The Science of Interstellar

^{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.