The Science of Interstellar

In my interpretation of the movie, the tesseract ascends from the singularity into the bulk. Being an object with the same number of space dimensions as the bulk (four), it happily inhabits the bulk. And it transports three-dimensional Cooper, lodged in its three-dimensional face, through the bulk.

Now, recall that the distance from Gargantua to Earth is about 10 billion light-years as measured in our brane (our universe, with its three space dimensions). However, as measured in the bulk, that distance is only about 1 AU (the distance from the Sun to the Earth); see Figure 23.7. So, traveling with whatever propulsion system the bulk beings provided, the tesseract, in my interpretation, can quickly carry Cooper across our universe, via the bulk, to Earth.

Figure 29.4 is a snapshot from that trip. One spatial dimension is suppressed from the snapshot, so the tesseract is a three-dimensional cube in a three-dimensional bulk, and Cooper has become a two-dimensional icon of a man, in a two-dimensional face of the cube, traveling parallel to our two-dimensional universe (brane).

To match what is shown in the movie, I imagine this trip is very quick, just a few minutes, while Cooper is still dazed and falling. As he comes to rest, floating in the large chamber, the tesseract docks beside Murph’s bedroom.

^{Fig. 29.4. The Cooper icon transported through the bulk, above our brane, riding in a face of the tesseract. One space dimension is removed from this picture.}

Docking: The View into Murph’s Bedroom

How does this docking work? In my interpretation, arriving in the bulk near Earth the tesseract must penetrate the 3-centimeter-thick AdS layer that encases our brane (Chapter 23) in order to reach Murph’s bedroom. Presumably the bulk beings who built the tesseract equipped it with technology to push the AdS layer to the side, clearing the way for its descent.

Figure 29.5 shows the tesseract, after the clearing, docked alongside Murph’s bedroom in Cooper’s farmhouse. Again, one spatial dimension is suppressed, so the tesseract is depicted as a three-dimensional cube and the farmhouse and bedroom and Murph are two dimensional, as, of course, is Cooper.

^{Fig. 29.5. The tesseract docked alongside Murph’s bedroom.}

The back face of the tesseract coincides with Murph’s bedroom. I’ll explain that more carefully. The back face is a three-dimensional cross section of the tesseract that resides in Murph’s bedroom in the same sense as the circular cross section of a sphere resides in a two-dimensional brane in Figure 22.2, and a spherical cross section of a hypersphere resides in a three-dimensional brane in Figure 22.3. So everything in Murph’s bedroom, including Murph herself, is also inside the tesseract’s back face.

When a light ray traveling out from Murph reaches the common edge of Murph’s bedroom and the tesseract, it has two places to go: The ray can stay in our brane, traveling along route 1 of Figure 29.5 out an open door or into a wall where it is absorbed. Or the ray can stay in the tesseract, traveling along route 2 into and through the next tesseract face, and then onward to Cooper’s eyes. Some of the ray’s photons go along route 1; others go along route 2, bringing Cooper an image of Murph.

Now look at Figure 29.6, in which I restore the suppressed dimension. When Cooper looks through the right wall of his chamber, he sees into Murph’s bedroom through its right wall (right white light ray). Looking through the left wall of his chamber, Cooper sees into Murph’s bedroom through its left wall (left white light ray). Looking through his back wall, he sees into the bedroom through its back wall. Looking through his front wall (orange light ray), he sees into the bedroom through its front wall (though this is not obvious in Figure 29.6; can you explain why it is true?). Looking along the yellow ray, he sees down through her ceiling. Looking along the red ray, he sees up through her floor. To Cooper, as he changes his gaze from one direction to another to another, it seems like he is orbiting Murph’s bedroom. (This is how Chris described it when he first showed me his complexified tesseract.)

^{Fig. 29.6. The Cooper icon can see into Murph’s bedroom (orange edges) by looking through each of the six walls of his face of the tesseract (purple edges). Here he sees an icon of Murph herself.}