The Human Condition:

My Problems with Interstellar - November 30, 2014

Black Hole

I finally broke down and saw the movie Interstellar in a theater last week, rather than waiting for it to come out on disk, as I do with most movies these days. There are many fine things in this film. It has good characters, good actors, an interesting picture of love arcing across the years, and a superficially satisfying ending. But I have a few nits to pick with the actual science and, at the end, a plot hole you can drive a starship through. (Spoiler alert at this point! However, I’m assuming most of the people who care have already seen the film.)

First, the science. In a distant galaxy reached through a mysterious wormhole,1 the crew of the starship Endurance is tasked with visiting at least three planets which are candidates for a new Earth. The first planet they go to is orbiting “the rim” of a black hole. As one of the characters aboard the starship mentions in passing, this is some kind of special black hole—tame? tired? incompetent? incomplete?—I didn’t catch exactly how it was special.2 The plot point is that if they land on this planet, their experience of time will be slowed, so that one hour on the surface will equal seven years for anyone back on board the starship or on Earth. So they will have to move quickly and get out of there fast. The way they protect the starship from this time dilation is by not going into orbit around the planet itself but instead staying in an orbit around the black hole just beyond the planet’s orbit but somehow keeping pace with the planet so that travel down to its surface is still covers a manageable distance.3

My major science nit is that black holes and their environment are not magical time dilators, as the film appears to suggest. Small black holes can have fierce tidal effects that tear you apart, and large ones can draw you into an orbital acceleration that tends to break up matter into an accretion disk full of plasma and particles. But the only way to have your personal time slowed so significantly, compared with “normal time” for the rest of us, is either to increase your speed dramatically or to visit an area with high gravitational acceleration. This is because the calculations of general relativity make no distinction between mass acquired through inertia (going fast) and that conferred by the acceleration of gravity (getting heavy). At near lightspeed or deep inside a gravity well, a person’s time slows markedly, as in the film, so that hours spent at speed or being heavy become years for someone not so accelerated. And at the speed of light itself, the traveler’s or mass-gainer’s time stops completely, relative to outside observers.4

Inside a deep gravitational field, a person’s time also slows dramatically, such as this one hour for seven years exchange. But how strong does that gravity acceleration have to be to create a noticeable effect? The Earth’s gravity, one g, slows our clocks by about 0.02 seconds per year compared to an observer hanging around—i.e., not traveling or orbiting—out in interstellar space. A clock on the surface of the Sun, at about 28 g, loses 66 seconds per year compared to clocks on Earth. So the gravitational field of a small stellar mass, such as our Sun’s, has negligible effect on a visitor’s clocks. If I vacationed on the Sun for a year—having found a solid surface on which to stand and managing not to burn up—and then came back, my relative lack of aging would hardly arouse my doctor’s suspicions. But long before that the gravity load would have flattened me, because 28 g is not physically sustainable for humans.

In Interstellar, a visitor to the first planet orbiting the film’s black hole near to, but still somewhere outside of, its event horizon is said to lose 61,362 hours—seven years’ worth of Earthly hours—for each hour spent on the surface. For comparison, you only lose 0.00753 seconds for each hour spent on the surface of our Sun. By my rough calculations—and not trying to figure out radial distances and the black hole’s Schwarzschild limit—to create a time dilation on this order of magnitude, you would need a black hole with a mass 2.93 x 1010 times the mass of our Sun.5

To orbit close to the event horizon of this monster, you would be traveling very fast, probably close to the speed of light—assuming you could accelerate fast enough to establish a stable orbit and not just spiral inward toward the event horizon. Any planet that got so close would be torn apart, rather than simply experience massive tidal waves. The planet’s crust would bulge monstrously in time to the planet’s rotation, unless its own rotation were first locked to its orbit, as our Moon’s rotation and revolution are locked. The atmosphere and the ocean would be torn away. People landing on this planet could ignore its puny gravity and would live under the gravitation of the black hole itself, which would smear them into a thin paste of plasma and particles.

