A striking consequence
of the new picture of the world is that there should be an infinity of
regions with histories absolutely identical to ours. That's right, scores
of your duplicates are now reading copies of this article. They live on
planets exactly like Earth, with all its mountains, cities, trees, and
butterflies. There should also be regions where histories are somewhat
different from ours, with all possible variations. For example, some readers
will be pleased to know that there are infinitely many O-regions where
Al Gore is the President of the United States.

In this astonishing
world view, our Earth and our civilization are anything but unique. Instead,
countless identical civilizations are scattered across the infinite expanse
of the cosmos. With humankind reduced to absolute cosmic insignificance,
our descent from the center of the world, a process begun by Copernicus,
is now complete.

**THE
PRINCIPLE OF MEDIOCRITY** *[9.15.06]*

By Alexander Vilenkin

INTRODUCTION

In
1981, Alan Guth made what some considered at the time to be the most important
contribution to cosmology in a generation: the theory of inflation. In
Guth's model, the very early universe underwent a period of rapid expansion;
this accounts for, among other puzzles in big-bang theory, the present-day
universe's puzzling homogeneity.

Today,
more than 25 years later, Guth's inflationary model still holds sway, as
other cosmologists have moved the theory in new directions, i.e. chaotic
inflation, eternal inflation, brane inflation, among others.

The
implications of inflation are particularly important in the context of
the landscape of string theory. One of the leading researchers studying
how inflationary cosmology evolves through the landscape is Alex Vilenkin,
a theoretical physicist at Tufts who has been working in the field of cosmology
for 25 years and is a pioneer in introducing the ideas of eternal inflation
and quantum creation of the universe from nothing. Here he sets forth his
ideas of how the set of theories which began with Guth's inflationary scenario
are playing out.

—JB

ALEXANDER
VILENKIN is
Professor of Physics and Director of the Institute of Cosmology at Tufts
University. He
is the author of the *Many
Worlds in One: The Search for Other Universes*.

Alexander Vilenkin's *Edge* Bio
Page

**THE
PRINCIPLE OF MEDIOCRITY**

by
Alexander Vilenkin

*I consider
myself an average man, except for the fact that I consider myself
an average man.*

— Michel
de Montaigne

We live in
the aftermath of a great explosion. This awesome event, called somewhat
frivolously the big bang, took place about 14 billion years ago. We can
actually see some of the cosmic history unfolding before us since that
moment—light from remote galaxies takes billions of years to reach
our telescopes on earth, so we can see galaxies as they were in their youth.
But there is a limit to how far we can see into space. Our horizon is set
by the maximum distance light could have traveled since the big bang. Sources
more distant than the horizon cannot be observed, simply because their
light has not yet had time to reach Earth.

But if there
are parts of the universe we cannot detect, who can resist wondering what
they look like? Until recently physicists thought that the answer to this
question is rather
boring: it’s just more of the same – more galaxies, more stars.
But now, recent developments in cosmology have led to a drastic revision
of that view.

According to
the new picture, distant parts of the universe are in the state of explosive,
accelerated expansion, called “inflation”. The expansion is
so fast that in a tiny fraction of a second a region the size of an atom
is blown to dimensions much greater than the entire currently observable
universe. The expansion is caused by a peculiar form of matter, called “false
vacuum”, which produces a strong repulsive force. The word “false” refers
to the fact that, unlike the normal “true” vacuum, this type
of vacuum is unstable and typically decays after a brief period of time,
releasing a large amount of energy. The energy ignites a hot fireball of
particles and radiation. This is what happened in our cosmic neighborhood
14 billion years ago – the event we refer to as the big bang.

The idea of
inflation was little more than a speculative hypothesis when Alan Guth
first proposed it in 1980. But in the late 1990s observations of distant
supernovae and of the cosmic microwave background radiation—a faint
afterglow of the big bang—gave the theory a boost of corroborating
observational evidence. So today, inflation is well on its way to becoming
one of the cornerstones of modern cosmology. And since the theory is supported
by the data in the observable part of the universe, this gives us reason
to believe its conclusions about the parts that we cannot observe.

In a way, inflation
is similar to the reproduction of bacteria. There are two competing processes
at play: bacteria multiply by division, but occasionally they are also
destroyed by antibodies. The outcome depends on which process is more efficient.
If the bacteria reproduce faster, their numbers rapidly grow. If destruction
is faster, the bacteria quickly die out.

