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Hunting for Higher Dimensions
Source: From Science News, Vol. 157, No. 8, February 19, 2000, p.
122. By P. Weiss
19th Feb 2000
 Experimenters scurry
to test new theories suggesting that extra dimensions are detectable.
Energy spike from a gluon stands alone because a graviton has fled into
extra dimensions, taking energy with it. This simulation models an experiment
planned for the Tevatron accelerator, slated to start up again in 2001.
(Maria Spiropulu/Harvard U.)
Only 2 years ago, the idea of extra dimensions inhabited a nebulous
region somewhere between physics and science fiction.
Many physicists had already begun to see the up-and-coming string theory
as the next major step for theoretical physics. In that theory, everything
in the universe is composed of tiny loops, or strings, of energy vibrating
in a space-time that has six or seven extra dimensions beyond the seemingly
endless three standard dimensions of space and one of time. Conveniently,
however, those extra dimensions are compactified, as physicists say,
crumpled up in a space so small as to be unobservable.
The idea that extra dimensions might be larger-perhaps detectable-was
something that scientists mostly talked about "late at night, after
a lot of wine," says Gordon L. Kane, a theorist from the University
of Michigan in Ann Arbor. Kane therefore felt he was walking on the
wild side when he penned a fictional news story about experimenters
discovering extra dimensions.
Kane's story, which appeared in the May 1998 Physics Today, was one
of three winners of an essay contest sponsored by that magazine. Basing
his tale on some innovative theorizing published in 1990 by Ignatius
Antoniadis of the cole Polytechnique in Palaiseau, France, Kane wrote
of peculiar sprays of particles yielding "startling data." He set his
experiments in 2011 at a European accelerator, known as the Large Hadron
Collider (LHC), which is currently under construction.
The results could imply the existence of one or two extra spatial dimensions,
the story stated, "a surprise to everyone."
Even by the time his article came out, however, the possibility no longer
seemed quite as surprising as it had when he wrote it a few months earlier.
Between the submission of Kane's story and its publication, two theoretical
studies had come out that suddenly pushed the idea of relatively large
extra dimensions into the spotlight.
One study came from a team at CERN, the European Laboratory for Particle
Physics in Geneva where LHC is being built. It examined the consequences
of extra dimensions being 10,000 trillion times larger than the extra
dimensions of string theory are typically imagined to be. At the larger
size, still only about one-ten-thousandth the size of a proton, the
extra dimensions might produce effects detectable by the current generation
of particle accelerators or their immediate successors, such as LHC,
the researchers found.
The other study argued that certain types of extra dimensions could
be even larger, as grand as a millimeter. They might then be accessible
not only in colliders but in small-scale, table-top experiments as well,
say researchers at Stanford University and the International Center
for Theoretical Physics (ICTP) in Trieste, Italy.
Today, teams of experimentalists in both the United States and Europe
are searching for the signatures of extra dimensions. The hunt for such
indicators "is certainly one of the best chances of making a very spectacular
discovery in the next couple of years," says Joseph Lykken of the Fermi
National Accelerator Laboratory in Batavia, Ill.
Meanwhile, the wave of novel, extradimension theory continues to roll
on. In the latest splash, researchers have proposed extra dimensions
of infinite size.
Imagining any of these extra dimensions isn't easy. Depending on how
many extra dimensions there are, physicists say, they might curl into
a simple loop or sphere or bend into a tortuous 6-dimensional pretzel
popular in string theory. Every point in the traditional, apparently
4-dimensional universe is then a tiny, multidimensional volume. Theorists
suggest that an extra dimension might be on the order of 10-35 meter.
Physicists also measure the extra dimensions in terms of the energy
needed to probe them. A particle accelerated to 1 trillion electron
volts (TeV) has, according to standard arguments from quantum mechanics,
a wave aspect with a wavelength of about 2 x 10-19 m. It
can therefore explore facets of the subatomic world on that scale. Doubling
the energy means seeing features half that size, and so on. So far,
the smallest length scale observable with accelerators is a little greater
than 10-19 m.
The idea of extra dimensions dates back to at least the 1920s. At that
time, physicist Oskar Klein, building upon work by mathematician Theodor
Kaluza, added a curled-up fifth dimension to the familiar universe in
an ingenious but unsuccessful attempt to unite the forces of electromagnetism
and gravity.
Physicists believe that the four forces-electromagnetic, weak, strong,
and gravitational-were joined as a single superforce at the time of
the Big Bang. In theory, they could merge only if the forces were about
the same strength under conditions of high energy. However, gravity
is much weaker than the others.
