This buckling, if not counteracted, will make the confining branes collide with our brane—with our universe (Figure 25.6).[43] Our universe will be destroyed!
Obviously, our universe has not been destroyed, the Professor observes in my extrapolation. So something must prevent the confining branes from buckling. The only thing he can think of to do the job is bulk fields. Whenever a confining brane starts to bend, bulk fields must somehow exert a force on it, pushing it back into its proper, straight shape.
The Professor’s Equation, at Last!
The laws of physics are expressed in the language of mathematics. Before Cooper met Professor Brand (in my extrapolation of the movie’s story), the Professor tried to build a mathematical description of the bulk fields and how they might generate anomalies, control our universe’s gravitational constant G, hold the wormhole open, and protect our brane from collisions.
In creating this mathematics, the Professor was guided by the trove of observational data his team was collecting (Chapter 24), and by Einstein’s relativistic laws of physics in five dimensions.
The Professor embodied all his insights in a single equation, THE equation, which he wrote on one of the sixteen blackboards in his office (Figure 25.7).[44] Cooper sees the equation on his first visit to NASA, and the equation is still there thirty years later, when Murph has grown up to become a brilliant physicist in her own right, and is helping the Professor try to solve it.
This equation is called an “Action.” There is a well-known (to physicists) mathematical procedure to begin with such an Action, and from it deduce all the nonquantum physical laws. The Professor’s equation, in effect, is the mother of all nonquantum laws. But for it to give birth to the right laws—the laws that predict correctly how the anomalies are produced, how the wormhole is held open, how G is controlled, and how our universe is protected—the equation must have precisely the correct mathematical form. The Professor doesn’t know the correct form. He is guessing. His is an educated guess, but a guess nevertheless.
His equation contains lots of guessing: guesses for the things called “U(Q), Hij(Q2), Wij, and M(standard model fields)” on his blackboard (Figure 25.7). In effect, these are guesses for the nature of the bulk fields’ force lines, and how they influence our brane, and how fields in our brane influence them. (For more explanation see Some Technical Notes at the end of this book.)
When the Professor and his team speak of “solving his equation,” in my extrapolation they mean two things. First, figure out the right forms for all these things they are guessing: “U(Q), Hij(Q2), Wij, and M(standard model fields).” Second (following the well-known procedure), deduce, from his equation, everything he wants to know about our universe, about the anomalies, and most important, about how to control the anomalies so as to lift colonies off the Earth.
When characters in the movie speak of “solving gravity,” they mean the same thing.
In the movie, when the Professor is very old, we see him and grown-up Murph trying to solve his equation by iterations. On a blackboard, they make a list of guesses for the unknown things (guesses that I wrote on the board just before the scene was filmed; Figures 25.8 and 25.9). Then, in my extrapolation, Murph inserts each guess into a huge computer program that they’ve written. The program computes the physical laws for that guess, and those laws’ predictions for how the gravitational anomalies behave.
In my extrapolation, none of the guesses predicts anomalies that look anything like the observations. But in the movie, the Professor and Murph keep trying. They keep iterating: making a guess, computing the consequences, abandoning the guess, and going on to the next guess, one guess after another after another after another, until exhaustion sets in. Then they begin again the next day.
A bit later in the movie, when the Professor is on his deathbed, he confesses to Murph: “I lied, Murph. I lied to you.” It is a poignant scene. Murph infers that he knew something was wrong with his equation, knew from the outset. And Dr. Mann tells the Professor’s daughter as much in an equally poignant scene on Mann’s planet.
But, in fact—Murph realizes, soon after the Professor’s death—“His solution was correct. He’d had it for years. It’s half the answer.” The other half can be found inside a black hole. In a black hole’s singularity.
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Singularities and Quantum Gravity
In Interstellar Cooper and TARS seek quantum data inside Gargantua, data that could help the Professor solve his equation and lift humanity off Earth. The data, they believe, must reside inside a singularity that inhabits Gargantua’s core—a “gentle” singularity, Romilly predicts. What are the quantum data? How could they help the Professor? And what is a gentle singularity?
The Primacy of Quantum Laws
Our universe is fundamentally quantum. By this I mean that everything fluctuates randomly, at least a little bit. Everything!
When we use high-precision instruments to look at tiny things, we see big fluctuations. The location of an electron inside an atom fluctuates so rapidly and so randomly, that we can’t know where the electron is at any moment of time. The fluctuations are as big as the atom itself. That’s why the quantum laws of physics deal with probabilities for where the electron is and not with its actual location (Figure 26.1).
When we use instruments to look at big things, we also see fluctuations, if our instruments are precise enough. But the fluctuations of big things are minuscule. In the LIGO gravitational wave detectors (Chapter 16), laser beams monitor the locations of hanging mirrors that weigh 40 kilograms (90 pounds).[45] Those locations fluctuate randomly, but by amounts far less than the size of an atom: one ten-billionth of an atom’s size, in fact (Figure 26.2). Nevertheless, LIGO’s laser beams will see those fluctuations a few years from now. (LIGO’s design prevents those random fluctuations from getting in the way of measuring gravitational waves. My students and I helped make sure of this.)
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Or the buckling could make one or both branes spring outward, releasing the AdS layer and so destroying Newton’s inverse square law and making the planets all fly away from the Sun—not quite so bad for our universe, but pretty miserable for humans.
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The meanings of the various symbols in the equation are spelled out on the Professor’s other fifteen blackboards, along with other information about the equation, all of which I ghost-wrote for the movie’s filming. You can see photographs of all sixteen blackboards on this book’s page at Interstellar.withgoogle.com.