New York Times Science Online
June 26, 2001 


Back to Basics: How Did Space Get Its Dimensions?

By GEORGE JOHNSON





Beginnings of Space 


In the beginning, there was little need for physicists.
The universe, poised at the moment of creation, was
ruled not by the four different forces observed in
later times, but by just a single superforce. Instead
of a smattering of different particles, there was only
the tiny primordial mass — the grandmother of all
particles — ready to explode in the Big Bang.

Then came the detonation, giving scientists some
messiness to study. As the newborn universe cooled,
the single force splintered into four forces,
radiating through the four dimensions of space and
time, and the various classes of particles sprang
forth one by one.

This scientific creation story, embraced by physicists
and cosmologists alike, seems to account for just
about everything — with one glaring exception: Where
did the dimensions come from?

Now some physicists are adding a new touch to the
Edenic tale. A paper published last month in Physical
Review Letters suggests that the dimensions, like the
forces and particles, may have popped into being as
the universe cooled. Though the idea is still in a
very preliminary form, physicists are intrigued by the
implication that reality may have started with just a
single dimension: time. As temperatures dropped in the
moments after the primordial explosion, the spatial
dimensions — height, length and breadth — crystallized
into existence. Creation was not just a matter of "let
there be light," but "let there be space" as well.

"For the first time, this gives us an opportunity to
investigate what we mean by space," said Dr. Andrew G.
Cohen, a physicist at Boston University who wrote the
paper with Dr. Nima Arkani-Hamed of the University of
California at Berkeley and Dr. Howard Georgi of
Harvard. "We all got very excited when we realized
that this was a way to get a handle on that idea."

For decades physicists have been inclined to take
space for granted as an eternal backdrop, the stage on
which particles and forces commune and reality
unfolds. The new study is part of a growing attempt to
reverse figure and ground. In this emerging view, it
is space that is secondary, arising from the
interaction of new kinds of particles — particles that
came into existence only as the universe cooled.
Throughout the field, theorists are re-examining what
they had taken for granted: the nature of space, and
even time. A team based at the Fermi National
Accelerator Center in Batavia, Ill., has come up with
its own version of dimension- generating particles.

"Everybody thinks space-time should be an output
rather than an input of a fundamental theory," said
Dr. Nathan Seiberg, a theorist at the Institute for
Advanced Study in Princeton, N.J.

The title of the new work, "(De) Constructing
Dimensions," has a postmodernist ring that one might
expect in the table of contents of a journal of
literary criticism. But the densely mathematical
paper, with its talk of "Weyl fermions," "cyclic
symmetries," "Kaluza-Klein excitations" and other
arcana, is a precise attempt to get to the heart of
what is meant by a dimension. If the theory is right,
Dr. Arkani-Hamed said, "Space can appear and
disappear, depending on the energy."

The research was motivated by an attempt to explain
the origin of the weird extra dimensions required by
string theory, an attempt to unite the laws of physics
into a single framework. According to this view,
everything is generated from the interactions of tiny
stringlike objects, but the theory works only if they
are allowed 10 dimensions to play around in. Dr.
Arkani-Hamed and his colleagues set out to shed some
light on where the extra ones might have come from.
But, he said, the ultimate aim is to take the idea
even further: "It is tempting to think that our own
familiar dimensions are also made this way."

Dr. Steve Giddings of the University of California at
Santa Barbara suggested that even more interesting
possibilities could exist. "Perhaps one can get even
more bizarre models with different dimensions in
different places," he said.

Explaining how fundamental ideas, like space, emerge
from particles is a tradition in physics. Atoms are
made of protons, neutrons and electrons. Light is
carried by photons, gravity by gravitons, the strong
nuclear force by gluons. At the extreme energies and
temperatures of the Big Bang, the matter-making
particles and the force-carrying particles were fused
together into a single primal substance, separating
into individual entities only later on.

