The Science of Interstellar

We first met tidal gravity in Chapter 4: the tidal gravity produced by a black hole, and tidal gravity on Earth produced by the Moon and Sun. In Chapter 17 we saw Gargantua’s tidal gravity in action on Miller’s planet, triggering gigantic “Millerquakes,” tsunamis, and tidal bores. In Chapter 16 we met the tiny stretching and squeezing of tidal gravity in a gravitational wave.

Tidal gravity is produced not only by black holes, the Sun, the Moon, and gravitational waves but also, in fact, by all gravitating objects. For example, regions of the Earth’s crust that contain oil are less dense than regions containing only rock, so their gravitational pull is weaker. This leads to a peculiar pattern of tidal gravitational forces.

In Figure 24.6, I use tendex lines to illustrate that tidal-force pattern. (See Chapter 4 for a discussion of tendex lines.) Squeezing tendex lines (drawn blue) stick out of the oil-bearing region, while stretching tendex lines (drawn red) stick out of the denser, oil-free region. As always, the two families of tendex lines are perpendicular to each other.

^{Fig. 24.6. Tendex lines above a portion of the Earth’s crust. The red lines produce a tidal stretch along themselves. The blue lines produce a tidal squeeze.}

An instrument called a gravity gradiometer can measure these tidal patterns (Figure 24.7). It consists of two crossed, solid rods attached to a torsional spring. On the ends of each rod are masses that feel gravity. The rods are normally perpendicular to each other, but in the figure the blue tendex lines squeeze the top two masses together and squeeze the bottom two together, while the red tendex lines stretch the right pair of masses apart and stretch the left pair apart. As a result, the angle between the rods decreases until the spring counterbalances the tidal forces. This is the gradiometer’s readout, its “readout angle.”

^{Fig. 24.7. A simple version of a gravity gradiometer, designed and built by Robert Forward at Hughes Research Laboratories in 1970.}

If this gradiometer is flown rightward through the tidal pattern of Figure 24.6, its readout angle opens up above the oil-bearing region, and then closes down over the oil-free region. Gradiometers like this, but more sophisticated, are used by geologists to search for oil and also for mineral deposits.

NASA has flown a more sophisticated gradiometer called GRACE[40] (Figure 24.8) to map tidal fields everywhere above the Earth, and watch slow changes of tidal gravity produced, for example, by the melting of ice sheets.

^{Fig. 24.8. GRACE: Two satellites, which track each other with a beam of microwaves, are pushed together by blue tendex lines and stretched apart by red tendex lines. The tendex lines, from the Earth below, are not shown.}

In my interpretation of Interstellar, most of the gravitational anomalies that Professor Brand’s team measures are sudden and unexpected changes in the patterns of tendex lines above the Earth’s surface, changes that occur for no obvious reason. The rocks and oil in the Earth’s crust are not moving. The melting of ice sheets is much too slow to produce these quick changes. People see no new gravitating masses coming near the gradiometers. Nevertheless, the gradiometers report changing tidal patterns. Falling dust accumulates in radial lines. Cooper sees the coin plunge to the floor.

The members of Professor Brand’s team monitor these changing patterns and eagerly record Cooper’s observations. Their trove of data becomes grist for the Professor’s quest to understand gravity, a quest that centers on the Professor’s equation.

25 The Professor’s Equation

In Interstellar, the gravitational anomalies excite Professor Brand for two reasons. If he can discover their cause, that may trigger a revolution in our understanding of gravity, a revolution as great as Einstein’s relativistic laws. More important: If he can figure out how to control the anomalies, that could enable NASA to lift large colonies of people off the dying Earth, and launch them toward a new home elsewhere in the universe.

For the Professor, the key to understanding and controlling the anomalies is an equation he has written on his blackboard (Figure 25.7, below). In the movie, he and Murph struggle to solve his equation.

Murph’s and the Professor’s Notebooks—and the Blackboard

Before filming began, two impressive Caltech physics students filled notebooks with calculations about the Professor’s equation. Elena Murchikova filled a clean, new notebook with calculations by grown-up Murph, calculations written with elegant calligraphy. Keith Matthews filled a beat up, old notebook with calculations by Professor Brand, in the more sloppy handwriting common for old guys like the Professor and me.

In the movie, grown-up Murph (played by Jessica Chastain) discusses the math in her notebook with the Professor (played by Michael Caine). Murchikova, an expert in quantum gravity and cosmology, was on set to advise Chastain about her dialog and notebook, and things she was to write on the blackboard. It was startling to see these two brilliant and beautiful women from very different worlds, both with bright red hair, huddled together.

As for me, I filled Professor Brand’s blackboard with diagrams and mathematics (Figure 25.8, below), including the Professor’s equation—THE equation—at Christopher Nolan’s request, of course. And I took great pleasure in talking with Michael Caine (Figure 25.1), who seemed to view me as a sort of prototype for the Professor he was playing. And great pleasure in watching Chris, a master craftsman, mold the scenes he was filming into precisely the form he wanted.

^{Fig. 25.1. Michael Caine (the Professor) and I, on set in the Professor’s office.}

Some weeks before filming in the Professor’s office, Chris and I went back and forth about what should be the nature of THE equation. (In Figure 1.2, back in Chapter 1, Chris is holding a sheaf of papers about the equation, which we are discussing.) Here’s my long scientist’s interpretation for what we wound up with—my extrapolation of the movie’s story.

Source of the Anomalies—The Fifth Dimension

In my extrapolation, it does not take long for the Professor to convince himself that the anomalies are due to gravity from the fifth dimension. From the bulk. Why?

The sudden changes in tidal gravity have no apparent source in our four-dimensional universe. For example, in my extrapolation the Professor’s team sees the tidal gravity above an oil deposit switch, in just a few minutes, from the pattern we expect (top picture in Figure 25.2) to a radically different pattern (bottom picture). The oil has not moved. The rocks have not shifted. Nothing in our four-dimensional universe has changed except the tidal gravity.

^{Fig. 25.2. Tendex lines (Chapter 4) describing the tidal gravity above an oil deposit before and after a sudden change.}

These sudden changes must have a source. If the source is not in our universe, on our brane, then there is only one other place it can be, the Professor reasons: in the bulk.

In my extrapolation, the Professor can think of just three ways that something in the bulk could produce these anomalies, and the first two he quickly rejects:

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The Gravity Recovery and Climate Experiment, a joint US/German space mission launched in May 2002 and still collecting data in 2014.