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 some 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 this
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 an enormous 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.
In this
scenario, decay of the false vacuum plays the role of the big bang.
It is not 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. Inflation is a runaway process
that has stopped in our neighborhood, but that 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"
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 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.] |