As some researchers today explore extra dimensions, they are on the
lookout for implications regarding unification of the four forces. Other
scientists striving for models that unify the forces have found extra
dimensions a useful tool.
Testing unification theories directly appears to be impossible, however,
since the phenomenon would only occur at energies in the range of 1013
to 1016 TeV. The highest-energy collisions achieved in accelerators
today approach only 1 TeV.
 Oskar Klein (left) proposed
in the 1920s that hidden spatial dimensions might influence observed
physics. He poses with physicists George Uhlenbeck (middle) and Samuel
Goudsmit in 1926 at the University of Leiden, the Netherlands. (AIP
Emilio Segr Visual Archives)
CERN theorists Keith R. Dienes, Emilian Dudas, and Tony Gherghetta wondered
what would happen if they uncurled one or more of the extra dimensions
in string theory to 10-19 m, the largest size that would not already
have been detected. To their surprise, they discovered that the three
nongravitational forces could unify in the energy range of 1 TeV. This
unification could then be observed directly in LHC and indirectly in
less-powerful colliders. They posted their study on the physics
archive maintained by Los Alamos (N.M.) National Laboratory in March
1998.
For physicists, an energy of 1 TeV was already a landmark. Both theory
and experiment had established that a mixing of the electromagnetic
and weak forces begins to take place a little below that energy level.
Physicists have been troubled because unification of even three forces
requires much higher energies. They refer to this puzzle as the hierarchy
problem. Scientists at Stanford University and ICTP used extra dimensions
in their attempt to solve the hierarchy problem. They focused first
on gravity and looked for a way to make it comparable in strength to
the other forces at an energy of about 1 TeV.
They accomplished that feat by hypothesizing extra dimensions that affect
only gravity and are as large as 1 mm. Only a yawning gap in the scientific
record makes such extra dimensions feasible. While physicists have probed
the other forces of nature down to nearly 10-19 m, they've made extensive
measurements of gravity only down to about 1 centimeter.
To describe extra dimensions that would affect gravity alone, the Stanford-Trieste
researchers made use of entities known as branes. Those complex, membranous
objects, which can have many spatial dimensions themselves, have become
a central part of string theory. In some versions of the theory, the
universe itself is a brane with three spatial dimensions-a 3-brane-moving
through a higher-dimensional space-time.
String theory dictates that any extra dimensions outside a brane affect
only gravity. In other words, just the force-carrying particles of gravity,
called gravitons, could travel in the space-time beyond the brane, leaving
the other forces confined to the brane. By contrast, extra dimensions
associated with the brane influence all the forces.
Therefore, even if gravity boasts an intrinsic strength similar to that
of the other three forces, because it diffuses throughout the external
space-time, also called the bulk, its apparent strength in the 3-brane
universe is much reduced.
Any extra dimensions affecting gravity would alter Isaac Newton's inverse-square
law, which holds that objects attract each other with a force inversely
proportional to the square of the distance between them. The theorists
calculated that one extra dimension in the bulk would have a scale of
100 million kilometers-about the distance from Earth to the sun. That
option isn't feasible because Earth's orbit obeys the inverse-square
law. If there were two extra dimensions, however, each would have a
scale of 0.1 to 1.0 mm-large enough to be detectable but small enough
not to be ruled out by tests of the inverse-square law to date. With
more extra dimensions, the length scale shrinks far below the millimeter
range.
Combining both approaches, "you wind up with a very compelling picture,"
says Dienes, a CERN team member, now at the University of Arizona in
Tucson. "These two scenarios together lower all the fundamental high-energy
scales of physics."
Inspired by these proposals, experimenters are looking for signs of
extra dimensions both at accelerators and in gravitational laboratories.
Most of the accelerator searches have begun in the past year, says Kingman
Cheung of the University of California, Davis. Before that, researchers
had been translating the theorists' proposals into concrete predictions.
Cheung presented a summary of ongoing and proposed searches last December
at the Seventh International Symposium on Particles, Strings, and Cosmology
'99 (PASCOS '99) conference at Tahoe City, Calif.
To find extra dimensions of the type studied by the CERN group, experimenters
are on the alert for what they call Kaluza-Klein towers, which are associated
with carriers of the nongravitational forces, such as the photon of
electromagnetism and the Z boson of the weak force. Excitations of energy
within the extra dimensions would turn each of these carriers into a
family of increasingly massive clones of the original particle-analogous
to the harmonics of a musical note.
"I like to think of these Kaluza-Klein states as echoes off the fifth
dimension," Dienes says.
Because these towers tend to magnify the strengths of the forces, their
influence might even be detected at energies below those at which the
towers themselves become apparent, researchers say.