With inflation,
the two competing processes are the decay of the false vacuum and its “reproduction” by
rapid expansion of the inflating regions. My calculations, and those of
Andrei Linde, show that false-vacuum regions multiply much faster than
they decay, and thus their volume grows without bound. At this very moment,
some distant parts of the universe are undergoing exponential inflationary
expansion. Other regions like ours, where inflation has ended, are also
constantly being produced. They form “island universes” in
the inflating sea of false vacuum. Because of inflation, the space between
the islands rapidly expands, making room for more island universes to form.

Inflation is
thus a runaway process that has stopped in our neighborhood, but still
continues in other parts of the universe, causing them to expand at a furious
rate and constantly spawning new island universes like our own. This never
ending process is referred to as “eternal inflation”. The role
of the big bang in this scenario is played by the decay of the false vacuum.
It is no longer a one-time event in our past: multiple bangs went off before
it in remote parts of the universe, and countless others will erupt elsewhere
in the future.

Analysis shows
that the boundaries of island universes expand faster than the speed of
light. (Einstein’s ban on super-luminal speeds applies to material
bodies, but not to geometric entities such as the boundary of an island.)
It follows that, regrettably, we will never be able to travel to another
island, or even send a message there. Other island universes are unobservable,
even in principle.

Back in 1983,
when this new world view was gradually taking shape in my mind, I discussed
it with Alan Guth — Mr. Inflation himself. I told Alan about runaway
expansion and how it could be described mathematically. But then, when
I was in the middle of unveiling my new dazzling picture of the universe,
I noticed that Alan was beginning to doze off. Years later, when I got
to know Alan better, I learned that he is a very sleepy fellow. We organize
a joint seminar for the Boston area cosmologists, and at every seminar
meeting Alan falls peacefully asleep a few minutes after the talk begins.
Miraculously, when the speaker is finished, he wakes up and asks the most
penetrating questions. Alan denies any supernatural abilities, but not
everybody is convinced. So, in retrospect, I should have continued the
discussion. But at the time I was not aware of Alan's magical powers and
hastily retreated. (I should add that later Alan Guth became a great enthusiast
of eternal inflation.)

The initial
response of other colleagues was also less than enthusiastic. Physics is
an observational science, they said, so we should refrain from making claims
that cannot be observationally confirmed. We cannot observe other big bangs,
nor can we observe distant inflating regions. They are all beyond our horizon,
so how can we verify that they really exist?

However, surprising as this may seem, the existence of unobservable island
universes can be used to make testable predictions in our local region. Even
more surprisingly, some of the predictions have already been confirmed! These
tests of eternal inflation involve anthropic considerations, which have recently
become a subject of great controversy. But before I get to the tests, I would
like to discuss some striking — and I would say metaphysical — implications
of eternal inflation.

~

In the global
view of eternal inflation, the boundaries of island universes are the regions
where big bangs are happening right now. Newly formed islands are microscopically
small, but they grow without limit as they get older. Central parts of
large island universes are very old: big bangs once took place there long
time ago. Now they are dark and barren: all stars have long since died
there. But regions at the periphery of the islands are new and must be
teeming with shining stars.

The inhabitants
of island universes, like us, see a different picture. They do not perceive
their universe as a finite island. For them it appears as a self-contained,
infinite universe. That dramatic difference in perspective is a consequence
of the differences imposed by the ways of keeping time appropriate to the
global and internal views of the island universe. (According to Einstein's
theory of relativity, time is not fixed, but instead is observer dependent.)

In the global
view, the definition of a "moment of time" is largely arbitrary,
because there is no obvious way to synchronize the clocks of observers
in false vacuum and in different island universes. By contrast, to describe
one specific island universe from the point of view of its inhabitants,
there is a natural rather than arbitrary choice for the origin of time.
All observers in a given island universe can count time from the big bang
at their respective locations. Their big bang is thus set as time zero.
Remarkably, from such an internal viewpoint the island universe is infinite.

Perhaps the
easiest way to see this is to count galaxies. In the global view, new galaxies
are continually formed near the expanding boundaries, so as time passes,
we have an infinite number of galaxies in the limit. In the internal view,
all this infinity of galaxies exists simultaneously (say, at time 14 billion
years). The implications are extraordinary.

Since each island
universe is infinite from the viewpoint of its inhabitants, it can be divided
into an infinite number of regions having the same size as our own observable
region. My collaborator Jaume Garriga and I call them O-regions for short.
As it happens, the most distant objects visible from Earth are about 40
billion light-years away, so the diameter of our own O-region is twice
that number.

