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.
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).
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 pulclass="underline" 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.
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.
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Why leftward? So the tube is always at the same transverse position at any specific moment of bedroom time. Think about it.