (local bulk time): toward the future. They cannot move backward, locally. If backward time travel is possible in the bulk, it can be achieved only by journeying out through the bulk’s space and returning before the journey started while always moving forward in local bulk time. This is a bulk analog of the round trip in Figure 30.3.
Messaging Murph: My Physicist’s Interpretation
This description of time underlies my physicist’s interpretation of Cooper’s messaging Murph.
Recall that the tesseract is an object whose faces have three space dimensions and interior has four. The interior is part of the bulk. Everything we see in the movie’s tesseract scenes lies in the faces: Cooper, Murph, Murph’s bedroom, the bedroom’s extrusions, the world tubes of the boo
k and watch—all lie in tesseract faces. We never see the tesseract’s bulk interior. We can’t see it, since light can’t travel through four space dimensions, only three. However, gravity can do so.
In my interpretation, when Cooper sees a book in Murph’s bedroom, he does so via a light ray that travels in faces of the tesseract (for example, the red dashed ray in Figure 30.5). And when he pushes on a book’s world tube, or on the world tube of the watch’s second hand, he generates a gravitational signal (a gravitational wave in the bulk) that spirals into and through the tesseract’s bulk interior, along the violet curve in Figure 30.5. The signal travels forward in local, bulk time, but backward in bedroom time, arriving before it started out.57 It is this gravitational signal that pushes the book out of the bookcase and twitches the watch’s second hand.
Fig. 30.5. A Cooper icon sees a book via the red dashed light ray and exerts a force on the book via a gravitational signal that spirals along the violet curve. I’ve suppressed one of our brane’s spatial dimensions.
This is rather like one of my favorite Escher drawings, Waterfall (Figure 30.6). Downward in the drawing is analogous to the forward flow of bedroom time, and the flowing water is analogous to the forward flow of local time. A leaf on the water is carried forward with the water just like signals in the bulk are carried forward in local time.
Fig. 30.6. Waterfall. [Drawing by M. C. Escher.]
When carried by water down the waterfall, the leaf is like the light ray from the book to Cooper: It travels not only forward in local time but also downward (forward in bedroom time). When carried along the aqueduct, the leaf is like the gravitational signal from Cooper to the book: it travels forward in local time but upward58 (so backward in bedroom time).
