This week saw the publication of Visualizing Interstellar’s Wormhole, co-authored by Professor Kip Thorne and Dneg’s Oliver James, Eugénie von Tunzelmann and Paul Franklin, in the prestigious American Journal of Physics (AJP).

 “This is a wonderful article that provides some of the background and detailed calculations that went into creating the beautiful images seen in the movie.” 

David P. Jackson, Editor – American Journal of Physics

What is a wormhole?

Wormhole-featured-imageA wormhole is a hypothetical region of warped space – warped to such a degree that its behaviour is radically different from anything we normally experience:  If you had a wormhole, then from the exterior it would appear like a crystal ball. You could travel around it and peer in to it from all directions.

What you would see are kaleidoscopic-like images of another place. Unlike a crystal ball, the wormhole would have no solid boundary – you could travel into it and explore, but as you travel through it, instead of converging on its centre, you would find yourself emerging from another sphere, located in a completely different part of the universe. Curiously, if you then look back, you would see the place you just came from within the crystal ball you just emerged from.

How one might create such an object is unknown, they have never been observed in nature, and it is likely (though not certain) that the laws of quantum physics and of relativity, taken together, forbid them to ever exist. Nevertheless they are valid solutions to Einstein’s relativity equations, when one ignores quantum effects, and we can use those equations to model some of their theoretical properties.

The Double Negative Gravitational Renderer described here models the trajectory of beams of light through warped spacetime and was used to create the images of the wormhole in the movie Interstellar.

The Paper

The Open Access paper has been written to offer a variety of opportunities for students in elementary courses on general relativity theory.

These include:

  1. At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations sAmerican-Journal-of-Physics-Covereen in the movie;
  2. At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie;
  3. Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera’s local sky to a wormhole’s two celestial spheres;
  4. Implementing this map, for example, in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole;
  5. With the student’s implementation, exploring how the wormhole’s three parameters influence what the camera sees—which is precisely how Christopher Nolan, using our implementation, chose the parameters for ‘s wormhole;
  6. Using the student’s implementation, exploring the wormhole’s Einstein ring and particularly the peculiar motions of star images near the ring, and exploring what it looks like to travel through a wormhole.

The full paper “Visualizing Interstellar’s Wormhole” is freely downloadable from AJP:

Visualizing Interstellar’s Wormhole
Published by the American Journal of Physics
Oliver James, Eugénie von Tunzelmann, Paul Franklin and Kip S. Thorne

Supplementary material for Visualizing Interstellar’s Wormhole can be found here.

This work is further described in Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar which is available online at:

Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar
Published by IoP in Classical and Quantum Gravity
James O, von Tunzelmann E, Franklin P and Thorne K S
2015 Class. Quantum Grav. 32 065001

Further information and supplementary material for Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar can be found here.

The Authors

 

Blackhole-Paper-Authors-3

From left to right: Oliver James, Chief Scientist, Double Negative; Professor Kip S. Thorne, Caltech; Eugénie von Tunzelmann, CG Supervisor, Double Negative; Paul Franklin, VFX Supervisor, Double Negative.