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increase with time. High-entropy states greatly outnumber
low-entropy ones; almost any change to the system will land it in a
higher-entropy state, simply by the luck of the draw. That is why
milk mixes with coffee but never unmixes. Although it is physically
possible for all the milk molecules to spontaneously conspire to
arrange themselves next to one another, it is statistically very
unlikely. If you waited for it to happen of its own accord as
molecules randomly reshuffled, you would typically have to wait much
longer than the current age of the observable universe. The arrow of
time is simply the tendency of systems to evolve toward one of the
numerous, natural, high-entropy states.

But explaining why low-entropy states evolve into high-entropy
states is different from explaining why entropy is increasing in our
universe. The question remains: Why was the entropy low to start
with? It seems very unnatural, given that low-entropy states are so
rare. Even granting that our universe today has medium entropy, that
does not explain why the entropy used to be even lower. Of all the
possible initial conditions that could have evolved into a universe
like ours, the overwhelming majority have much higher entropy, not
lower [see "The Arrow of Time," by David Layzer; Scientific
American, December 1975].

In other words, the real challenge is not to explain why the entropy
of the universe will be higher tomorrow than it is today but to
explain why the entropy was lower yesterday and even lower the day
before that. We can trace this logic all the way back to the
beginning of time in our observable universe. Ultimately, time
asymmetry is a question for cosmology to answer.

The Disorder of Emptiness

The early universe was a remarkable place. All the particles that
make up the universe we currently observe were squeezed into an
extraordinarily hot, dense volume. Most important, they were
distributed nearly uniformly throughout that tiny volume. On
average, the density differed from place to place by only about one
part in 100,000. Gradually, as the universe expanded and cooled, the
pull of gravity enhanced those differences. Regions with slightly
more particles formed stars and galaxies, and regions with slightly
fewer particles emptied out to form voids.

Clearly, gravity has been crucial to the evolution of the universe.
Unfortunately, we do not fully understand entropy when gravity is
involved. Gravity arises from the shape of spacetime, but we do not
have a comprehensive theory of spacetime; that is the goal of a
quantum theory of gravity. Whereas we can relate the entropy of a
fluid to the behavior of the molecules that constitute it, we do not
know what constitutes space, so we do not know what gravitational
microstates correspond to any particular macrostate.

Nevertheless, we have a rough idea of how entropy evolves. In
situations where gravity is negligible, such as a cup of coffee, a
uniform distribution of particles has a high entropy. This condition
is a state of equilibrium. Even when particles reshuffle themselves,
they are already so thoroughly mixed that nothing much seems to
happen macroscopically. But if gravity is important and the volume
is fixed, a smooth distribution has relatively low entropy. In this
case, the system is very far from equilibrium. Gravity causes
particles to clump into stars and galaxies, and entropy increases
noticeably--consistent with the second law.

Indeed, if we want to maximize the entropy of a volume when gravity
is active, we know what we will get: a black hole. In the 1970s
Stephen Hawking of the University of Cambridge confirmed a
provocative suggestion of Jacob Bekenstein, now at the Hebrew
University of Jerusalem, that black holes fit neatly into the second
law. Like the hot objects that the second law was originally
formulated to describe, black holes emit radiation and have
entropy--a lot of it. A single million-solar-mass black hole, such
as the one that lives at the center of our galaxy, has 100 times the
entropy of all the ordinary particles in the observable universe.

Eventually even black holes evaporate by emitting Hawking radiation.
A black hole does not have the highest possible entropy--but just
the highest entropy that can be packed into a certain volume. The
volume of space in the universe, however, appears to be growing
without limit. In 1998 astronomers discovered that cosmic expansion
is accelerating. The most straightforward explanation is the
existence of dark energy, a form of energy that exists even in empty
space and does not appear to dilute away as the universe expands. It
is not the only explanation for cosmic acceleration, but attempts to
come up with a better idea have so far fallen short.

