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Edward Witten EDWARD
WITTEN strings
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string theory
An important theory in modern physics in which the fundamental particles
in nature are thought of as the musical notes or excitation modes of
elementary strings. These strings have the shortest meaningful length,
known as the
Planck length (equal to about 10-33 cm), but no
thickness, and for the theory to make sense, the universe must have nine
space dimensions and one time dimension, for a total of ten dimensions.
This idea of a ten-dimensional universe was first mooted in the
Kaluza-Klein theory. We're familiar with time and three of the space
dimensions: the other six together are known as
Calabi-Yau spaces.
In string theory, as in a stringed instrument, the string must be
stretched under tension in order to become excited. This tension is
fantastically high – equivalent to a loading of about 1039
tons. String theories are classified according to whether or not the
strings are required to be closed loops, and whether or not the particle
spectrum includes
fermions. In order to include fermions in string theory, there must
be a special kind of symmetry called
supersymmetry, which means that for every
boson (a particle, of integral spin, that transmits a force) there
is a corresponding fermion (a particle, of half-integral spin, that
makes up matter). So supersymmetry relates the particles that transmit
forces to the particles that make up matter. Supersymmetric partners to
currently known particles have not been observed in particle
experiments, but theorists believe this is because supersymmetric
particles are too massive to be detected using present-day high-energy
accelerators. Particle accelerators could be on the verge of finding
evidence for high energy supersymmetry in the next decade. Evidence for
supersymmetry at high energy would be compelling evidence that string
theory was a good mathematical model for nature at the smallest distance
scales.
In string theory, all of the properties of elementary particles –
charge, mass, spin, etc – come from the vibration of the string. The
easiest to see is
mass. The more frenetic the vibration, the more energy. And since
mass and energy are the same thing, higher mass comes from greater
vibration.
Gravity and the development of string theory
One of the major outcomes of work on the
electroweak unification was the so-called
Standard Model of particle physics, which neatly describes all the
elementary particles in nature and the forces between them – with one
notable exception. It includes six different types of
lepton, or lightweight particle, six different types of
quark, and the exchange particles for the weak, strong and
electromagnetic interactions. It also calls upon an enigmatic new
particle, the
Higgs boson, named after its inventor, Peter Higgs of the University
of Manchester (England), which, although not yet detected, is expected
to play an important role in fixing the masses of all the other
particles in the scheme. The Standard Model has agreed well, so far,
with experimental data collected using particle accelerators. Yet
physicists aren’t completely happy with it. For one thing, it leaves too
many arbitrary properties undecided – important values that simply have
to be stuck into the Model ad hoc. For another, it has no place for
gravity.
How then to get gravity into the scheme? A clue to this emerged while
researchers were working on the quantum field theory of the
strong force. Along the way, they came up with a wonderfully
creative explanation for the observed relationship between the mass and
spin of hadrons. Called string theory, it treats particles as specific
vibrations or excitations of very, very small lengths of a peculiar kind
of string. In the end,
quantum chromodynamics (QCD) proved to be a better theory for
hadrons. Yet string theory wasn’t consigned to the trashcan of ideas
that had passed their sell-by date. It made one extremely interesting
prediction: the existence of a particle – a certain excitation of string
– with a
rest mass of zero and an intrinsic spin of two units. Theorists had
long known that there ought to be such a particle. It was none other
than the hypothetical exchange particle of gravitation – the
graviton.
With this discovery, that one of the essential vibrational modes of
string corresponded to the graviton, string theorists realized they had
a bigger fish to fry than trying to explain the ins and outs of hadrons.
Their notions of elemental quivering threads might, it seemed, bear
directly on the much sought-after
quantum theory of gravity – and not just because the graviton is
predicted by string theory. You can stick a graviton into quantum field
theory by hand if you like, but it won’t do you any good because you’ll
be blown away by infinities. Particle interactions happen at single
points in spacetime, so that the distance between interacting particles
is zero. In the case of gravitons, the mathematics behaves so badly at
zero distance that the answers come out as gobbledygook. String theory
gets around this problem because the interacting entities aren’t points
but lengths, which collide over a small but finite distance. As a
result, the math doesn’t self-destruct and the answers make sense.
Vibrating strings
To get the hang of string theory, think of a guitar string that’s been
tuned by stretching it between the head and the bridge. Depending on how
the string is plucked and how tense it is, different musical notes are
created. These notes can be thought of as excitation modes of the guitar
string under tension. Similarly, in string theory, the elementary
particles observed in particle accelerators correspond to the notes or
excitation modes of elementary strings. One mode of vibration makes the
string appear as an electron, another as a photon, and so on.
In string theory, as in guitar playing, the string has to be under
tension in order to become excited. A big difference is that the strings
in string theory aren’t tied down to anything but instead are floating
in spacetime. Even so, they’re under tension – by an amount that
depends, roughly speaking, on one over the square of the string’s
length. Now, if string theory is to work as a theory of quantum gravity,
then the average length of a string has to be in the ballpark of the
distance over which the quantization of spacetime – the granularity of
space and time – becomes noticeable. This outrageously tiny distance,
known as the Planck length, is about 10-33 centimeters, or
one billion trillion trillionth of a centimeter. So much tinier is it
than anything that current or planned particle physics technology can
hope to be able to see that string theorists have to look for craftier,
more indirect ways to test their ideas.
