by Thorne, Kip
Fig. 26.2. A 40-kilogram mirror being prepared for installation in LIGO. Its location fluctuates, quantum mechanically, very, very slightly: one ten-billionth the diameter of an atom.
Because objects of human size and larger have only minuscule quantum fluctuations, physicists almost always ignore those fluctuations. Discarding the fluctuations, in our mathematics, simplifies the laws of physics.
If we begin with the ordinary quantum laws that ignore gravity and then discard the fluctuations, we obtain the Newtonian laws of physics—the laws used for the past few centuries to describe planets, stars, bridges, and marbles. See Chapter 3.
If we begin with the ill-understood laws of quantum gravity and then discard the fluctuations, we must obtain Einstein’s well-understood relativistic laws of physics. The fluctuations we discard are, for example, a froth of fluctuating, exquisitely tiny wormholes (“quantum foam” that pervades all of space; Figure 26.3 and Chapter 14).46 With the fluctuations gone, Einstein’s laws describe the precise warping of space and time around black holes, and the precise slowing of time on Earth.
This is all the preamble to a punch line: If Professor Brand could discover the quantum gravity laws for the bulk as well as our brane, then by discarding those laws’ fluctuations, he could deduce the precise form of his equation (Chapter 25). And that precise form would tell him the origin of the gravitational anomalies and how to control the anomalies—how to employ them (he hopes) to lift colonies off Earth.
Fig. 26.3. Quantum foam. There is some probability (say, 0.4) that the foam will have the upper left shape, another probability (say, 0.5) for the upper right shape, and another (say, 0.1) for the lower shape. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]
In my extrapolation of the movie, the Professor knows this. And he also knows a place where the quantum gravity laws can be learned: inside singularities.
Singularities: The Domain of Quantum Gravity
The beginning of a singularity is a place where the warping of space and time grows without bound. Where space warps and time warps become infinitely strong.
If we think of our universe’s warped space as like the undulating surface of the ocean, then the beginning of a singularity is like the tip of a wave that is about to break, and the interior of the singularity is like the froth after it breaks (Figure 26.4). The smooth wave, before it breaks, is governed by smooth laws of physics, analogs of Einstein’s relativistic laws. The froth after it breaks requires laws capable of dealing with frothing water, analogs of the laws of quantum gravity with their quantum foam.
Fig. 26.4. A singularity at the tip of an ocean wave that is about to break.
Singularities inhabit the cores of black holes. Einstein’s relativistic laws predict them unequivocally, even though those laws can’t tell us what happens inside the singularities. For that, we need the quantum gravity laws.
In 1962 I moved from Caltech (my undergraduate school) to Princeton University, to study for a PhD in physics. I chose Princeton because John Wheeler taught there. Wheeler was that era’s most creative genius, when it comes to Einstein’s relativistic laws. I wanted to learn from him.
One September day, with trepidation I knocked on the door of Professor Wheeler’s office. It would be my first meeting with the great man. He greeted me with a warm smile, ushered me in, and immediately—as though I were an esteemed colleague, not a total novice—began discussing the mysteries of the implosions of stars. Implosions that produce black holes with singularities in their cores. These singularities, he asserted, “are a place in which the fiery marriage of Einstein’s relativistic laws with the quantum laws is consummated.” The fruits of that marriage, the laws of quantum gravity, come into full blossom in singularities, Wheeler asserted. If we could understand singularities, we would learn the laws of quantum gravity. Singularities are a rosetta stone for deciphering quantum gravity.
Fig. 26.5. John Wheeler in 1971, lecturing about singularities, black holes, and the universe.
From that private lecture, I emerged a convert. From Wheeler’s public lectures and writings, many other physicists emerged as converts and embarked on a quest to understand singularities and their quantum gravity laws. That quest continues today. That quest produced superstring theory, which in turn led to a belief that our universe must be a brane residing in a higher dimensional bulk (Chapter 21).
Naked Singularities?
It would be fabulous if we could find or make a singularity outside a black hole. A singularity not hidden beneath a black hole’s event horizon. A naked singularity. Then in Interstellar the Professor’s task could be easy. He might extract the crucial quantum data from a naked singularity in his NASA lab.
In 1991, John Preskill and I made a bet about naked singularities with our friend Stephen Hawking. Preskill, a Caltech professor, is one of the world’s great experts on quantum information. Stephen is the “wheelchair guy” who appears on Star Trek, The Simpsons, and The Big Bang Theory. He also happens to be one of the greatest geniuses of our era. John and I bet the laws of physics permit naked singularities. Stephen bet they are forbidden (Figure 26.6).
None of us thought the bet would be resolved quickly, but it was. Just five years later Matthew Choptuik, a postdoctoral student at the University of Texas, carried out a simulation on a supercomputer that he hoped would reveal new, unexpected features of the laws of physics; and he hit the jackpot. What he simulated was the implosion of a gravitational wave.47 When the imploding wave was weak, it imploded and then disbursed. When it was strong, the wave imploded and formed a black hole. When its strength was very precisely “tuned” to an intermediate strength, the wave created a sort of boiling in the shapes of space and time. The boiling produced outgoing gravitational waves with shorter and shorter wavelengths. It also left behind, at the end, an infinitesimally tiny naked singularity (Figure 26.7).