Imagine, then,
an infinite island universe packed with O-regions — gigantic spheres,
80 billion light-years in diameter each. The key observation is that the
number of distinct configurations of matter that can possibly be realized
in any O-region — or, for that matter, in any finite system — is
finite. One might think that arbitrarily small changes could be made in
the system, thus creating an infinite number of possibilities. But that
is not the case. If I move my chair by one centimeter, I change the state
of our own O-region. I could instead move it by 0.9 centimeter, 0.99 centimeter,
0.999 centimeter, and so forth — an infinite sequence of possible
displacements, which more and more closely approach the limit of one centimeter.
There is a problem, though. Displacements too close to one another cannot
be distinguished, even in principle, because of quantum mechanical uncertainty.
As a result, there is only a finite number of distinct states.

The
number of possible histories of an O-region is finite as well. A history
is described by a sequence of states at successive moments of time. Which
histories are possible in quantum physics differ immensely from the ones
possible in the classical world. In the quantum world the future is not
uniquely determined by the past; the same initial state can lead to a multitude
of different outcomes, and so only the probabilities of those outcomes
can be determined. Consequently, the range of possible histories is greatly
enlarged. Once again, though, the fuzziness imposed by quantum uncertainty
makes it impossible to distinguish histories that are too close to each
other. An estimate of the number of distinct histories that can unfold
in an O-region between the big bang and the present gives 10 to the power
10 to the power of 150 . This number is fantastically huge, but the important
point is that the number is finite.

Let us now
take stock of the situation. The theory of inflation tells us that island
universes are internally infinite, so that each of them comprises an infinite
number of O-regions. And quantum uncertainty implies that only a finite
number of histories can unfold in any O-region. The initial states of the
O-regions at the big bang are set by random quantum processes during inflation,
so all possible initial states are represented in the ensemble. Putting
those statements together, it follows that every single history should
be repeated an infinite number of times within any of the island universes — including,
of course, the one we inhabit.

Among the infinitely
replayed scripts are some very bizarre histories. For example, a planet
similar to our Earth can suddenly collapse to form a black hole. Such an
event is extremely unlikely, but all that means is that, before encountering
it, one would have to survey an enormous number of O-regions within our
island universe.

A striking consequence
of the new picture of the world is that there should be an infinity of
regions with histories absolutely identical to ours. That's right, scores
of your duplicates are now reading copies of this article. They live on
planets exactly like Earth, with all its mountains, cities, trees, and
butterflies. There should also be regions where histories are somewhat
different from ours, with all possible variations. For example, some readers
will be pleased to know that there are infinitely many O-regions where
Al Gore is the President of the United States.

In this astonishing
world view, our Earth and our civilization are anything but unique. Instead,
countless identical civilizations are scattered across the infinite expanse
of the cosmos. With humankind reduced to absolute cosmic insignificance,
our descent from the center of the world, a process begun by Copernicus,
is now complete.

~

I now turn to
possible observational tests of eternal inflation. The clue to the structure
of the universe may be right in front of our eyes, encoded in the values
of the fundamental constants. According to string theory, the quantities
we call "constants of nature" — like Newton's gravitational
constant or the electron mass — may in fact be variables that can
take a wide spectrum of values. This has been discussed on *Edge* by
Lenny Susskind. Despite some recent fire that string theory has attracted,
it remains the best candidate we now have for the fundamental theory of
nature. (There are also other particle physics theories predicting variation
of the "constants". I will mention one example below.)

Quantum fluctuations
in the course of eternal inflation ensure that all possible values of the
constants are realized somewhere in the universe. As a result, remote regions
of the universe may drastically differ in their properties from our observable
region. The values of the constants in our vicinity are determined partly
by chance and partly by how suitable they are for the evolution of life.
The latter effect is called anthropic selection.

If some
"constant" varies from one region of the universe to another, its
value cannot be predicted with certainty, but we can still try to make a
statistical prediction. Suppose, for example, I want to predict the height
of the first man I am going to see when I walk out into the street. Having
consulted the statistical data on the height of men in the United States,
I find that the height distribution follows a bell curve with a median value
at 1.77 meters. The first man I meet is not likely to be a giant or a dwarf,
so I expect his height to be in the mid-range of the distribution. To make
the prediction more quantitative, I can assume that he will not be among
the tallest 2.5% or shortest 2.5% of men in the United States. The remaining
95% have heights between 1.63 and 1.90 meters. If I predict that the man
I meet will be within this range of heights and then perform the experiment
a large number of times, I can expect to be right 95% of the time. This is
known as a prediction at 95% confidence level.

In order to
make a 99% confidence level prediction, I would have to discard 0.5% at
both ends of the distribution. As the confidence level is increased, my
chances of being wrong get smaller, but the predicted range of heights
gets wider and the prediction less interesting.

A similar technique
can be used to make predictions for the constants of nature. Suppose the
Statistical Bureau of the Universe collected and published the values of
some constant X measured by observers in different parts of the universe.
We could then discard 2.5% at both ends of the resulting distribution and
predict the value of X at a 95% confidence level.