Varieties of string theory
String theories come in various forms. All of these assume that the
basic stuff of creation are tiny wriggling strings. However, if the
theory deals with only closed loops of string, like Spaghetti
Hoops, then it’s limited to describing bosons – the force-carrying
particles – and so is called bosonic string theory. The first
string theory to be developed was of this type. If open
strings, like strands of ordinary spaghetti, are allowed into the
theoretical picture then these provide a description of fermions, or
particles of matter. But a very interesting thing happens when string
theory is extended in this way to let in fermions. It demands that there
must be a special kind of symmetry in the particle world, know as
supersymmetry. In this expanded masterplan of things, there’s a
corresponding fermion for every boson. In other words, supersymmetry
relates the particles that transmit forces to the particles that make up
matter. A supersymmetric string theory is called, not surprisingly, a
superstring theory.
Theorists uncovered three different string theories that were
mathematically consistent and therefore made good sense. Two of these
were bosonic, the other of the superstring ilk. But in order to make any
of them work, they had to resort to a strategy first employed by Kaluza
and Klein in the days when Einstein first started wandering down his
blind unification alley: they had to call upon higher dimensions, rolled
up so small that they’re way below the threshold of detection. The
bosonic string theories needed an awesome 26 dimensions (25 of space
plus one of time) in order to work properly, which seemed a bit of a
stretch even for scientists who enjoyed some wayout sci-fi in their
off-hours. Compared with this, the mere ten dimensions of spacetime
required by superstring theory seemed positively modest. Six of the ten
would have to be curled up, or “compactified,” to leave visible the four
normal spacetime dimensions (three of space plus one of time). But these
compactified dimensions, far from being an embarrassment to be swept
under the cosmic carpet and forgotten about, come in very handy if
string theory is to aspire to become a theory of everything: motion in
them can be used to explain the values taken by important constants in
nature, such as the charge on the electron.
Combining the best features of bosonic and superstring theory has led to
two other consistent schemes known as heterotic string theories. So,
there are five viable string theories in all, which, if we’re hoping to
arrive at the one true TOE, is a tad too many. Fortunately, it’s
beginning to look as if the quintet of finalists for the Miss Universe
Theory competition is really the same contestant dressed up in five
different costumes. This supersymmetric mistress of disguise has been
given the rather enigmatic name M-theory.
Some say that the M is for Mother of All Theories. Others that it stands
for Magic or Mystery. But, although no one seems to know for sure, there
may be a more prosaic reason for this particular choice of initial.
Before string theory rose to scientific superstardom, the most popular
unified theory in town was supergravity, which was basically
supersymmetry plus gravity without the string. Like any respectable
quantum gravity candidate it boasted a surfeit of spacetime dimensions –
in this case, eleven (the compactified ones all wrapped up neatly on an
itty-bitty 7-dimensional sphere). Unfortunately, it had to be abandoned
because of the problems mentioned earlier involving point particles and
string.
But along came M-theory. Still under development, it carries the hopes
of many that it will combine the various flavors of string theory soup
into one single, satisfying broth. The cost of this in conceptual terms
is the addition of a single dimension: M-theory is 11-dimensional but
with the unusual trait that it can appear 10-dimensional at some points
in its space of parameters. Supergravity rides again – but this time
with strings attached.
And the M in M-theory? We omitted to say earlier that while strings,
with their one-dimensional extension, are the fundamental objects in
string theory, they’re not the only objects allowed. String theory can
accommodate multidimensional entities, called
branes, with anywhere from zero (points) to nine spatial dimensions.
A brane with an unspecified number, p, of dimensions is called a p-brane.
In M-theory, with its extra dimension, the fundamental object is an M-brane,
which resembles a sheet or membrane. Like a drinking straw seen at a
distance, the membranes would look like strings since the eleventh
dimension is compactified into a small circle. Membranes, M-branes,
M-theory. Hmmm ...
End In Sight?
Building a theory of everything is one thing, testing it quite another.
The physical conditions that have to prevail for the four forces of
nature to be unified into a single force haven’t existed since the
universe was about 10-43 seconds (one ten million trillion
trillion trillionth of a second) old. There’s not the remotest chance of
recreating that kind of environment in the lab any time soon, if ever.
But what physicists can do is look for other clues that their
unification scheme is on the right track.
We saw above that supersymmetry predicts there are supersymmetric
fermion partners of all the force-carrying bosons. The supersymmetric
partner of the graviton, for example, is a spin 3/2 particle that, like
all its supersymmetry cousins is expected to be very massive – maybe a
thousand times more massive than a proton. This high mass has put the
creation of such particles beyond the reach of accelerators thus far.
But that may be about to change. A new generation of more powerful
instruments, including the
Large Hadron Collider (LHC) at the European CERN facility near
Geneva, Switzerland, is about to come on line capable of exploring the
energy domain in which the new particles might be found. Evidence for
supersymmetry at high energy would be compelling evidence that string
theory was a good mathematical model for nature at the smallest distance
scales.
In some ways, the invention of string theory was premature – its
physical concepts running ahead of the mathematical techniques needed to
describe them. One of the architect’s of string theory in its modern
form, Edward Witten of the Institute for Advanced Study in Princeton
(where Einstein spent his latter days), has said:
By rights, twentieth century physicists shouldn’t
have had the privilege of studying this theory. What should have
happened, by rights, is that the correct mathematical structures
should have been developed in the 21st or 22nd century, and then
finally physicists should have invented string theory as a physical
theory that is made possible by those structures... [T]hen the first
physicists working with string theory would have known what they
were doing, just like Einstein knew what he was doing when he
invented general relativity.
There are other theories of quantum gravity besides string theory. One
of the leading rivals is called loop quantum gravity, founded in the
late 1980s by Abhay Ashtekar of Penn State University, Carlo Rovelli of
the Center for Theoretical Physics in Marseille, France, and Lee Smolin
of Harvard. Its strategy is to focus on quantizing the spacetime of
general relativity without getting involved in trying to unify gravity
with the three other forces. Smolin, however, has suggested that string
theory and loop quantum gravity might eventually be reconciled as
different aspects of the same underlying theory.
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