__How Wormholes Got Their
Name__

My mentor, John Wheeler, gave astrophysical wormholes their name. He based
it on wormholes in apples (Figure below). For an ant walking on an apple,
the apple’s surface is the entire universe. If the apple is threaded by a
wormhole, the ant has two ways to get from the top to the bottom: around
the outside (through the ant’s universe) or down the wormhole. The
wormhole route is shorter; it’s a shortcut from one side of the ant’s
universe to the other.

* An ant explores a wormhole-endowed apple.*

The apple’s delicious interior, through which the wormhole passes, is not
part of the ant’s universe. It is a three-dimensional bulk or hyperspace .
The wormhole’s wall can be thought of as part of the ant’s universe. It
has the same dimensionality as the universe (two dimensions) and it joins
onto the universe (the apple’s surface) at the wormhole’s entrance. From
another viewpoint, the wormhole’s wall is not part of the ant’s universe;
it is just a shortcut by which the ant can travel across the bulk, from
one point in its universe to another.

** **__Flamm’s Wormhole__

In 1916, just one year after Einstein formulated his general relativistic
laws of physics, Ludwig Flamm in Vienna discovered a solution of
Einstein’s equations that describes a wormhole (though he did not call it
that). We now know that Einstein’s equations allow many kinds of wormholes
(wormholes with many different shapes and behaviors), but Flamm’s is the
only one that is precisely spherical and contains no gravitating matter.
When we take an equatorial slice through Flamm’s wormhole, so it and our
universe (our brane) have just two dimensions rather than three, and when
we then view our universe and the wormhole from the bulk, they look like
the left part of Figure A.

*Fig.A. Flamm’s wormhole.*

With one of our universe’s dimensions lost from the picture, you must
think of yourself as a two-dimensional creature confined to move on the
bent sheet or on the wormhole’s two-dimensional wall. There are two routes
for travel from location A in our universe to location B: the short route
(dashed blue curve) down the wormhole’s wall, or the long route (dashed
red curve) along the bent sheet, our universe.

Of course, our universe is really three dimensional. The concentric
circles in the left part of FigureA are really the nested green spheres
shown to the right. As you enter the wormhole along the blue path from
location A, you pass through spheres that get smaller and smaller. Then
the spheres, though nested inside each other, cease changing circumference.
And then, as you exit the wormhole toward location B, the spheres get
larger and larger.

For nineteen years, physicists paid little attention to Flamm’s outrageous
solution of Einstein’s equations, his wormhole. Then in 1935 Einstein
himself and fellow physicist Nathan Rosen, unaware of Flamm’s work,
rediscovered Flamm’s solution, explored its properties, and speculated
about its significance in the real world. Other physicists, also unaware
of Flamm’s work, began to call his wormhole the “Einstein-Rosen bridge.

It is often difficult to extract, from the mathematics of Einstein’s
equations, a full understanding of their predictions. Flamm’s wormhole is
a remarkable example. From 1916 until 1962, nearly a half century,
physicists thought that the wormhole is static, forever unchanging. Then
John Wheeler and his student Robert Fuller discovered otherwise. Looking
much more closely at the mathematics, they discovered that the wormhole is
born, expands, contracts, and dies, as shown in Figure B

*Fig.B Dynamics of Flamm’s wormhole (the Einstein-Rosen bridge). *

Initially, in picture (a), our universe has two singularities. As time
passes, the singularities reach out to each other through the bulk and
meet to create the wormhole (b). The wormhole expands in circumference,
(c) and (d), then shrinks and pinches off (e), leaving behind the two
singularities (f). The birth, expansion, shrinkage, and pinch-off happen
so quickly that nothing, not even light, has time to travel through the
wormhole from one side to the other. Anything or anyone that attempts the
trip will get destroyed in the pinch-off!

This prediction is inescapable. If the universe were ever, somehow, to
develop a spherical wormhole that contains no gravitating matter, this is
how the wormhole would behave. Einstein’s relativistic laws dictate it.

Wheeler was not dismayed by this conclusion. On the contrary, he was
pleased. He regarded singularities (places where space and time are
infinitely warped) as a “crisis” for the laws of physics. And crises are
wonderful tutors. By probing wisely, we can get great insights into the
physical laws.

