Wormholes, and Time Machines

Introduction

Time Machines “Time is the fire in which we all burn,” says a character in a Star Trek movie.

This quote captures the hold that time has on our imaginations. Time, especially the fascinating and philosophically thorny issue of time travel, has been a common topic of science fiction since the classic story of H. G. Wells. The ability to manipulate time remains beyond our grasp, but physicists have conducted a remarkable exploration of time in the last decade that once again brings us to the frontiers of physics.

Separation of time from space has been a part of physical thinking since at least the era of Galileo.

The equations physicists use to describe nature are symmetric in time. They do not differentiate time running forward from time running backward. A movie of dust particles floating in a sunbeam would look essentially the same run forward or backward. If the projectionist ran a regular film backward, you would notice immediately.

• Where does the difference, the “arrow of time,” arise?
• Why is it that we age from teen age to middle age, but not the other way around?
• Is that progression immutable?

New approaches to thinking about time, came from new thinking about the connectedness of space, and all that came from the desire to make a film that could, among other things, explore issues of science and faith.

Worm Holes

This particular attack on time travel arose from a work of science fiction. Carl Sagan envisaged a film that would invoke, among other inventive ideas, rapid travel though the Galaxy. The film stalled, and Sagan turned to writing a novel first. The novel was a great success, and the film finally moved out of the perdition of production hell.

The film, too, was a great success, but Sagan succumbed to a leukemia-related disease before it was released.

In the original draft of his novel, Contact, Sagan wrote of a mode of interstellar travel created by an ancient extraterrestrial civilization. He had in mind that his passageway was a black hole where you could fly into the event horizon and emerge – elsewhere. Sagan sent the draft of the book to Kip Thorne, a physicist at Caltech, and one of the world’s experts on black holes. Thorne has written his personal version of this story in the book Black Holes and Time Warps: Einstein’s Outrageous Legacy. Thorne realized that what Sagan proposed would not work.

Thorne proposed a solution with both different physics and more imagination!

Einstein’s equations for a black hole do describe a passage between two universes or between two parts of the same universe: a structure called an Einstein-Rosen bridge, or in more casual language, a worm hole. This is yet another phrase invented by the word-master physicist, John A. Wheeler. Black hole experts have known for decades that the apparent worm hole represents only a single moment in time in the two-Universe Schwarzschild solution for a nonrotating black hole described in Chapter 9 (Section 8.2).

Just before or just after that instant, there is no passage, only the terrible maw of the singularity, waiting to destroy anything that passed into the event horizon. For an intrepid explorer who tried to race at anything less than the speed of light through the worm hole in the instant it opened, the worm hole would snap shut. The explorer would be trapped and pulled into the singularity.

In principle, Sagan might have invoked a rotating Kerr black hole wherein there is the possibility of travel through the inner “normal” space where tidal forces are less than infinite if one avoids the singularity and thence out into another Universe as described in Chapter 9, Section 8.2.

That passage might be slammed shut by the blue sheet of infalling star light. In any case, Thorne pursued a different route. With further reflection, Thorne realized that there might be another approach. Suppose, he reasoned, you were dealing with a very advanced civilization that could engineer anything that was not absolutely forbidden by the laws of physics.

Thorne devised a solution that was bizarre and unlikely, but could not be ruled out by the currently known laws of physics. His solution involved what he came to call exotic matter.

Ordinary matter has a finite energy and exerts a finite pressure and creates a normal, pulling, gravitational field. One can envisage mathematically, however, matter that has a negative energy, that exerts a negative pressure, like the tension in a rubber band.

For exotic matter, this tension is at such an extreme level that the tension energy is greater than the rest mass energy, E = Mc², of the rubber band.

Such material has the property one would label “antigravity.” Whereas ordinary matter pushes outward with pressure and pulls inward with gravity, exotic matter pulls inward with its tension and pushes outward with its gravity. Remarkably, related stuff has become a prominent topic in cosmology, as described in Chapter 12.

