The Science of Interstellar

^{Fig. 22.4. A bulk being, passing through our brane, bends and swirls our view of a paint-swatch wall.}

And if the bulk being is spinning, it might drag space into a whirling motion that I can feel and see, as in the bottom of Figure 22.4.

Interstellar’s Bulk Beings

All the characters in Interstellar are convinced that bulk beings exist, though they use that name only rarely. Usually, the characters call the bulk beings “They.” A reverential They. Early in the movie, Amelia Brand says to Cooper, “And whoever They are, They appear to be looking out for us. That wormhole lets us travel to other stars. It came along right as we needed it.”

One of Christopher Nolan’s clever and intriguing ideas is to imagine that They are actually our descendants: humans who, in the far future, evolve to acquire an additional space dimension and live in the bulk. Late in the movie, Cooper says to TARS, “Don’t you get it yet, TARS? They aren’t beings. They’re us, trying to help, just like I tried to help Murph.” TARS responds, “People didn’t build this tesseract” (in which Cooper is riding; Chapter 29). “Not yet,” Cooper says, “but one day. Not you and me but people, people who’ve evolved beyond the four dimensions we know.”

Cooper, Brand, and the crew of the Endurance never actually feel or see our bulk descendants’ gravity or their space warps and whirls. That, if it ever occurs, is left for a sequel to Interstellar. But older Cooper himself, riding through the bulk in the closing tesseract of Chapter 30, reaches out to the Endurance’s crew and his younger self, reaches out through the bulk, reaches out gravitationally. Brand feels and sees his presence, and thinks he is They.

23 Confining Gravity

The Trouble with Gravity in Five Dimensions

If the bulk does exist, then its space must be warped. If it were not warped, then gravity would obey an inverse cube law instead of inverse square, our Sun could not hang onto its planets, and the solar system would fly apart.

OK. I’ll slow down and explain this more carefully.

Recall (Chapter 2) that the Sun’s gravitational force lines, like those of the Earth and any other spherical body, point radially toward its center and pull objects along themselves toward the Sun (Figure 23.1). The strength of the Sun’s gravitational pull is proportional to the density of the force lines (the number of lines passing through a fixed area). And since the transverse areas (spheres) through which the lines pass have two dimensions, the lines’ density goes down with increasing radius r as 1/r², and so does gravity’s strength. This is Newton’s inverse square law for gravity.

^{Fig. 23.1. The gravitational force lines around the Sun.}

String theory insists that gravity in the bulk is also described by force lines. If space in the bulk is not warped, then the Sun’s gravitational force lines will spread radially outward into the bulk (Figure 23.2). Because of the bulk’s extra dimension (just one in Interstellar), there are three transverse dimensions into which gravity can spread instead of just two. Therefore, if the bulk exists and is not warped, then the density of force lines and thence gravity’s strength should decrease as 1/r² when we move away from the Sun, rather than as 1/r³. The sun’s pull on the Earth would be two hundred times weaker, and on Saturn 2000 times weaker. With gravity weakening so rapidly, the Sun couldn’t hold onto its planets; they would fly away into interstellar space.

^{Fig. 23.2. Gravitational force lines spread radially into the bulk, if the bulk is not warped. The dotted circles are solely to guide your eyes. [Patterned on a figure in Lisa Randall’s Warped Passages (Randall 2006).]}

But they don’t fly away. And their measured motions reveal unequivocally that the Sun’s gravity weakens as the inverse square of the distance. The conclusion is inescapable: if there is a bulk, it must be warped in some manner that prevents gravity from spreading into the fifth dimension, the out-back dimension.

Is Out-Back Curled Up?

If the bulk’s out-back dimension were curled up into a tight roll, then gravity could not spread far into the bulk, and the inverse square law would be restored.