__Contact__

Fast-forward a quarter century, to May 1985: a phone call from Carl Sagan
asking me to critique the relativistic science in his forthcoming novel
Contact. I happily agreed. We were close friends, I thought it would be
fun, and, besides, I still owed him one for introducing me to Lynda Obst.

Carl sent me his manuscript. I read it and I loved it. But there was one
problem. He sent his heroine, Dr. Eleanor Arroway, through a black hole
from our solar system to the star Vega. But I knew that a black-hole
interior cannot be a route from here to Vega or to anywhere else in our
universe. After plunging through the black hole’s horizon, Dr. Arroway
would get killed by its singularity. To reach Vega fast, she needed a
wormhole, not a black hole. But a wormhole that does not pinch off. A
traversable wormhole.

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 below.. 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.

*Fig. . A radial light beam traveling through a spherical,
traversable wormhole. Left: As seen from the bulk with one space dimension
removed. *

*Right: As seen in our universe.*

Now, gravitating bodies such as the Sun or a black hole bend rays inward (Figure
below). 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.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.

*Fig. The Sun or a black hole bends a beam of light inward.*

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.

So for wormholes, I can make only an educated guess, but one in which I
have considerable confidence.

*The images seen through a wormhole’s two mouths*

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 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” (Fig
Below). 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 . 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.

*Quantum foam.*

The other tiny hope for natural wormholes is the big bang creation of the
universe. It is conceivable, but very unlikely, that traversable wormholes
could have formed in the big bang itself. Conceivable for the simple
reason that we don’t understand the big bang well at all. Unlikely because
nothing we do know about the big bang gives any hint that traversable
wormholes might form there.

__Can Wormholes Be Created by an Ultra-Advanced Civilization?__

An ultra-advanced civilization is my only serious hope for making
traversable wormholes. But it would face huge obstacles, so I’m
pessimistic.

One way to make a wormhole, where previously there were none, is to
extract it from the quantum foam (if the foam exists), enlarge it to human
size or larger, and thread it with exotic matter to hold it open. This
seems like a pretty tall order, even for an ultra-advanced civilization,
but perhaps only because we don’t understand the quantum gravity laws that
control the foam, the extraction, and the earliest stages of enlargement .
Of course, we don’t understand exotic matter very well either.

At first sight, making a wormhole seems easy *. Just push a *piece of
our brane (our universe) downward in the bulk to create a thimble, fold
our brane around in the bulk, tear a hole in our brane just below the
thimble, tear a hole in the thimble itself, and sew the tears together.
Just!

*Creating a wormhole*

In Interstellar, Romilly demonstrates the same thing with a sheet of paper
and a pencil . As easy as this may look from the outside, playing with
pencils and paper, it is horrendously daunting when the sheet is our brane
and these manipulations must be carried out from within the brane, by a
civilization that lives in our brane. In fact, I have no idea how to
execute any of these maneuvers from inside our brane except the first,
creating a thimble in our brane (which requires only a very dense mass,
such as a neutron star). Moreover, if it is possible at all to tear holes
in our brane, it can only be done with the help of the laws of quantum
gravity. Einstein’s relativistic laws forbid tearing our brane, so the
only hope is to make the tear where his laws fail, in a realm of quantum
gravity. We then are back to the domain of terra almost incognita.

*Romilly explaining wormholes. Left: He bends a sheet of paper. Right:
He punches a pencil (the wormhole) through the paper, joining its two
edges.*

__The Bottom Line__

I doubt the laws of physics permit traversable wormholes, but this may be
pure prejudice. I could be wrong. If they can exist, I doubt very much
that they can form naturally in the astrophysical universe. My only real
hope for forming them is artificially, in the hands of an ultra-advanced
civilization. But we are extremely ignorant of how such a civilization
could do it. And it appears more than daunting, at least from inside our
brane (our universe), even for the most advanced of civilizations.

In Interstellar, however, the wormhole is thought to have been made, held
open, and placed near Saturn by a civilization that lives in the bulk, a
civilization whose beings have four space dimensions, like the bulk.