Fig. 26.6. Our bet about naked singularities.
Fig. 26.7. Left: Matthew Choptuik. Middle: An imploding gravitational wave. Right: The boiling produced by the wave, and the naked singularity at the center of the magnifying glass.
Now, such a singularity can never occur in nature. The required tuning is not a natural thing. But an exceedingly advanced civilization could produce such a singularity artificially by precisely tuning a wave’s implosion, and then could try to extract the laws of quantum gravity from the singularity’s behavior.
Upon seeing Choptuik’s simulation, Stephen conceded our bet—“on a technicality,” he said (bottom of Figure 26.6). He thought precise tuning unfair. He wanted to know whether naked singularities can occur naturally, so we renewed our bet with a new wording that the singularity must arise without any need for precise tuning. Nevertheless, Stephen’s concession, in a very public venue (Figure 26.8) was a big deal. It made the front page of the New York Times.
Fig. 26.8. Hawking conceding to Preskill and Thorne at a 1997 Caltech lecture by Hawking.
Despite our renewed bet, I doubt that naked singularities do exist in our universe. In Interstellar, Dr. Mann firmly asserts that “the laws of nature prohibit a naked singularity,” and Professor Brand never even mentions that possibility. Instead, the Professor focuses on singularities inside black holes. Those, he thinks, are the only hope for learning the laws of quantum gravity.
The BKL Singularity Inside a Black Hole
In Wheeler’s era (the 1960s), we thought of a singularity inside a black hole as like a sharp point. A point that squeezes matter until the matter becomes infinitely dense and is destroyed. That’s how, until now in this book, I have depicted a black hole’s singularity (Figure 26.9, for example).
Since Wheeler’s era, mathematical calculations with Einstein’s laws have taught us that these pointy singularities are unstable. To create th
em inside a black hole requires precise tuning. When perturbed ever so slightly, for example by something falling in, they change enormously. Change into what?
Three Russian physicists—Vladimir Belinsky, Isaac Khalatnikov, and Eugene Lifshitz—used long, complicated calculations to guess the answer, in 1971. And in the 2000s, when computer simulations became sufficiently advanced, their guess was confirmed by David Garfinkle at Oakland University. The resulting, stable singularities now carry the name BKL in honor of Belinsky, Khalatnikov, and Lifshitz.
Fig. 26.9. Lia Halloran’s fanciful drawing of several black holes with singularities at their pointy tips. [A segment out of Fig. 4.5.]
A BKL singularity is chaotic. Highly chaotic. And lethal. Highly lethal.
In Figure 26.10, I depict the warping of space outside and inside a fast-spinning black hole. The BKL singularity is at the bottom. If you fall into this black hole, its interior at first is smooth and perhaps pleasant. But as you near the singularity, the space around you begins to stretch and squeeze in a chaotic pattern. And tidal forces begin to stretch and squeeze you, chaotically. The stretch and squeeze are gentle at first, but quickly they become strong, then ultrastrong. Your flesh and bones are pummeled and give way. Then the atoms of which your body was made are pummeled and give way—distorted beyond recognition.
Fig. 26.10. The warped space of a fast-spinning black hole such as Gargantua, with the BKL singularity at the bottom. The chaotic stretch and squeeze near the singularity are depicted heuristically, not precisely.
All this and its chaotic pattern are described by Einstein’s relativistic laws. It is this that the Russians, B, K, and L, predicted. What they could not predict, what nobody can predict today, is the fate of your atoms and subatomic particles when the chaotic pummeling grows to an infinite crescendo. Only the laws of quantum gravity know their fate. But you, yourself, are long since dead, with no possibility to retrieve the quantum data and escape.
I labeled this section for educated guess, because we are not absolutely certain that the singularity inside a black hole’s core is a BKL one. BKL singularities are surely allowed by Einstein’s relativistic laws. Garfinkle confirmed it by computer simulations. But more sophisticated simulations are needed to confirm that the BKL patterns of humongous stretch and squeeze do actually occur in the core of a black hole. I’m almost sure the result of those simulations will be “yes, they do occur.” But I’m not completely certain.
A Black Hole’s Infalling and Outflying Singularities
My physicist colleagues and I were pretty sure in the 1980s, as an educated guess, that there is just one singularity inside a black hole, and it’s a BKL singularity. We were wrong.
In 1991 Eric Poisson and Werner Israel at the University of Alberta, Canada, working with the mathematics of Einstein’s laws, discovered a second singularity. This one grows with time as the black hole ages. It’s caused by extreme slowing of time inside the black hole.
If you fall into a spinning black hole such as Gargantua, lots of other stuff inevitably will fall in after you: gas, dust, light, gravitational waves, and so forth. This stuff may take millions or billions of years to enter the hole as seen by me, watching from outside. But as seen by you, now inside the hole, it may take only a few seconds or less, due to the extreme slowing of your time compared with mine. As a result, as seen by you this stuff all piles up in a thin sheet, falling inward toward you at the speed of light, or nearly the speed of light. This sheet generates intense tidal forces that distort space and will distort you, if the sheet hits you.
