Relativistic quantum field theory
has worked very well to describe the observed behaviors and properties of
elementary particles. But the theory itself only works well when gravity is so weak
that it can be neglected. Particle theory only works when we pretend gravity doesn't
exist.
General relativity has yielded a wealth of insight into the Universe, the orbits of
planets, the evolution of stars and galaxies, the Big Bang and recently observed
black holes and gravitational lenses. However, the theory itself only works when we
pretend that the Universe is purely classical and that quantum mechanics is not
needed in our description of Nature.
String theory is believed to close this gap.
Originally, string theory was proposed as an explanation for the observed
relationship between mass and spin for certain particles called hadrons, which
include the proton and neutron. Things didn't work out, though, and Quantum
Chromodynamics eventually proved a better theory for hadrons.
But particles in string theory arise as excitations of the string, and included in the
excitations of a string in string theory is a particle with zero mass and two units
of spin.
If there were a good quantum theory of gravity, then the particle that would carry
the gravitational force would have zero mass and two units of spin. This has
been known by theoretical physicists for a long time. This theorized particle is called
the graviton.
This led early string theorists to propose that string theory be applied not as a
theory of hadronic particles, but as a theory of quantum gravity, the unfulfilled
fantasy of theoretical physics in the particle and gravity communities for decades.
But it wasn't enough that there be a graviton predicted by string theory. One can
add a graviton to quantum field theory by hand, but the calculations that are
supposed to describe Nature become useless. This is because, as illustrated in the
diagram above, particle interactions occur at a single point of spacetime, at zero
distance between the interacting particles. For gravitons, the mathematics behaves
so badly at zero distance that the answers just don't make sense. In string theory,
the strings collide over a small but finite distance, and the answers do make sense.
This doesn't mean that string theory is not without its deficiencies. But the zero
distance behavior is such that we can combine quantum mechanics and
gravity, and we can talk sensibly about a string excitation that carries the
gravitational force.
This was a very great hurdle that was overcome for late 20th century physics, which
is why so many young people are willing to learn the grueling complex and abstract
mathematics that is necessary to study a quantum theory of interacting strings
.
Think of a guitar string that has
been tuned by stretching the string under tension across the guitar. Depending on
how the string is plucked and how much tension is in the string, different musical
notes will be created by the string. These musical notes could be said to be
excitation modes of that guitar string under tension.
In a similar manner, in string theory, the elementary particles we observe in particle
accelerators could be thought of as the "musical notes" or excitation modes of
elementary strings.
In string theory, as in guitar playing, the string must be stretched under tension in
order to become excited. However, the strings in string theory are floating in
spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The
string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is
pronounced "alpha prime"and is equal to the square of the string length scale.
If string theory is to be a theory of quantum gravity, then the average size of a
string should be somewhere near the length scale of quantum gravity, called the
Planck length, which is about 10-33 centimeters, or about a millionth of a billionth
of a billionth of a billionth of a centimeter. Unfortunately, this means that strings are
way too small to see by current or expected particle physics technology (or
financing!!) and so string theorists must devise more clever methods to test the
theory than just looking for little strings in particle experiments.
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 for every boson (particle that transmits a
force) there is a corresponding fermion (particle that makes up matter). So
supersymmetry relates the particles that transmit forces to the particles that make
up matter.
Supersymmetric partners to 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 at current 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.
There are several ways theorists can build string theories. Start with the
elementary ingredient: a wiggling tiny string. Next decide: should it be an open
string or a closed string? Then ask: will I settle for only bosons ( particles that
transmit forces) or will I ask for fermions, too (particles that make up matter)?
(Remember that in string theory, a particle is like a note played on the string.)
If the answer to the last question is "Bosons only, please!" then one gets bosonic
string theory. If the answer is "No, I demand that matter exist!" then we wind up
needing supersymmetry, which means an equal matching between bosons
(particles that transmit forces) and fermions (particles that make up matter). A
supersymmetric string theory is called a superstring theory. There are five kinds of
superstring theories, shown in the table below.
The final question for making a string theory should be: can I do quantum
mechanics sensibly? For bosonic strings, this question is only answered in the
affirmative if the spacetime dimensions number 26. For superstrings we can whittle
it down to 10. How we get down to the four spacetime dimensions we observe
in our world is another story.
A Brief Table of String Theories
Type
Spacetime
Details
Dimensions
Only bosons, no fermions means only forces, no matter,
Bosonic
26
with both open and closed strings. Major flaw: a particle
with imaginary mass, called the tachyon
Supersymmetry between forces and matter, with both
I
10
open and closed strings, no tachyon, group symmetry is
SO(32)
Supersymmetry between forces and matter, with closed
IIA
10
strings only, no tachyon, massless fermions spin both
ways (nonchiral)
IIB
10
Supersymmetry between forces and matter, with closed
strings only, no tachyon, massless fermions only spin one
way (chiral)
Supersymmetry between forces and matter, with closed
HO
10
strings only, no tachyon, heterotic, meaning right moving
and left moving strings differ, group symmetry is SO(32)
Supersymmetry between forces and matter, with closed
HE
10
strings only, no tachyon, heterotic, meaning right moving
and left moving strings differ, group symmetry is E8 x E8
If we ask how to get from ten spacetime dimensions to four spacetime dimensions,
then the number of string theories grows, because there are so many possible
ways to make six dimensions much much smaller than the other four in string
theory. This process of compactification of unwanted spacetime dimensions yields
interesting physics on its own.
But the number of string theories has also been shrinking in recent years,
because string theorists are discovering that what they thought were completely
different theories were in fact different ways of looking at the same theory!
This period in string history has been given the name the second string
revolution.
And now the biggest rush in string research is to collapse the table above into one
theory, which some people want to call M theory, for it is the Mother of all
theories.
Stay tuned to this web site, we may some day soon be changing the name to The
Official M Theory Web Site!