If dark energy does not dilute away, the universe will expand
forever. Distant galaxies will disappear from view [see "The End of
Cosmology?" by Lawrence M. Krauss and Robert J. Scherrer; Scientific
American, March]. Those that do not will collapse into black holes,
which in turn will evaporate into the surrounding gloom as surely as
a puddle dries up on a hot day. What will be left is a universe that
is, for all intents and purposes, empty. Then and only then will the
universe truly have maxed out its entropy. The universe will be in
equilibrium, and nothing much will ever happen.

It may seem strange that empty space has such a huge entropy. It
sounds like saying that the most disorganized desk in the world is a
completely empty desk. Entropy requires microstates, and at first
glance empty space does not have any. In actuality, though, empty
space has plenty of microstates--the quantum-gravitational
microstates built into the fabric of space. We do not yet know what
exactly these states are, any more than we know what microstates
account for the entropy of a black hole, but we do know that in an
accelerating universe the entropy within the observable volume
approaches a constant value proportional to the area of its
boundary. It is a truly enormous amount of entropy, far greater than
that of the matter within that volume.

Past vs. Future

The striking feature of this story is the pronounced difference
between the past and the future. The universe starts in a state of
very low entropy: particles packed together smoothly. It evolves
through a state of medium entropy: the lumpy distribution of stars
and galaxies we see around us today. It ultimately reaches a state
of high entropy: nearly empty space, featuring only the occasional
stray low-energy particle.

Why are the past and future so different? It is not enough to simply
posit a theory of initial conditions--a reason why the universe
started with low entropy. As philosopher Huw Price of the University
of Sydney has pointed out, any reasoning that applies to the initial
conditions should also apply to the final conditions, or else we
will be guilty of assuming the very thing we were trying to
prove--that the past was special. Either we have to take the
profound asymmetry of time as a blunt feature of the universe that
escapes explanation, or we have to dig deeper into the workings of
space and time.

Many cosmologists have tried to attribute the time asymmetry to the
process of cosmological inflation. Inflation is an attractive
explanation for many basic features of the universe. According to
this idea, the very early universe (or at least some part of it) was
filled not with particles but rather with a temporary form of dark
energy, whose density was enormously higher than the dark energy we
observe today. This energy caused the expansion of the universe to
accelerate at a fantastic rate, after which it decayed into matter
and radiation, leaving behind a tiny wisp of dark energy that is
becoming relevant again today. The rest of the story of the big
bang, from the smooth primordial gas to galaxies and beyond, simply
follows.

The original motivation for inflation was to provide a robust
explanation for the finely tuned conditions in the early
universe--in particular, the remarkably uniform density of matter in
widely separated regions. The acceleration driven by the temporary
dark energy smooths out the universe almost perfectly. The prior
distribution of matter and energy is irrelevant; once inflation
starts, it removes any traces of the preexisting conditions, leaving
us with a hot, dense, smooth early universe.

The inflationary paradigm has been very successful in many ways. Its
predictions of slight deviations from perfect uniformity agree with
observations of density variations in the universe. As an
explanation for time asymmetry, however, cosmologists increasingly
consider it a bit of a cheat, for reasons that Roger Penrose of the
University of Oxford and others have emphasized. For the process to
work as desired, the ultradense dark energy had to begin in a very
specific configuration. In fact, its entropy had to be fantastically
smaller than the entropy of the hot, dense gas into which it
decayed. That implies inflation has not really solved anything: it
"explains" a state of unusually low entropy (a hot, dense, uniform
gas) by invoking a prior state of even lower entropy (a smooth patch
of space dominated by ultradense dark energy). It simply pushes the
puzzle back a step: Why did inflation ever happen?

