The Science of Interstellar

Christopher Nolan wanted the wormhole to have a mild gravitational pull. Strong enough to hold the Endurance in orbit around itself, but weak enough that a modest rocket blast would slow the Endurance, letting it drop gently into the wormhole. This meant a gravitational pull much less than the Earth’s.

Einstein’s law of time warps tells us that the slowing of time inside the wormhole is proportional to the strength of the wormhole’s gravitational pull. With that pull weaker than the Earth’s pull, the slowing of time must be smaller than on Earth, which is only a part in a billion (that is, one second of slowing during a billion seconds of time, thirty years). Such slowing is so tiny that Oliver and I paid no attention to it at all when designing the wormhole.

“Handles” for Adjusting the Wormhole’s Shape

The ultimate decision about the wormhole’s shape was in the hands of Christopher Nolan (the director) and Paul Franklin (the visual-effects supervisor). My task was to give Oliver and his colleagues at Double Negative “handles” (or in technical language, “parameters”) that they could use to adjust the shape. They then simulated the wormhole’s appearance for various adjustments of the handles and showed the simulations to Chris and Paul, who chose the one that was most compelling.

I gave the wormhole’s shape three handles—three ways to adjust the shape (Figure 15.1).

^{Fig. 15.1. A wormhole viewed from the bulk and my three handles for adjusting its shape. (The inset on the left is the same wormhole, viewed from farther away in the bulk so we see its outer parts.)}

The first handle is the wormhole’s radius as measured by an ultra-advanced engineer looking in from the bulk (analog of Gargantua’s radius). If we multiply that radius by 2π = 6.28318…, we get the wormhole’s circumference as measured by Cooper when he pilots the Endurance around or through it. Chris chose the radius before I began to work. He wanted the wormhole’s gravitational lensing of stars to be barely visible from Earth with the best large-telescope technology then available to NASA. That fixed the radius at about a kilometer.

The second handle is the wormhole’s length, as measured equally well by Cooper or by an engineer in the bulk.

The third handle determines how strongly the wormhole lenses the light from objects behind it. The details of the lensing are fixed by the shape of space near the wormhole’s mouths. I chose that shape similar to the shape of space outside the horizon of a nonspinning black hole. My chosen shape has just one adjustable handle: the width of the region that produces strong lensing. I call this the lensing width[29] and depict it in Figure 15.1.

How the Handles Influence the Wormhole’s Appearance

Just as I had done for Gargantua (Chapter 8), I used Einstein’s relativistic laws to deduce equations for the paths of light rays around and through the wormhole, and I worked out a procedure for manipulating my equations to compute the wormhole’s gravitational lensing and thence what a camera sees when it orbits the wormhole or travels through it. After checking that my equations and procedure produced the kinds of images I expected, I sent them to Oliver and he wrote computer code capable of creating the quality IMAX images needed for the movie. Eugénie von Tunzelmann added background star fields and images of astronomical objects for the wormhole to lens, and then she, Oliver, and Paul began exploring the influence of my handles. Independently, I did my own explorations.

Eugénie kindly provided the pictures in Figures 15.2 and 15.4 for this book, in which we look at Saturn through the wormhole. (The resolutions of her pictures are far higher than my own crude computer code can produce.)

The Wormhole’s Length

We first explored the influence of the wormhole’s length, with modest lensing (small lensing width); see Figure 15.2.

When the wormhole is short (top picture), the camera sees one distorted image of Saturn through the wormhole, the primary image, filling the right half of the wormhole’s crystal-ball-like mouth. There is an extremely thin secondary, lenticular image on the left edge of the crystal ball. (The lenticular structure at the lower right is not Saturn; it is a distorted part of the external universe.)