So I asked myself, What do I have to do to Flamm’s wormhole to save it from pinching off; to hold it open, so it can be traversed? A simple thought experiment gave me the answer.
Suppose you have a wormhole that is spherical like Flamm’s, but unlike Flamm’s it does not pinch off. Send a light beam into the wormhole, radially. Since all the beam’s light rays travel radially, the beam must have the shape shown in Figure 14.4. It is converging (its cross-sectional area is decreasing) as it enters the wormhole, and it is diverging (its area is increasing) as it leaves the wormhole. The wormhole has bent the light rays outward, as would a diverging lens.
Now, gravitating bodies such as the Sun or a black hole bend rays inward (Figure 14.5). They can’t bend rays outward. To bend light rays outward, a body must have negative mass (or equivalently, negative energy; recall Einstein’s equivalence of mass and energy). From this fundamental fact, I concluded that any traversable, spherical wormhole must be threaded by some sort of material that has negative energy. At least the material’s energy must be negative as seen by the light beam, or by anything or anyone else that travels through the wormhole at nearly the speed of light.[27] I call such material “exotic matter.” (I later learned that, according to Einstein’s relativistic laws, any wormhole, spherical or not, is traversable only if it is threaded by exotic matter. This follows from a theorem proved in 1975 by Dennis Gannon at the University of California at Davis. Being somewhat illiterate, I was unaware of Gannon’s theorem.)
Now, it is an amazing fact that exotic matter can exist, thanks to weirdnesses in the laws of quantum physics. Exotic matter has even been made in physicists’ laboratories, in tiny amounts, between two closely spaced electrically conducting plates. This is called the Casimir effect. However, it was very unclear to me in 1985 whether a wormhole can contain enough exotic matter to hold it open. So I did two things.
First, I wrote a letter to my friend Carl suggesting that he send Eleanor Arroway to Vega through a wormhole rather than a black hole, and I enclosed a copy of the calculations by which I had shown that the wormhole must be threaded by exotic matter. Carl embraced my suggestion (and wrote about my equations in the acknowledgment of his novel). And that is how wormholes entered modern science fiction—novels, films, and television.
Second, with two of my students, Mark Morris and Ulvi Yurtsever, I published two technical articles about traversable wormholes. In our articles, we challenged our physicist colleagues to figure out whether the combined quantum laws and relativistic laws permit a very advanced civilization to collect enough exotic matter inside a wormhole to hold it open. This triggered a lot of research by a lot of physicists; but today, nearly thirty years later, the answer is still unknown. The preponderance of the evidence suggests that the answer may be NO, so traversable wormholes are impossible. But we are still far from a final answer. For details, check out Time Travel and Warp Drives by my physicist colleagues Allen Everett and Thomas Roman (Everett and Roman 2012).
What Does a Traversable Wormhole Look Like?
What does a traversable wormhole look like to people like us who live in our universe? I can’t answer definitively. If a wormhole can be held open, the precise details of how remain a mystery, so the precise details of the wormhole’s shape are unknown. For black holes, by contrast, Roy Kerr has given us the precise details, so I can make the firm predictions described in Chapter 8.
So for wormholes, I can make only an educated guess, but one in which I have considerable confidence. Hence the symbol on this section’s header.
Imagine we have a wormhole here on Earth, stretching through the bulk from Grafton Street in Dublin, Ireland, to the desert in Southern California. The distance through the wormhole might be only a few meters.
The entrances to the wormhole are called “mouths.” You are sitting in a sidewalk cafe alongside the Dublin mouth. I am standing in the desert beside the California mouth. Both mouths look rather like crystal balls. When I look into my California mouth, I see a distorted image of Grafton Street, Dublin (Figure 14.6). That image is brought to me by light that travels through the wormhole from Dublin to California, rather like light traveling through an optical fiber. When you look into your Dublin mouth, you see a distorted image of Joshua trees (cactus trees) in the California desert.
Can Wormholes Exist Naturally, as Astrophysical Objects?
In Interstellar, Cooper says, “A wormhole isn’t a naturally occurring phenomenon.” I agree with him completely! If traversable wormholes are allowed by the laws of physics, I think it extremely unlikely they can exist naturally, in the real universe. I must confess, though, that this is little more than a speculation, not even an educated guess. Maybe a highly educated speculation, but speculation nonetheless, so I labeled this section .
Why am I so pessimistic about natural wormholes?
We see no objects in our universe that could become wormholes as they age. By contrast, astronomers see huge numbers of massive stars that will collapse to form black holes when they have exhausted their nuclear fuel.
On the other hand, there is reason to hope that wormholes do exist naturally on submicroscopic scales in the form of “quantum foam” (Figure 14.7). This foam is a hypothesized network of wormholes that is continually fluctuating in and out of existence in a manner governed by the ill-understood laws of quantum gravity (Chapter 26). The foam is probabilistic in the sense that, at any moment, there is a certain probability the foam has one form and also a probability that it has another form, and these probabilities are continually changing. And the foam is truly tiny: the typical length of a wormhole would be the so-called Planck length, 0.000000000000000000000000000000001 centimeters; a hundredth of a billionth of a billionth the size of the nucleus of an atom. That’s small!!
Back in the 1950s John Wheeler gave persuasive arguments for quantum foam, but there is now evidence that the laws of quantum gravity might suppress the foam and might even prevent it from arising.
If quantum foam does exist, I hope there is a natural process by which some of its wormholes can spontaneously grow to human size or bigger, and even did so during the extremely rapid “inflationary” expansion of the universe, when the universe was very, very young. However, we physicists have no hint of any evidence at all that such natural enlargement can or did occur.
27
Energy is weird in relativistic physics; the energy one measures depends on how fast one moves and in what direction.