One of the reasons many cosmologists invoke inflation as an
explanation of time asymmetry is that the initial configuration of
dark energy does not seem all that unlikely. At the time of
inflation, our observable universe was less than a centimeter
across. Intuitively, such a tiny region does not have many
microstates, so it is not so improbable for the universe to stumble
by accident into the microstate corresponding to inflation.
Unfortunately, this intuition is misleading. The early universe,
even if it is only a centimeter across, has exactly the same number
of microstates as the entire observable universe does today.
According the rules of quantum mechanics, the total number of
microstates in a system never changes. (Entropy increases not
because the number of microstates does but because the system
naturally winds up in the most generic possible macrostate.) In
fact, the early universe is the same physical system as the late
universe. One evolves into the other, after all.

Among all the different ways the microstates of the universe can
arrange themselves, only an incredibly tiny fraction correspond to a
smooth configuration of ultradense dark energy packed into a tiny
volume. The conditions necessary for inflation to begin are
extremely specialized and therefore describe a very low entropy
configuration. If you were to choose configurations of the universe
randomly, you would be highly unlikely to hit on the right
conditions to start inflation. Inflation does not, by itself,
explain why the early universe has a low entropy; it simply assumes
it from the start.

A Time-Symmetric Universe

Thus, inflation is of no help in explaining why the past is
different from the future. One bold but simple strategy is just to
say: perhaps the very far past is not different from the future
after all. Perhaps the distant past, like the future, is actually a
high-entropy state. If so, the hot, dense state we have been calling
"the early universe" is actually not the true beginning of the
universe but rather just a transitional state between stages of its
history.
Some cosmologists imagine that the universe went through a "bounce."
Before this event, space was contracting, but instead of simply
crashing to a point of infinite density, new physical
principles--quantum gravity, extra dimensions, string theory or
other exotic phenomena--kicked in to save the day at the last
minute, and the universe came out the other side into what we now
perceive as the big bang. Though intriguing, bouncing cosmologies do
not explain the arrow of time. Either entropy was increasing as the
prior universe approached the crunch--in which case the arrow of
time stretches infinitely far into the past--or the entropy was
decreasing, in which case an unnatural low-entropy condition
occurred in the middle of the universe's history (at the bounce).
Either way, we have again passed the buck on the question of why the
entropy near what we call the big bang was small.

Instead let us suppose that the universe started in a high-entropy
state, which is its most natural state. A good candidate for such a
state is empty space. Like any good high-entropy state, the tendency
of empty space is to just sit there, unchanging. So the problem is:
How do we get our current universe out of a desolate and quiescent
spacetime? The secret might lie in the existence of dark energy.

In the presence of dark energy, empty space is not completely empty.
Fluctuations of quantum fields give rise to a very low
temperature--enormously lower than the temperature of today's
universe but nonetheless not quite absolute zero. All quantum fields
experience occasional thermal fluctuations in such a universe. That
means it is not perfectly quiescent; if we wait long enough,
individual particles and even substantial collections of particles
will fluctuate into existence, only to once again disperse into the
vacuum. (These are real particles, as opposed to the short-lived
"virtual" particles that empty space contains even in the absence of
dark energy.)

Among the things that can fluctuate into existence are small patches
of ultradense dark energy. If conditions are just right, that patch
can undergo inflation and pinch off to form a separate universe all
its own--a baby universe. Our universe may be the offspring of some
other universe.

Superficially, this scenario bears some resemblance to the standard
account of inflation. There, too, we posit that a patch of
ultradense dark energy arises by chance, igniting inflation. The
difference is the nature of the starting conditions. In the standard
account, the patch arose in a wildly fluctuating universe, in which
the vast bulk of fluctuations produced nothing resembling inflation.
It would seem to be much more likely for the universe to fluctuate
straight into a hot big bang, bypassing the inflationary stage
altogether. Indeed, as far as entropy is concerned, it would be even
more likely for the universe to fluctuate straight into the
configuration we see today, bypassing the past 14 billion years of
cosmic evolution.

