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鈥淎ll modern thought,鈥� the French philosopher Michel Foucault once claimed,
鈥渋s permeated by the idea of thinking the unthinkable.鈥� That sounds about right,
especially when it comes to modern physics. Rifle through the latest research
journals, and you鈥檒l see a magnificent celebration of the human imagination.
According to physicists, the Universe has 11 dimensions, or maybe 26, although
most are curled up so tightly that you can鈥檛 see them. Subatomic particles a
billion times smaller than a speck of dust exist in several places at once and
capriciously flit backward and forward through time. Some physicists even think
there might be bizarre links between gravity, the weird properties of the
quantum world, and that most enduring of human mysteries鈥攃onsciousness.
Thinking on the edge has become so fashionable that even the most cherished
scientific notions are subject to pitiless revision. What is the fundamental
stuff of the world? Elementary particles? Think again. For the past 20 years,
physicists have quietly been undermining even this most basic of our beliefs.
Particles, it seems, just aren鈥檛 enough.
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It鈥檚 not that theorists like to be destructive. They prefer a nice tidy
picture as much as anyone鈥攁nd that鈥檚 the trouble. Since the 1970s, the
more they鈥檝e tried to tie up the loose ends in their theories, the more strange
and unexpected mathematical creatures have come tumbling out of the algebra. The
mathematics now suggests that the Universe may be populated not only by the
electrons, quarks and neutrinos of modern scientific folklore, but by a zoo of
even more exotic things鈥攕uch as wiggly lines of stringy stuff that stretch
millions of kilometres across space, and superheavy pretzel-like knots of
energy. As of yet, no one has managed to subdue one of these elusive things in
the lab. But now astronomers may finally be close to tracking them down, for as
remnants from the early Universe, they should have left their footprints all
over the nighttime sky.
Physicists, of course, have traditionally discovered new objects by using
particle accelerators. So why are they now inspecting the darkest depths of
outer space? To see why, you need to know a bit about Grand Unified Theories
(GUTs), the modern relatives of most durable theories in physics鈥擩ames
Clerk Maxwell鈥檚 electromagnetic theory.
In Maxwell鈥檚 theory, every point in space has both an electric and a magnetic
field associated with it, and each is represented by an arrow pointing in a
definite direction. The pattern of arrows gives the state of the field, which
changes in time according to Maxwell鈥檚 equations. These explain how electric
charges generate the field, and how waves travel through it at the speed of
light. In the 1920s and 30s, physicists updated Maxwell鈥檚 theory to make it
consistent with quantum theory, which showed that light comes in particle-like
packets called photons.
That鈥檚 an old story. But there is a lot more to the world, of course, than
electricity and magnetism. In 1973, Howard Georgi and Sheldon Glashow of Harvard
University generalised Maxwell鈥檚 field theory in an attempt to combine three of
the four basic forces of nature into a single theory. The GUT theories that
emerged from their efforts contain electromagnetic theory as a special case, but
go further to include the weak and strong nuclear forces too鈥攅verything
except gravity.
At first glance, GUT field theories don鈥檛 seem too terribly
different from Maxwell鈥檚 theory. Quantum theory implies that the GUT field, like
the electromagnetic field, has its energy bound up in particle-like packets.
Technically these are called 鈥渆lementary excitations,鈥� but we know them as the
familiar elementary particles. The electron, photon or quark correspond to the
simplest ways that bundles of energy can be injected into a quantum field.
But GUTs differ from Maxwell鈥檚 theory in a crucial way. The equations for
Maxwell鈥檚 theory are of a particularly simple kind, and imply that two separate
elementary excitations鈥攖wo photons鈥攚on鈥檛 interact with one another.
This makes the theory rather easy to understand, but a little boring too. The
equations of grand unified theories are far more complex, and describe particles
that interact. At the same time, the equations of GUT theories also open the
door to solutions that are far more intricate than those for ordinary particles.
Some of these are known as 鈥渢opological solitons鈥�, and correspond to kinks or
tangles in the field lines that, once created, can persist and move about.
While the mathematics is daunting, the reasons for the existence of
topological solitons can be seen in something far simpler鈥攁 liquid
crystal. The liquid inside the display of a laptop computer consists of long,
thin rod-like molecules. Voltages applied behind the display cause the rods to
line up parallel or perpendicular to the surface, making the liquid either
transparent or opaque to light.