The tidal forces grow to become infinite. The result is an “infalling singularity” (Figure 26.11),48 governed by the laws of quantum gravity. However, the tidal forces grow so swiftly (Poisson and Israel deduced) that, if they hit you, they will have deformed you by only a finite amount at the moment you reach the singularity. This is explained in Figure 26.12, which plots your net stretch along the up-down direction and squeeze along the north-south and east-west directions, as time passes. When you hit the singularity, your net stretch and squeeze are finite, but the rates at which you are being stretched and squeezed (the slopes of the black curves) are infinite. Those infinite rates are the infinite tidal forces, signaling the singularity.
Fig. 26.11. The infalling singularity, created by stuff that falls into the black hole after you. The stuff is epitomized by alternating layers of black, red, gray, and orange.
Fig. 26.12. Your net stretch and squeeze, as time passes, when the infalling singularity descends on you.
Because your body has been stretched and squeezed by only a finite net amount, when you reach the singularity, it is conceivable you might survive. (Conceivable but unlikely, I think.) In this sense, the infalling singularity is far more “gentle” than the BKL singularity. If you do survive, what happens next is known only to the laws of quantum gravity.
In the 1990s and 2000s, we physicists thought this was the whole story: A BKL singularity, created when the black hole is born. And an infalling singularity that grows afterward. That’s all.
Then in late 2012, while Christopher Nolan was negotiating to rewrite and direct Interstellar, a third singularity was discovered by Donald Marolf (University of California at Santa Barbara) and Amos Ori (The Technion, in Haifa, Israel). It was discovered, of course, via an in-depth study of Einstein’s relativistic laws and not via astronomical observations.
In retrospect, this singularity should have been obvious. It is an outflying singularity that grows as the black hole ages, just like the infalling singularity grows. It is produced by stuff (gas, dust, light, gravitational waves, etc.) that fell into the black hole before you fell in; Figure 26.13. A tiny fraction of that stuff is scattered back upward toward you, scattered by the hole’s warpage of space and of time, much like sunlight scattered off a curved, smooth ocean wave, which brings us an image of the wave.
Fig. 26.13. The outflying singularity, created by back-scattered stuff that fell into the black hole before you; and the infalling singularity, created by stuff that falls in after you. You are sandwiched between them. Shown dimmed out is the exterior of the black hole and the BKL singularity, with which you can no longer have contact because they are beyond the singularities that sandwich you.
The upscattered stuff gets compressed, by the black hole’s extreme slowing of time, into a thin layer rather like a sonic boom (a “shock front”). The stuff’s gravity produces tidal forces that grow infinitely strong and thence become an outflying singularity. But as for the infalling singularity, so also for this outflying one, the tidal forces are gentle: They grow so quickly, so suddenly, that, if you encounter one, your net distortion is finite, not infinite, at the moment you hit the singularity.
In Interstellar, Romilly tells Cooper about these gentle singularities: “I have a suggestion for your return journey [from Mann’s planet]. Have one last crack at the black hole. Gargantua’s an older, spinning black hole. [It has] what we call a gentle singularity.” “Gentle?” Cooper asks. “They’re hardly gentle, but their tidal gravity is quick enough that something crossing the horizon fast might survive.” Cooper, lured by this conversation and the quest for quantum data, later plunges into Gargantua (Chapter 28). It’s a brave plunge. He can’t know in advance whether he’ll survive. Only the laws of quantum gravity know for sure. Or the bulk beings . . .
We’ve now laid the extreme-physics foundations for Interstellar’s climactic scenes, so let’s turn to the climax.
* * *
45 More precisely, the locations of the mirrors’ centers of mass.
46 In 1955, John Wheeler pointed out the likely existence of quantum foam, with wormhole sizes 10-35 meters: 10 trillion trillion times smaller than an atom; the so-called Planck length.
47 The thing he simulated was actually something called a scalar wave, but that is an irrelevant
technicality. A few years later Andrew Abrahams and Chuck Evans at the University of North Carolina repeated Choptuik’s simulations using a gravitational wave and got the same result: a naked singularity.
48 Israel and Poisson gave this singularity the name mass inflation singularity, and that is the name that physicists have used ever since. I prefer infalling singularity and use that name in this book.
VII
CLIMAX
27
The Volcano’s Rim
Late in Interstellar, Cooper has just dragged the Endurance out of its death spiral at Mann’s planet and feels a great sense of relief when the robot Case says to him: “We’re heading into Gargantua’s pull.”
Cooper makes a quick decision: “The navigation mainframe’s destroyed and we don’t have enough life support to make it back to Earth. But we might scrape to Edmunds’ planet.” “What about fuel?” Amelia Brand asks. “Not enough,” Cooper responds. “Let Gargantua suck us right to [near] the horizon, then a powered slingshot around to launch us at Edmunds’ planet.” “Manually?” “That’s what I’m here for. I’ll take us just inside the critical orbit.”
