Misc,
Visualizing Interstellar's Wormhole
(Feb 16, 2015)
Abstract
Christopher Nolan's science fiction movie Interstellar offers a variety of
opportunities for students in elementary courses on general relativity theory.
This paper describes such opportunities, including: (i) At the motivational
level, the manner in which elementary relativity concepts underlie the wormhole
visualizations seen in the movie. (ii) 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. (iii) 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. (iv) 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. (v) 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 Interstellar's wormhole. (vi)
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.