Even in the absence of voltages, forces between neighbouring rods tend to
make them line up, although what actually happens depends on the liquid鈥檚
temperature. When hot, the rods jiggle about violently and their collisions
overwhelm the aligning forces, leaving the rods in overall disarray. But, in
principle, if the liquid is cooled slowly, the rods will come into line to make
a nice, ordered state of low energy
(see Diagram, top of p 32).
Opposing sides
In practice, however, defects in the form of twists and distortions can get
locked into the pattern of rods as the liquid cools. For example, a slice
through the cooled liquid might show a region where the rods are arranged
radially about a single point, with those on opposing sides misaligned by 180
degrees. Because the liquid is three-dimensional, there are two possibilities
for this defect鈥檚 form. If deeper slices show that the pattern extends into the
liquid, this means that the defect has the form of a curvy string. On the other
hand, the misalignment might not extend into deeper slices, which would mean
that the defect is a lumpy object called a monopole in which the rods are
arranged like the spikes on a hedgehog
(see Diagram, bottom of p 32).
The misalignment of rods in these defects introduces stress into the liquid
crystal and the rods can try to move to alleviate them. But they will never
quite succeed. If a rod flips to align with some of its neighbours, it becomes
out of joint relative to others, and when many do this the only consequence is
that the string or monopole moves. These defects act just like the kinks that
appear in coiled telephone cables and which connect regions of cable that are
coiled in different senses. Removing a kink necessitates either pushing it off
the end of the cable, or bringing a kink and an antikink together so that they
annihilate. These defects, then, owe their existence to their
topology鈥攖hey are tangles that simply cannot be undone.
But what is the connection between liquid crystals and grand unified field
theories? In such a theory, the field lines interact with one another just as
the rods do in a liquid crystal. Neighbouring field lines prefer to be parallel.
So if we think of the rods of the liquid crystal as the field lines in a GUT,
then strings and monopoles become more than mere mathematical curiosities in a
computer screen鈥攖hey become new objects that might very well be lurking in
the real world. In grand unified theories, twists and windings of field lines
lock energy into the core of the solitons. And because of the link between
energy and mass so central to the theory of relativity, this means that solitons
should be heavy, massive, substantial things.
And there are good reasons to suppose that such objects might really exist.
For according to modern cosmology, the Universe is rather like an immense liquid
crystal that has been cooling down ever since its beginning. Immediately after
the big bang, the Universe would have been unimaginably hot, with its primeval
fields鈥攚hich can be modelled by grand unified theories鈥攋umbled up
haphazardly like the rod-like molecules in a hot liquid crystal. As the Universe
expanded and cooled the fields would have straightened out to form smooth
patterns. But defects would inevitably have formed in the basic fields of the
Universe just as they do in a liquid crystal when it cools. The early Universe
would have been a horrendous mess of tangles, each locked forever into the
fabric of the world.
If so, then there must be things like monopoles and strings out there
somewhere. In the 1970s, Gerard `t Hooft of Utrect University and Russian
physicist Alexander Polyakov proved that the hedgehog-like solitons that appear
in GUTs have exactly the properties that one would expect from a magnetic
monopole鈥攁n isolated magnetic charge. Such a monopole would be at once 10
million billion times smaller and 10 million billion times heavier than a
proton鈥攖ruly a strange beast. For nearly 20 years, physicists have been
searching for monopoles, but without much success鈥攖hey think. On St
Valentine鈥檚 Day in 1983 a detector at Stanford University picked up something
like a monopole. And in 1985, a team of experimenters from Imperial College
London saw what is now known as the 鈥淪outh Kensington鈥� monopole. But two chance
events is hardly convincing. Were these real detections, or merely experimental
glitches? No one really knows.
Grabbing hold of a cosmic string might be even harder than finding a
monopole. According to the mathematics of GUTs, cosmic strings shouldn鈥檛 exist
as single, disconnected strands, but always in the form of closed loops. And
unlike a monopole which is stable and can exist forever once it is formed,
cosmic loops can slowly shrink up and eventually disappear. Consequently, even
if the Universe was once brimming with cosmic loops, they may have mostly
vanished by now. If it were possible to find one, the 鈥渟tring鈥� would be far
thinner than the most tenuous fishing line, or even a chain of single atoms. And
the loop might be small, hula-hoop sized, or perhaps even encircle galaxies or
large portions of the entire Universe.