Cosmologists describe an inflationary stage occurring in the split seconds after the big bang, in which the Universe underwent a rapid expansion that led to its current size and smoothness. The condition that is hypothesized to cause inflation is some form of negative energy field that would have a negative pressure that pushed against normal gravity resulting in rapid expansion. After a brief interval of hyper-expansion, this field is presumed to decay away leaving what we regard today as the normal vacuum with its small but nonzero quantum vacuum energy density. Another version of these ideas arises in the context of the current apparently accelerating Universe presented in Chapter 12.

If the Universe is accelerating its expansion, there must be something involved other than the gravitating matter in it, some quantum energy of the vacuum that anti-gravitates, the Dark Energy. Thorne did not attempt to make the nature of exotic matter explicit. In the most general sense, however, the exotic matter needed to create worm holes would share some of the repulsive properties of the inflationary energy and the Dark Energy.

Because it was not forbidden by physics, and might even be a part of physics, Thorne speculated that an advanced civilization could slather some of this exotic matter on a mortar board, pick up a trowel, and do something with it. Cleverly applied, the repulsive nature of the anti-gravity of the exotic cement could hold open an Einstein-Rosen bridge indefinitely!

Thorne had discovered, conceptually at least, a way to traverse through hyperspace from one place in the Galaxy to a very distant one in a short time.

The result would effectively be faster-than-light travel through a worm hole, just the mechanism that Sagan wanted to further his plot. Sagan adopted Thorne’s basic idea and described such a worm hole in the book that went to press.

The movie was finally released in the summer of 1997.

Having passed the basic idea on to Sagan, Thorne remained deeply intrigued. He continued to work on the idea with students and together they published a number of papers showing that a proper arrangement of exotic matter could lead to a stable, permanent worm hole. It is tempting to ask what a worm hole would look like. A worm hole would not necessarily look black, like a black hole, even though the outer structure of their space-time geometries were similar. A black hole has an event horizon from within which nothing can escape.

By design, however, you can both see and travel through a worm hole. In its simplest form, a worm hole might appear spherical from the outside, that is, all approaches from all directions would look the same. If you travel through one, you would head straight toward the center of the spherical space. Without changing the direction of your propagation, you would eventually find yourself traveling away from the center, to emerge in another place.

A worm hole is not literally a tunnel in the normal sense with walls you could touch, but from inside a spherical worm hole, the perspective would be tunnel-like. You would be able to see light coming in from the normal space at either end of the worm hole. The view sideways, however, would seem oddly constricted. The space-time of the interior of a worm hole is highly curved. Light heading off in any direction “perpendicular” to the radius through the center of the worm hole would travel straight in the local space but end up back where it started, like a line drawn around the surface of a sphere, only in three-dimensional space.

If you faced sideways in a worm hole, you could, in principle, see the back of your head. In practice, the light might be distorted and your view very fuzzy. The effect might look like a halo of light around you that differentiated the “sideways” direction from that straight through the center of the worm hole. Figure 13.1 shows how it might look to you as you shined a flashlight on the interior of the worm hole.

A common misconception is to confuse the tunnel-like aspects of a worm hole with the funnel-like diagram that physicists use to make a two-dimensional representation, an embedding diagram, of the real three-dimensional space around a black hole or worm hole. In a two-dimensional embedding diagram, a circle in two-dimensional space is the analog of a sphere in three-dimensional space.

The real curved space around a three-dimensional worm hole is represented in two dimensions by a stretched two-dimensional space that resembles a funnel, just as it was for a black hole, as discussed in Chapter 9. In this two-dimensional analog, you cannot travel through what we perceive to be the mouth of the funnel. That is a third-dimensional hyperspace in the two-dimensional analog.

You have to imagine crawling, spider-like, along the surface of the two-dimensional space to get the true meaning of the nature of that space and some feeling for the three-dimensional reality. A version of this two-dimensional analog of a worm hole is shown in Figure 13.2. The worm hole in Figure 13.2 connects two different parts of an open, saddle-shaped universe.