The Origin of Star Trek's Wormhole

By Jesco von Puttkamer

When Gene Roddenberry wanted to know what a “wormhole” was, he asked his technical advisor. Here is the historic memo that von Puttkamer sent in response.

National Aeronautics and
Space Administration

MEMORANDUM
October 12, 1978

To: Gene Roddenberry,
Producer, Star Trek

From: Jesco von Puttkamer, Technical Adviser, Star Trek

SUBJECT: Wormholes

This is in response to your telephone request of last night.

The key concept of “hyperspace”has played a key role in science-fiction literature since the days of the “classics” in the 40s.

During the 60s, however, scientists—mathematicians and cosmologists—began to catch up with science fiction and have since actually moved far ahead. A large number of modern cosmologists today are convinced of the existence fo hyperspace—except that they call it superspace. The word was coined in 1962 by John Archibald Wheeler, Professor of Physics at the University of Texas. An important part in this modern cosmology (description of the Universe) is wormholes.

Superspace is fundamentally based on Albert Einstein's General Theory of Relativity (1915) which deals with gravitation. Superspace is envisioned as an unlimited, huge, timeless region in which our three-dimensional space is contained, along with innumerable other three-dimensional universes Superspace is eternal. Time stands still, and billions of years worth of developments are compressed into a split second. Superspace defies imagination (or screen treatment) and has obvious mystical character.*

The three-dimensional space embedded in superspace changes continuously with time (i.e., it isn't static but dynamic), but it is the geometry of space which changes, notice itself—as in the previous picture of a “space-time continuum” still used by science-fiction writers. While the latter was seen as a four-dimensional, space-time continuum which describes the dynamics of particles (form smallest subatomic particles to the largest stellar masses), the concept of superspace describes the dynamics of curved “empty” space itself, taken as a structure or geometry. Wheeler's science is therefore called “geometrodynmics;” it is more comprehensive and powerful (as well as elegant) than the older space-time continuum concept, but both have been developed from and are consistent with Einstien's General Theory of Relativity. (There are still other interpretations as well.)

Wheeler's reason for a developing geometrodynmics was to find a purely geometrical (space-structural) description of all of physics, in particular gravitation, electromagnetism, unquantized electrical charge and mass-energy particles. Wheeler expressed this in 1957, when he wrote, “Thereis nothing in the world except empty curved space. Matter, charge, electromagnetism and other fields are only manifestations od the bending of space. Physics is geometry.”

In order for Einstein's General Theory to “work” and for superspace truly to exist, three-dimensional space must be “multiply connected” (as the jargon goes), like New York City is multiply connected by subway tunnels through superspace. Thus, entrances to superspace and exits form it are believed to exist everywhere in our Universe: between the galaxies, in spaces between the stars and even as close to us as the edges of our solar system. These have been called “bridges” by Einstein (1935), “wormholes” by Wheeler (1955) and in the science of topology they are called “handles”:

Im the above sketch, what looks like a flat and curved sheet should be three-dimensional space. For simplicity, in order to draw the picture, the third dimension (vertical to the “sheet”) has been left off.

The wormhole connect two regions in space (not two different spaces or universes).

Thus, a spaceship could possibly fly in one mouth of the wormhole and out the other. The two tunnel mouths could be quite far apart (light years, perhaps), but the distance between them measured along the route through the tunnel itself (the throat of the wormhole)could be orders of magnitude different form the distance between them measured along the three-dimensional space (here: along the flat surface). Einstein's field equations do permit this. Thus, the spaceship could travel through the tunnel (almost) instantaneously (or not, depnding on the superspace “outside” the handle and the commensurate handle shape).

Why did Wheeler require wormholes in his view Einstein's cosmology? What is their purpose? Because they alone allow a purely geometrical description of localized “point” events such as electrical charges. He avers that what appears to us as an electrical charge (either positive or negative) is really the local area of a mouth of a wormhole through which the continuous lines of electrical force are threaded (see sketch). These field lines are described by Maxwell's equations of electromagnetism which combine with Einstein's 10 gravitational equations (of General Theory of Relativity) into a set of 16 equations which form the unified (gravitation/electromagnetism) cosmology of modern physics. (But it should also be said, that—as shown by such scientists as Andrei Sakharov—geometrodynamics has some deficiencies after all and cannot explain everything—for instance, quantum effects and gravitational collapse. It appears, as of now, that an even more universal answer lies in quantum physics itself—waiting for a new Einstein of the future.)

Finally, some words of caution:

Wormholes and black holes are two entirely different things. They are similar in their dynamics, but wormholes are very much smaller and presumably much more frequent. On the other hand, it appears that several black holes have actually been discovered in space already, while wormholes, are still concepts of mathematical conjecture, and held in doubt by some scientists. [See following article on black holes.]

A wormhole is much smaller, and since we know even less about wormholes that about black holes, we have felt justified to assume for Star Trek–The Motion Picture that the Enterprise can pass through another wormhole mouth into another part of the universe (not another universe).

* This explains why the climax of the V'ger story must retain some mysticism (but without becoming too egnimatic, like Kubrick's 2001).

The above article was excepted from Starlog magazine, issue #33, April 1980.