Detecting such an enormous object directly might be impossible, so in recent
years astronomers have been searching for traces of strings and monopoles in the
light that comes to us from space. As massive objects, cosmic defects would have
been pulling on all the matter in their surroundings ever since their formation,
causing a subtle clumping in the way mass is distributed in the Universe. The
strings and these clumps of matter should affect the way photons from the cosmic
microwave backround radiation鈥攚hich fills the Universe as a remnant of the
big bang鈥攎ake their way to the Earth. So by looking closely at the
distribution of the microwave background radiation across the sky, it should be
possible to detect the signatures of monopoles or strings鈥攊f they are
there.
Fishing for strings
For the past few years, physicist Neil Turok of Cambridge University and
colleagues have been working out the kinds of clumping patterns one would expect
for strings, monopoles and other defects, and comparing them to the best images
of the microwave background as obtained by the Cosmic Background Explorer
satellite. A string, not surprisingly, should show up as a line-like feature and
the sky should show many lines and the features of other defects all
overlapping. Along with Ue-Li Pen and Uros Seljak of Harvard University, Turok
reported earlier this month in Physical Review Letters that the current
images don鈥檛 show the signatures predicted by theory.
But the satellite images aren鈥檛 quite good enough yet to draw any really
strong conclusions. Higher resolution images in the next few years should be,
but by then, the theory too may have changed. For although monopoles and cosmic
loops are the two basic kinds of topological solitons predicted by grand unified
theories, things could get a lot more complicated. In May of this year, Ludvig
Faddeev of the Steklov Mathematical Institute in St Petersburg, Russia, and
Antti Niemi of Uppsala University in Sweden published a paper in Nature
(vol 387, p 58) which shows that strings can also be tied up into knots. That
may not seem so profound. But whereas a normal cosmic loop can contract and
finally vanish, a knotted one cannot. So knotted strings possess a kind of
permanence that ordinary strings don鈥檛.
The basic forms of cosmic knot are the 鈥渦nknot鈥� and 鈥渢refoil鈥� of knot theory,
with certain twistings of the fields to render them stable. The unknot is just a
simple loop which has been cut and then glued back together, but not before one
of its ends has been twisted through 360 degrees. Once twisted like this, the
loop can no longer contract and disappear like an ordinary loop. The trefoil, on
the other hand, is a true knot in the common meaning of the word
(see Diagram).
It took a lot of thrashing about on the part of a supercomputer to find
evidence for these solutions鈥攁nd other groups are now trying to verify
that the solutions are correct. If so, and simple knots can be made out of
strings, there seems to be no reason why there couldn鈥檛 be far more complicated
knots as well. And as any angler knows, there is no end to the complexity of the
tangles that can find their way into a length of fine fishing line. So monopoles
and strings could easily have a set of very heavy and complex tangled
cousins.
How these might affect our view of the Universe is, for now, anyone鈥檚 guess.
Physicists have been exploring the implications of monopoles and ordinary cosmic
strings for some time, but are only now beginning to think about knots.
Too many monopoles
In standard cosmology, too many monopoles is a catastrophe, because if they
appear in the numbers predicted by standard theory, the Universe would have
stopped expanding long ago because of the increased mass the monopoles carry.
Explaining why the Universe hasn鈥檛 stopped expanding was the original motivation
for the inflationary Universe model, which introduces an extra period of
accelerated expansion to dilute the monopoles. In contrast, ordinary strings are
safe because loops can shrink and eventually evaporate. As a result, the
evolution of a network of strings should maintain their total mass at a constant
fraction of that of the entire Universe.
But knotted strings cannot decay, and might fill the Universe with massive
remnants that give the same problems as the monopoles. That would imply that the
Universe shouldn鈥檛 be here, and tell us that, well, something is dreadfully
wrong with current theory.
So Faddeev and Niemi鈥檚 knots could spell big trouble for cosmologists. Then
again, in combination with other defects such as ordinary strings and monopoles,
they might help to account for the observed patterns in the cosmic microwave
background radiation鈥攚hich would be a terrific victory for grand unified
theories.
But for now, there are many questions, and few answers. Can knots ever be
pulled apart? How many knots would have formed as the Universe cooled? Questions
like these will tax the imaginations of physicists for many years.