As physicists reach higher and higher energies with
their particle accelerators, they feel that they are
approaching temperatures and energies that existed
earlier in the universe, edging closer to the origins
of the particles and forces.

So far, space has been resistant to this approach. It
remains the ineffable something that is just there.

To picture how space might have been created on the
fly by particles, imagine an early world with no
dimensions, consisting of a single point. Motion would
not exist in this claustrophobic realm. There would be
no directions in which to move. There might be other
point worlds as well, each isolated in the void.

Suppose that as the cooling began, it led to the
appearance of a set of particles that carried a force
allowing an inhabitant imprisoned in a dot world to
move from its own point to the next and the next,
following the path of steppingstones. The result would
be a single-dimensional world shaped like a wavy line.

The inhabitants could go forward and backward but
nowhere else. Other line worlds might also have formed
at this stage, but all would be mutually inaccessible
— until the universe cooled further and the
dimension-creating particles grew strong enough to
allow motion in a new direction.

Now the one-dimensional-line worlds could link up to
form two- dimensional worlds shaped like undulating
planes. The inhabitants of each realm would be able to
move left and right and back and forth, but not up and
down.

Let the universe cool another notch, and particles
would grow stronger, opening up motion in the third
dimension. The disconnected planar worlds would be
linked to form familiar three-dimensional space, where
one can strike out in three different directions.

But why stop there? Before the universe reached its
present state, perhaps other dimensions emerged as
well — maybe even the extra ones required by string
theory.

As physicists usually explain it, these additional
dimensions aren't evident because they are curled up
too small to detect. Imagine again a single dimension
as a line, but join the ends to form a loop. A being
living on one of these tiny circles could hop from
point to point around the circumference. But when it
returned to the starting point, it would have covered
a distance only about one-thousandth the size of a
proton.

From a unifier's point of view, one of the most
interesting things about the new theory is the way it
conflates the seemingly very different notions of
dimensions and forces. A dimension arises when a force
is generated that allows movement into a new domain. 

Dr. Arkani-Hamed said the hypothetical particles
behind these forces would be similar to the gluons
that carry the strong nuclear force. Like gluons, the
dimension-creating particles might be very weak at
high energies and stronger at lower energies. That
would explain why there were fewer dimensions in the
heat of the Big Bang.

Of course it is possible that the theory explains
nothing at all — that its array of hypothetical
particles and forces is just a mesmerizing
mathematical plaything. "These ideas are extremely
speculative, but in a generic way they should be
testable," said Dr. Joseph Lykken, a theorist at
Fermilab. "High-energy colliders might turn up
evidence that quarks or gluons or photons are moving
in fewer dimensions, at the highest energies that we
are now producing. That would be relatively
straightforward to see."

Even if the theory doesn't ultimately survive as a
description of the way space really came about, it
might serve as a tool for studying what particles do
at extremely high energies. Generally, the higher the
energy, the harder a problem is to solve. With the new
technique, cranking up the energy makes some of the
dimensions melt away, simplifying the calculations.

"To coin a bad metaphor, it is a bit like television,
in that you can view the world of extra dimensions
without leaving the comfort of your own world," said
Dr. Christopher T. Hill, a theorist at Fermilab. He
and a colleague, Dr. Jing Wang, along with Dr. Stefan
Pokorski of Warsaw University and Dr. Hsin-Chia Cheng
of the University of Chicago, independently came up
with a similar scheme for generating dimensions from
particles. But Dr. Hill has a more pragmatic
perspective.

"We are very excited about this," he said. "However, I
differ somewhat philosophically with my competitors. I
see this as a very useful tool, but it is not yet
clear whether it is of fundamental importance."

Dr. Arkani-Hamed said what particularly attracted him
was the notion that space might have emerged from a
universe that started with just time. He hopes it may
be possible someday to explain how time arose as well.
"It sure looks like space is not going to survive in
some ultimate theory," he said, "and that makes it
likely that time will not survive either."