The Science of Interstellar

In Figure 29.6, all six light rays have to pass through intermediate cubes (tesseract faces) before reaching Murph’s bedroom. In the movie they don’t travel any noticeable distance from chamber to bedroom, so Chris and Paul must have shrunk the tesseract in one dimension; see the gray arrow and notation “make thin” in Figure 29.6.

After that shrinkage, every face of Cooper’s chamber looks directly and immediately into one of the faces (wall or floor or ceiling) of Murph’s bedroom with no intervening space, so to Cooper the situation looks like Figure 29.7. He sees six bedrooms, one bordering each face of his chamber but all identical except for his viewing direction.[53] In fact they are all identical. There is only one bedroom, although to Cooper there appear to be six.

^{Fig. 29.7. The six views of Murph’s bedroom seen by the Cooper icon from his tesseract face. [My own hand sketch.]}

Nolan’s Complexified Tesseract

Figure 29.8 is a still, showing Cooper floating in his chamber inside the tesseract. It looks very different from Figure 29.7 because of the complex and rich modifications that Chris conceived, and Paul and his team implemented.

^{Fig. 29.8. Cooper floating in Nolan’s complexified tesseract. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]}

The first thing I noticed when I saw Chris’s complexified tesseract was the threefold enlargement of Cooper’s chamber, so the bedroom attached to each chamber face covers only a third of the face. I depict this in Figure 29.9 with all the other tesseract complexities removed and the chamber’s back three faces hidden from view.[54]

^{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.