The Science of Interstellar

In 1985, we physicists thought the cores of all black holes were inhabited by chaotic, destructive BKL singularities, and everything that entered a black hole would be destroyed by the singularity’s stretch and squeeze (Chapter 26). That was our highly educated guess. We were wrong.

In the intervening quarter century, two additional singularities were discovered, mathematically, inside black holes: gentle singularities, to the extent that any singularity can be gentle (Chapter 26). Gentle enough that Cooper, falling into one, might possibly survive. I’m dubious of survival, but we can’t be sure. So I now think it respectable, in science fiction, to posit survival.

Also in the intervening quarter century, we have learned that our universe is probably a brane in a higher-dimensional bulk (Chapter 21). So it’s respectable, I think, to posit living beings that inhabit the bulk—a very advanced civilization of bulk beings—who might save Cooper from the singularity at the last moment. That’s what Christopher Nolan chose.

Through the Event Horizon

In Interstellar, when Ranger 2 piloted by Cooper (and lander 1, piloted by TARS) eject from the Endurance, they spiral down toward Gargantua’s event horizon and then through it. What do Einstein’s relativistic laws say about this downward spiral?

According to those laws, and hence my interpretation of the movie, Brand, watching from the Endurance, can never see the Ranger penetrate the horizon. No signal Cooper tries to send her from inside the horizon can ever get out. The flow of time inside the horizon is downward, and that downward time flow drags Cooper and all signals he sends downward with itself, away from the horizon. See Chapter 5.

So what does Brand see (if she and Case can stabilize the Endurance long enough for her to watch)? Because the Endurance and the Ranger are both deep in the cylindrical part of Gargantua’s warped space (Figure 28.1), they are both dragged circumferentially by Gargantua’s whirling space with almost the same angular velocity (the same orbital period). So as seen by Brand, in her orbiting reference frame, the Ranger drops away from the Endurance almost straight downward toward the horizon (Figure 28.1). That’s what the movie depicts.

^{Fig. 28.1. The Ranger’s trajectory through Gargantua’s warped space, as seen in the Endurance’s orbiting reference frame. The Endurance is drawn far larger than it should be, so you can see it. Inset: A larger portion of Gargantua’s warped space. [Image of the Endurance is from Interstellar.]}

As Brand watches the Ranger approach the horizon, she must see time on the Ranger slow and then freeze relative to her time, Einstein’s laws say. This has several consequences: She sees the Ranger slow its downward motion and then freeze just above the horizon. She sees light from the Ranger shift to longer and longer wavelengths (lower and lower frequencies, becoming redder and redder), until the Ranger turns completely black and unobservable. And bits of information that Cooper transmits to Brand one second apart as measured by his time on the Ranger arrive with larger and larger time separations as measured by Brand. After a few hours Brand receives the last bit that she will ever receive from Cooper, the last bit that Cooper emitted before piercing the horizon.

Cooper, by contrast, continues receiving signals from Brand even after he crosses the horizon. Brand’s signals have no trouble entering Gargantua and reaching Cooper. Cooper’s signals can’t get out to Brand. Einstein’s laws are unequivocal. This is how it must be.

Moreover, those laws tell us that Cooper sees nothing special as he crosses the horizon. He can’t know, at least not with any ease, which bit that he transmits is the last one Brand will receive. He can’t tell, by looking around himself, precisely where the horizon is. The horizon is no more distinguishable to him than the Earth’s equator is to you as you cross it in a ship.

These seemingly contradictory observations by Brand and Cooper are a result of two things: The warping of time, and the finite travel time for the light and information that they send to each other. When I think carefully about both of these things, I don’t see any contradiction at all.

Sandwiched Between Singularities

As the Ranger carries Cooper deeper and deeper into the bowels of Gargantua, he continues to see the universe above himself. Chasing the light that brings him that image is an infalling singularity. The singularity is weak at first, but it grows stronger rapidly, as more and more stuff falls into Gargantua and piles up in a thin sheet (Chapter 27). Einstein’s laws dictate this.