What would be
the meaning of such a prediction? If we randomly picked observers in the
universe, their observed values of X would be in the predicted interval
95% of the time. Unfortunately, we cannot perform this experiment, because
all regions with different values of X are beyond our horizon. We can only
measure X in our local region. What we can do, though, is to think of ourselves
as having been randomly picked. We are just one in the multitude of civilizations
scattered throughout the universe. We have no reason to believe a priori
that the value of X in our region is very large or small, or otherwise
very special compared with the values measured by other observers. Hence,
we can predict, at 95% confidence level, that our measurement will yield
a value in the specified range. The assumption of being unexceptional is
important in this approach; I called it "the principle of mediocrity".

In lieu of the
data from the Statistical Bureau of the Universe, we have to derive the
statistical distribution from the fundamental theory, combined with the
theory of eternal inflation. If the resulting predictions agree with the
measurements, this would provide evidence for the theory; if not, the theory
can be ruled out at a specified confidence level.

Of course, we
have no idea how to calculate the number of observers, because of our ignorance
about the origins of life and intelligence. But this problem can be circumvented
if we focus on the variation of the constants that do not directly affect
the physics and chemistry of life. The counting of observers can then be
reduced to the counting of galaxies (since all galaxies in this case will
have about the same number of observers).

This strategy
has been applied to the cosmological constant, with a very encouraging
result. Steven Weinberg and Andrei Linde were the first to suggest that
the cosmological constant should be non-zero if anthropic selection is
at work. The first quantitative attempts based on the principle of mediocrity
were by me and by George Efstathiou. A few years later, it came as a complete
shock to most physicists when observational evidence for a nonzero cosmological
constant was first announced. It was in a rough agreement with the anthropic
expectations. The most recent calculations, using the data from WMAP satellite,
give the probability of about 25% for the observed value — a good
agreement for a statistical model of this kind. Moreover, despite numerous
attempts, no other plausible explanation for the observed cosmological
constant has been suggested.

Critics often
argue that anthropic predictions cannot be falsified, but this is simply
not true. If the cosmological constant turned out to be an order of magnitude
smaller than its actual value, the underlying model would be ruled out
at 95% confidence level.

Another recent
application of the principle of mediocrity, unrelated to string theory**,** is
to the amount of dark matter in the universe. As its name suggests, dark
matter cannot be seen directly, but its presence is manifested by the gravitational
pull it exerts on visible objects. The composition of dark matter is unknown.
One of the best motivated hypotheses is that it is made up of very light
particles called axions. The density of axionic dark matter is set by quantum
fluctuations during inflation and varies from one place in the universe
to another. Its value affects the formation of galaxies; hence there
is an anthropic selection effect. In a recent paper, Max Tegmark, Anthony
Aguirre, Martin Rees and Frank Wilczek calculated the resulting probability
distribution. They found that the observed value of the dark matter density
is close to the peak of the bell curve, in excellent agreement with the
theory.

~

The reluctance
of many physicists to embrace anthropic explanations is easy to understand.
The standard of accuracy in physics is very high, you might say unlimited.
For example, the theoretically calculated magnetic moment of the electron
agrees with the observed value up to the 11th decimal point. In fact, failure
to agree at this level would be a cause for alarm, since any disagreement,
even in the 11th decimal point, would indicate some gap in our understanding
of the electron.

Anthropic predictions
are not like that. The best we can hope for is to calculate the statistical
bell curve. Further improvements in the calculation of that curve will
not lead to a dramatic increase in the accuracy of the prediction. If the
observed value falls within the predicted range, there will still be a
lingering doubt that this happened by sheer dumb luck. If it doesn't, there
will be doubt that the theory might still be correct, but we just happened
to be among a few percent of observers at the tails of the bell curve.

It's little
wonder that, given a choice, physicists would not give up their old paradigm
in favor of anthropic selection. But nature has already made her choice.
We only have to find out what it is. If the constants of nature are variable,
then, whether we like it or not, the best we can do is to make statistical
predictions based on the principle of mediocrity.

The observed
value of the cosmological constant gives a strong indication that there
is indeed a huge eternally inflating universe out there, with constants
varying from one region to another. The evidence for this view is, of course,
indirect, as it will always be. This is a circumstantial case, where we
are not going to hear eyewitness accounts or see the murder weapon. But
if, with some luck, we make a few more successful predictions, we may still
be able to prove the case beyond reasonable doubt.

[Excerpted from *Many
Worlds in One* by Alex Vilenkin. Hill and Wang, 2006. Copyright © Alex
Vilenkin. All rights reserved.]