In our new scenario, the preexisting universe was never randomly
fluctuating; it was in a very specific state: empty space. What this
theory claims--and what remains to be proved--is that the most
likely way to create universes like ours from such a preexisting
state is to go through a period of inflation, rather than
fluctuating there directly. Our universe, in other words, is a
fluctuation but not a random one.

Emit fo Worra

This scenario, proposed in 2004 by Jennifer Chen of the University
of Chicago and me, provides a provocative solution to the origin of
time asymmetry in our observable universe: we see only a tiny patch
of the big picture, and this larger arena is fully time-symmetric.
Entropy can increase without limit through the creation of new baby
universes.

Best of all, this story can be told backward and forward in time.
Imagine that we start with empty space at some particular moment and
watch it evolve into the future and into the past. (It goes both
ways because we are not presuming a unidirectional arrow of time.)
Baby universes fluctuate into existence in both directions of time,
eventually emptying out and giving birth to babies of their own. On
ultralarge scales, such a multiverse would look statistically
symmetric with respect to time--both the past and the future would
feature new universes fluctuating into life and proliferating
without bound. Each of them would experience an arrow of time, but
half would have an arrow that was reversed with respect to that in
the others.

The idea of a universe with a backward arrow of time might seem
alarming. If we met someone from such a universe, would they
remember the future? Happily, there is no danger of such a
rendezvous. In the scenario we are describing, the only places where
time seems to run backward are enormously far back in our past--long
before our big bang. In between is a broad expanse of universe in
which time does not seem to run at all; almost no matter exists, and
entropy does not evolve. Any beings who lived in one of these
time-reversed regions would not be born old and die young--or
anything else out of the ordinary. To them, time would flow in a
completely conventional fashion. It is only when comparing their
universe to ours that anything seems out of the ordinary--our past
is their future, and vice versa. But such a comparison is purely
hypothetical, as we cannot get there and they cannot come here.

As of right now, the jury is out on our model. Cosmologists have
contemplated the idea of baby universes for many years, but we do
not understand the birthing process. If quantum fluctuations could
create new universes, they could also create many other things--for
example, an entire galaxy. For a scenario like ours to explain the
universe we see, it has to predict that most galaxies arise in the
aftermath of big bang-like events and not as lonely fluctuations in
an otherwise empty universe. If not, our universe would seem highly
unnatural.

But the take-home lesson is not any particular scenario for the
structure of spacetime on ultralarge scales. It is the idea that a
striking feature of our observable cosmos--the arrow of time,
arising from very low entropy conditions in the early universe--can
provide us with clues about the nature of the unobservable universe.

As mentioned at the beginning of this article, it is nice to have a
picture that fits the data, but cosmologists want more than that: we
seek an understanding of the laws of nature and of our particular
universe in which everything makes sense to us. We do not want to be
reduced to accepting the strange features of our universe as brute
facts. The dramatic time asymmetry of our observable cosmos seems to
be offering us a clue to something deeper--a hint to the ultimate
workings of space and time. Our task as physicists is to use this
and other clues to put together a compelling picture.

If the observable universe were all that existed, it would be nearly
impossible to account for the arrow of time in a natural way. But if
the universe around us is a tiny piece of a much larger picture, new
possibilities present themselves. We can conceive of our bit of
universe as just one piece of the puzzle, part of the tendency of
the larger system to increase its entropy without limit in the very
far past and the very far future. To paraphrase physicist Edward
Tryon, the big bang is easier to understand if it is not the
beginning of everything but just one of those things that happens
from time to time.

Other researchers are working on related ideas, as more and more
cosmologists are taking seriously the problem posed by the arrow of
time. It is easy enough to observe the arrow--all you have to do is
mix a little milk into your coffee. While sipping it, you can
contemplate how that simple act can be traced all the way back to
the beginning of our observable universe and perhaps beyond.

This story was originally printed with the title "The Cosmic Origins
of Time's Arrow"