 Some theorists envision
the universe as multidimensional space-time embedding a membranous entity,
called a brane, also of multiple dimensions. Diagram depicts familiar
3-dimensional space (time not shown) as a vertical line. At every point
along line, one extra dimension curls around with a radius (r) of no
more that about 10-19 meter. Perpendicular to every point of the brane
extends the bulk, another extra dimension. (Adapted from Dienes et al.,
Nuclear Physics B)
Going back through the data from an earlier run of CERN's Large Electron-Positron
Collider (LEP), researchers have found no evidence of such extradimensional
influences at up to an energy of 4 TeV, Cheung told Science News. The
CERN team's extra dimensions must therefore be smaller than 0.5 x 10-19
m. The towers might become detectable in 6 or 7 years, when the completed
LHC will be able to probe energies of up to 14 TeV, he says. Gravity
doesn't lend itself to measurement in accelerators because the other
forces overwhelm its tiny influence on particle interactions. "The graviton
is so weakly interacting, it doesn't enter the picture," Cheung says.
Instead, physicists typically make precision measurements of gravity
by using extremely delicate experiments, named after the 18th-century
scientist Henry Cavendish, that determine the force between two suspended
masses. At very small separations, however, electrostatic influences
and molecular interactions known as van der Waals forces again swamp
the gravitational effects.
By conducting Cavendish experiments with extremely sensitive equipment,
at least two teams of scientists are testing for millimeter-scale extra
dimensions. If those dimensions exist, gravity in the submillimeter
range would increase not according to Newton's inverse-square law but
in inverse proportion to the fourth power of the separation.
Researchers at Stanford University led by Aharon Kapitulnik have developed
a micromachined cantilever that reacts to the gravitational tug of an
arm swinging back and forth 80 micrometers beneath it. A laser detects
motion in the cantilever, which is chilled to 4 kelvins to reduce random
thermal motion.
The experimenters intend to measure not only gravity but also van der
Waals and other short-distance forces. However, because of the hubbub
over extra dimensions right now, "we are neglecting all other experiments,"
Kapitulnik says.
Similarly in Boulder, Colo., a tungsten strip resembling a diving board
weighing a few grams sits in a vacuum over another strip of tungsten.
As a motor rapidly wiggles the diving board up and down, scientists
look for motion in the strip below. A next-generation instrument operating
at 4 K will eventually replace the current room-temperature version,
says John C. Price of the University of Colorado, who leads the effort.
Given the dearth of knowledge about gravity in the subcentimeter range,
the group is looking for any kind of deviation from expectations, not
just extradimensional effects, he says. Nonetheless, the excitement
about extra dimensions helps spur the group on, Price says.
If the strength of gravity takes a sharp turn upward at around 1 TeV,
as the Stanford-Trieste scenario implies, an opportunity opens for testing
this theory also in accelerators. Collisions at such energies could
produce gravitons in large numbers, and some of these particles would
immediately vanish into the extra dimensions, carrying energy with them.
Experimenters would look for an unusual pattern of so-called missing
energy events. This and more subtle effects of extra dimensions could
show up at existing accelerators, such as LEP and the Tevatron at Fermilab,
only if the dimensions have scales nearly as big as a millimeter. The
powerful LHC will greatly improve the chances for detecting missing
energy events and other prominent extradimension effects.
Despite his award-winning literary fling 2 years ago, Kane has soured
on large extra dimensions. He remains a firm believer in six or seven
extra dimensions, he says, but only at about 10-35 m. The theory is
cleaner that way, he argues, with just the three familiar, very large
spatial dimensions, and the rest reduced to the scale of strings themselves.
"If I was trying to win a contest today, I'd write on something else,"
he says.
By contrast to Kane's insistence on small extra dimensions, one pair
of researchers recently came up with an argument for extra dimensions
of unlimited extent, similar in size to the familiar dimensions. These
scientists noted that the 3-brane, like any other object with energy
or mass, would warp space-time and thereby confine gravitons to a region
just slightly larger than the brane.
The warping would also localize extra dimensions' effects on Newton's
inverse-square law of gravity to subcentimeter distances not yet explored.
Such localization allows the dimensions themselves to stretch indefinitely,
argue Lisa Randall of the Massachusetts Institute of Technology and
Princeton University and Raman Sundrum of Boston University. This novel
idea, described in the Dec. 6, 1999 Physical Review Letters, has many
implications and may suggest new indicators of extra dimensions. The
work has already sparked dozens of journal and online articles.
Whether or not large extra dimensions actually show up in the laboratory,
researchers are sparing no effort to push the limits of one hidden dimension
on which everyone agrees: imagination.
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