But there was no hint in the film that the watery planet was orbiting the black hole at anything approaching the speed of light. If it were, the starship would need to match that speed if it was going to orbit at a comfortable traveling distance beyond the planet’s own orbit. And whether by inertial or gravitational acceleration, the astronaut left aboard the starship would have experienced roughly the same time dilation as the crew that landed on the planet. In the film, however, this lone astronaut and the people back on Earth experience 23 years of time while the crew that lands experiences only a few hours. In any case, attaining the speed needed to match that planet’s orbit around the black hole, or to break away from that orbit later, would seem to be beyond the starship’s capabilities—or else why did it take the crew two years to travel from Earth to the vicinity of Saturn, where the mysterious wormhole awaited their passage?

Second, the plot hole. Because Cooper (Matthew McConaughey) and Brand (Anne Hathaway) spend three hours on the water planet, the story in the rest of the universe is advanced by 23 years. Cooper’s daughter Murph is now a young woman (Jessica Chastain). Brand’s father (Michael Caine) has become an old man near death. Then Cooper and Brand and the aging scientist who stayed aboard the starship go on to visit a second planet, where they are not apparently affected by any time dilation. On that planet, Dr. Mann (Matt Damon) has been faking his data about the planet’s habitability, turns homicidal when his deception is about to be discovered, tries to steal their starship, and in the process disables it.6 So, to reach the third, most distant, and yet most favorable planet of all, where Brand’s long-lost love is waiting to be rescued, Cooper and the ship’s robot assistant must drive the two remaining landers and use their thrust to slingshot the wrecked starship around the black hole to begin the journey.

Because of what I believe is a misinterpretation of Newton’s Third Law about action and reaction, Cooper and the robot agree that the starship must discard the two landers and their pilots when their fuel runs out. Or maybe they’re just shedding excess weight, because they mention that as a reason, too. The misinterpretation has to do with the difference between simply dropping off the excess material and actually accelerating it away from the starship as reaction mass under Newton’s law. If discarded weight added to your boost—the misinterpretation of Newton—then NASA missions would get a useful kick when they dropped their first and second stages, or when the Shuttle dropped its solid-fuel boosters and main fuel tank—and they don’t. Cooper and the robot then fall into the black hole, while Brand proceeds to the third planet and the discovery of a livable world.

Inside the black hole, Cooper and the robot are able to experience multiple instances of time in a single place—his daughter’s bedroom, where some strange things have been happening throughout the film—and the robot is able to make observations about gravity that Cooper then communicates to Murph. The young woman has been trying to solve equations related to gravity in order to move the entire population of Earth off the planet and into space. To do this, she needs to answer some unspecified question about gravity that apparently you can only find if you’ve experienced the inside of a black hole.7

Once Cooper gives Murph the new data, he realizes that he and the robot have somehow created this whole multi-dimensional effect, the wormhole and everything else, as an expression of their own will—and this is another gray area in the story line. With this realization, the tesseract, or multidimensional cube, that they inhabit, along with every second of time passing in that bedroom, automatically begins collapsing. They are somehow ejected from the black hole, returned to their own galaxy through the wormhole, and picked up by off-planet Earthlings about 100 years into Cooper’s future. He and the robot have experienced so much time dilation that Murph is now a frail old woman (Ellen Burstyn) about to die.

But Cooper finds nothing to interest him in this new world of off-planet living inside humankind’s new O’Neill colonies.8 He commandeers a small scout ship to go back through the wormhole to find Brand on that third planet where, inexplicably, the love of her life has now died and been buried. The plot hole I find is this: if Murph has gone from her 30s to her 90s while Cooper was inside the black hole, then why wouldn’t Brand, who never entered the black hole, have similarly aged and now be an old woman? She’s shown—apparently in real time, and not just in Cooper’s imagination—at the same age as when she rode the starship away from the black hole toward the planet of her lover.

As I said, Interstellar as a film offers many fine moments, good acting, and some interesting perspectives on time and human history. But these science issues and this plot hole are serious matters for me. Any working science fiction writer who brought this manuscript to a publisher would feel slightly embarrassed, knowing that corners had been cut. Any conscientious editor would require him or her to address these problems—and fixing them would necessarily change the story in significant ways. Otherwise, the author would be left with vigorous arm-waving, insisting this is a special black hole and the new galaxy is just different. And careful, caring readers would be left sputtering, “But, but, but …” The whole project would diverge into realms of science fantasy and magic. And that’s just not satisfying in a story so strongly dependent on its use of science.

