The Science of Interstellar

^{Fig. 29.9. The size of Cooper’s chamber enlarged threefold so the six bedrooms occupy the centers of his chamber’s faces. [My own hand sketch.]}

The next thing I noticed were two extrusions extending out of each bedroom along the two directions transverse to Cooper’s chamber (Figures 29.10 and 29.11). As Chris and Paul explained it to me, wherever these extrusions intersect there is a bedroom; for example, bedrooms 7, 8, and 9 as well as the original 1–6.

^{Fig. 29.10. Extrusions extend out of all the bedrooms, and time flows along them. [My own hand sketch.]}

The extrusions extend indefinitely, creating at their intersections a seemingly infinite lattice of bedrooms and of chambers[55] like Cooper’s [dashed edges in Fig. 29.10.]. For example, the labeled faces of bedrooms 7, 8, and 9 face into a chamber whose edges are indicated with dots; the back-left-bottom corner of that chamber overlaps the front-right-top corner of Cooper’s chamber.

TARS gives us a clue to the meaning of the extrusions and the latticework of bedrooms and chambers when he tells Cooper, “You’ve seen that time is represented here as a physical dimension.”

Chris and Paul elaborated on that clue for me. The bulk beings, they explained, are displaying time for the blue extrusions as flowing along the blue-arrowed direction in Figure 29.10, and for the green extrusions along the green-arrowed direction, and for the brown extrusions along the brown-arrowed direction.

^{Fig. 29.11. The lattice of extrusions, drawn by Christopher Nolan in his working notebook when developing the concepts for the complexified tesseract.}

To understand this in greater detail, let’s focus momentarily on the single pair of extrusions that intersect in bedroom 2; see Figure 29.12. Cross sections through the room that are vertical in the picture travel rightward with passing time, along the blue time arrow; and as they travel, they create the blue extrusion. Similarly, cross sections that are horizontal travel upward as time passes, along the green time arrow, creating the green extrusion. Where the two sets of cross sections intersect—where the extrusions intersect—there is a bedroom.

^{Fig. 29.12. Cross sections of Murph’s bedroom travel along two extrusions. Bedroom 2 resides where the two sets of cross sections intersect. [My own hand sketch.]}

The same is true for all other extrusions. At each intersection of two extrusions, the cross sections they carry produce a bedroom.

Because of the cross sections’ finite speed, the various bedrooms are out of time synch with each other. For example, if it takes one second for cross sections to travel along each extrusion from one bedroom to the next, then all the bedrooms in Figure 29.13 are to the future of image 0 by the number of seconds shown in black. In particular, bedroom 2 is one second ahead of bedroom 0, bedroom 9 is two seconds ahead of bedroom 0, and bedroom 8 is four seconds ahead of bedroom 0. Can you explain why?

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.]}

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.

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Chris and Paul call these chambers “voids” because they are regions through which no extrusions pass.