Are the equations appeared on the blackboard in the Interstellar movie real equations of Kip Thorne while working out equations for computing the image of a black hole? Or they are just random equations, I remind that I heard that they are real but not sure of any source.

Murphy near blackboard


In Chapter 25 of The Science of Interstellar by physicist Kip Thorne, it's confirmed that the equations on the board were written by physicists (mostly all by Thorne himself, though some of his students were involved in writing equations in notebooks and helping explain to the actors what to write when they were actually shown writing things on blackboards). They're supposed to involve some new future physics involving higher dimensions which are an attempt to explain "gravitational anomalies" that, in the movie's universe, had been observed in very careful measurements of gravitational tidal forces around the Earth. So, a lot of the equations would have been at least partly fictional, though inspired by real physics. Here's a part that talks about it:

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.

Thorne goes on to explain that the equation they were trying to find dealt with a higher spatial dimension, "the bulk", which in reality is theorized in models of brane cosmology (an extension of superstring theory). Part of the idea in the movie that the gravitational constant might depend on fields in the bulk, which would allow it to vary. Thorne writes that

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 prevent our brane from collisions.


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). 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 his 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 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.


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 inserted each guess into a huge computer program 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, until exhaustion sets in. Then they begin again the next day.

Finally, in a note at the end of the chapter Thorne adds this about "the equation" that the Professor and Murph are trying to guess the correct form of:

The meaning of the various symbols in the other equation are spelled out on the Professor's other fifteen blackboards, along with the 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.

For the photos of all the blackboards, go to the section of the site titled "Transmissions", click "Kip Thorne" and then "Explore Kip Thorne's new book", then scroll to the bottom of the page.

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David Ding, PhD Candidate in Theoretical Quantum Information, Stanford University said he noticed some of the equations on the blackboard were actually relevant to General Relativity.

"I absolutely loved the movie. I think it was relatively close to being scientifically accurate compared to other movies, although a lot of speculation was made, in particular regarding things inside a black hole. I couldn't help but notice references directed at physicists. For example, I laughed out loud when they were talking about how they cannot reconcile quantum mechanics and relativity and how they need to go into a black hole to get the necessary data. Also, when Murph was writing equations on the blackboard, I noticed that they're actually relevant to general relativity (e.g. I saw \int \sqrt{-g} d^4 x)."

REF: "What do physicists think about Interstellar (2014 Movie)?." Quora.com. N.p. Web. 15 Nov. 2014. http://www.quora.com/

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Kip Thorn, astrophysicist generated the mathematical models used by the software to create the visual effects in the movies. They used real astrophysical data and mathematics to create these models. In addition the models turned out to unexpectedly demonstrate visually warping of the universe in a way consistent with physicists theories.

  • Since Thorn was available for consultation, it is likely at least some of the equations on the blackboard were at least partially true and reliable as confirmed by other scientists who viewed the movie.

So he asked Thorne to generate equations that would guide their effects software the way physics governs the real world. They started with wormholes. If light around a wormhole wouldn't behave classically—that is, travel in a straight line—what would it do? How could that be described mathematically?

Thorne sent his answers to Franklin in the form of heavily researched memos. Pages long, deeply sourced, and covered in equations, they were more like scientific journal articles than anything else. Franklin's team wrote new rendering software based on these equations and spun up a wormhole. The result was extraordinary. It was like a crystal ball reflecting the universe, a spherical hole in spacetime. “Science fiction always wants to dress things up, like it's never happy with the ordinary universe,” he says. “What we were getting out of the software was compelling straight off.”

"How Building a Black Hole for Interstellar Led to an Amazing Scientific Discovery." Wired.com. N.p. Web. 15 Nov. 2014. http://www.wired.com/2014/10/astrophysics-interstellar-black-hole/

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As a general relativist, I was actually pretty impressed with this. The chalkboard most featured actually was headed with the title "Auxilary fields", which is certainly a very relevant topic if you're embedding our spacetime in an extra-dimensional space.

And I wouldn't be surprised if Thorne did them himself, as they were written very much in an older style that professors used before computers -- where equations were carefully written up in great detail and with many colors of chalk before the lecture began.

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  • +1 for the style. Do old professors still use this style now, or do they just give slideshows nevertheless? – Ooker May 13 '18 at 13:51

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