1. Okay, first minor quibble. Wormholes are accepted science fiction motifs for accomplishing faster-than-light, interstellar travel. We blink at them in movies like Stargate and in television shows like Deep Space Nine. But wormholes are mere conjecture, based on the unfounded premise that space is somehow tightly folded through alternate dimensions beyond the three—x, y, and z—that we actually perceive and experience. They are a mathematical game, not an artifact of accepted physical science. Like time travel, wormholes belong more properly to the realm of science fantasy than to serious speculative fiction.

2. From my reading to prepare for writing The Doomsday Effect, black holes are of two types: rotating and nonrotating. Other than that, the only distinguishing feature is their mass, which determines the depth of their gravity well and the size of their event horizon. At heart, the “hole” is simply an infinitesimal point, a singularity, harboring all that mass. And the event horizon is simply the distance at which the escape speed from the gravity well exceeds the speed of light. More than this, science—and all our theories—sayeth not.
       My understanding is that the spin of a rotating black hole is only important because the singularity cannot revolve around itself but instead describes a tiny circle. If you could dive through that circle—good luck with that!—you might travel outside the spreading “time cone” as described by the speed of light in normal space. (I planned something of this nature for a fragment of Kornilov’s wrist bone in a possible sequel to The Doomsday Effect.) I've never heard that the spin has any effect on surrounding space, unless it is to create gravity waves, much as from a rapidly spinning neutron star or pulsar. However, opinions on this differ: see the entry on black holes from The Physics of the Universe. But I would argue with the last paragraph to the extent that it’s not the event horizon you can never quite reach but the singularity itself. And again, all of this is conjecture supported by mathematics, not by our experience or direct observation.

3. Orbital mechanics are difficult and the first thing most theatrical depictions of science get wrong. (Remember that early Star Trek episode, where to stay in orbit a landing craft had to fire its thrusters? Unh-uh!) So here, if you want to orbit a primary like the black hole and still match speeds with another object in orbit, like the planet, you have to enter the same orbit as the object of your desire. To maintain an orbit just beyond it or further out from the primary, you must move at a different speed; you cannot “pace” the planet from a higher orbit as it goes around the black hole.

4. Which leads to a conundrum: if you ride a light wave, you experience time normally, while to observers outside your frame of reference you would appear frozen. If time actually “stops” for you, then it would follow that the universe around you experiences an infinite amount of time compared to your experience. When you finally get off the wave and return to a more manageable velocity, the universe will have expanded to a thin gas, the stars burned out, and you are left in a cold, dark, empty place. This is why travel at lightspeed is theoretically impossible. When you get where you’re going, it won’t be there anymore.

5. That’s 29,300,000,000 solar masses—a truly galactic-scale black hole! Even if my math is wrong by a couple of decimal places, we’re not dealing with a black hole formed by the collapse of any star we know about. This one eats out the hearts of entire galaxies.

6. Apparently, the starship Endurance is such a rickety contraption of modules assembled in a rotating ring that the explosive outgassing from overriding the airlock controls can blow it apart. One wonders how the IQs at NASA could have dropped so sharply since the Apollo missions. But I haven’t had so much fun with a scene since Dave Bowman crossed over to Discovery without his space helmet.

7. While it might be great fun to fall inside the event horizon of a black hole, the information you obtained would, in my opinion, be minimal. You would accelerate toward the singularity until you reached its terminal velocity. At some point you might reach the speed of light, experience time stoppage, and continue to exist in your own time frame, eating, drinking, laughing, and scratching, but not becoming aware of anything happening outside yourself. Before that happened, however, you’d probably fragment and turn into plasma and particles. In any case, you wouldn’t learn much about gravity—no matter how many spatial dimensions you invoked—and if you did learn anything, you wouldn’t be able to communicate it to the world outside the black hole. Regardless of what Stephen Hawking predicts about virtual particles appearing and annihilating each other—or not—black holes are famous for not giving up light rays, information, or their dead.

8. These are huge cylinders spinning in space to create the acceleration of artificial gravity on their inside surfaces. For stability, one usually places them at the Lagrange points in an orbital system, such as around the Moon. Creating them requires no unusual information or interpretation of gravity. You do, however, need to transport a lot of rebar, concrete, glass, hardware, potting soil, and money to some distant point in space.