Kip Thorne - The Science of Interstellar

Professor Brand tried to explain this as a change in the tidal forces produced by bulk fields, but had difficulty. The best explanation he could find is that the gravitational constant G increased inside the Earth, below South Africa, and decreased inside the Earth, below North America. Rock below South Africa was suddenly pulling more strongly; rock below North America was suddenly pulling more weakly! These changes must have been produced by some sort of bulk field that passes through our brane and controls G , he reasoned.

Bulk fields are not just the key to gravitational anomalies on Earth, Professor Brand believes (in my extrapolation). Bulk fields also play two other crucial roles: They hold the wormhole open, and they protect our universe from destruction.

The wormhole that connects our solar system to Gargantua’s neighborhood, if left to its own devices, will pinch off (Figure 25.5). Our connection to Gargantua will be severed. This is the unequivocal conclusion of Einstein’s relativistic laws (Chapter 14).

If there is no bulk, then the only way to hold the wormhole open is to thread it with exotic matter that repels gravitationally (Chapter 14). The dark energy that may accelerate our universe’s expansion (Chapter 24) is probably not repulsive enough. In fact, it seems likely, in 2014, that the laws of quantum physics prevent even an exceedingly advanced civilization from ever collecting enough exotic matter to hold the wormhole open. And I imagine this conclusion is even more certain in Professor Brand’s era.

But there is an alternative, the Professor realizes in my extrapolation of the movie’s story. Bulk fields may do the job. They may hold the wormhole open. And since the Professor thinks the wormhole has been constructed and placed near Saturn by bulk beings, bulk fields holding it open seem natural to him.

In order for gravity in our universe to obey Newton’s inverse square law to high accuracy, our brane must be sandwiched between two confining branes with AdS warping between them (Chapter 23). However, the confining branes are filled with pressure [42] According to Einstein’s relativistic laws the dark energy that (presumably) makes the expansion of our universe accelerate has a second effect: It produces an enormous tension in our brane, like the tension in a stretched rubber band or rubber sheet. And Einstein’s laws also dictate that, in order for spacetime outside the AdS sandwich to be free of warping, as we desire, each confining brane must have internal pressure that is half as big as our own brane’s internal tension. It is this pressure that is dangerous. and prone to buckle, like a playing card pinched between two fingers (Figure 23.8). This is the unequivocal prediction of Einstein’s relativistic laws, applied to the bulk and branes.

This buckling, if not counteracted, will make the confining branes collide with our brane—with our universe (Figure 25.6). [43] 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. 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 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] 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 . 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 ), H ij ( Q 2), W ij , 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 ), H ij ( Q 2), W ij , 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.