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.

Holding the Wormhole Open

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.

^{Fig. 25.5. The wormhole. Left: Pinching off. Right: Held open by bulk fields.}

Protecting Our Universe from Destruction

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] 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] 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.

^{Fig. 25.6. Brane collision.}

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.

^{Fig. 25.7. Professor Brand’s equation.}

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.