by Steve Bryson
We have learned that, according to the current 'standard model' of the interactions between particles, there are two forces that are important for interparticle interaction. These are the strong nuclear force (described by QCD) and the Electroweak force (described by the electroweak theory). (At everyday energies, the electroweak force acts like two forces, the weak nuclear force and electromagnetism.) So, when gravity is included, there seem to be three distinct forces in nature which are apparently independent. In addition, the standard model has many arbitrary numbers, such as the strength of the forces, the number and masses of the particles, the particular choice of gauge symmetries (= dimensions of the quantum wave space) and so on.
It has also been observed that, due to the fact that all the elementary particle forces in nature have a strength which depends on the distance between the interacting particles (the further the separation the stronger the force in QCD and the weak force while the further the separation the weaker the force for QED) there is a distance (about 10-28 centimeters) at which all the forces are of equal strength. This suggests that at that distance the separate forces may actually be a single force.
Inspired by the unification of the electromagnetic and the weak nuclear forces into a single electroweak force, the next question that is naturally asked is 'can we further unify these three forces into two or even one single force?' thereby reducing the number of arbitrary parameters in the theory. The theories that attempt to do this are called unified field theories. There are several brands of unified field theories currently in vogue which we will consider separately.
Here is a brief description of each brand:
Grand Unified Theories (GUTs): These are the first and most modest of the unified field theories in that they only attempt to unify the strong and the electroweak force, ignoring gravity. They are patterned on the successful electroweak theory without any conceptual modifications, and were introduced in 1974.
Supersymmetric Theories (also called supersymmetry): These theories start by postulating a new, unobserved symmetry of interchange between fermions and bosons. This automatically introduces many new particles and forces and it was hoped that we would discover a supersymmetric model that happened to contain all the known physical forces including gravity. While there was some hints at success in this for a while, supersymmetry itself has not panned out.
Kaluza-Klein Theories: These theories postulated the remarkable idea that spacetime has more than four dimensions. The most popular Kaluza-Klein model postulated that spacetime actually has 11 dimensions, 10 of space and 1 of time. Then all the gauge symmetries of quantum field theory are understood to be much like the rotational symmetries of the 11-dimensional spacetime.
Supersymmetric String Theories (also called superstring theories): This theory tries to combine the best of the above, but it starts by assuming that elementary particles are really tiny (10-30 cm) strings, and that the different particles are really different vibrations on otherwise identical strings. Then assume that the interactions are supersymmetric and take place in a ten dimensional (9 space and 1 time) spacetime. Discover that in this case certain technical difficulties that were present in the above models are absent for superstring theories. Hope (convince) that this means that superstrings are the correct approach, and as in any supersymmetric theory there are lots of particles and forces to fit nature into hope that this contains a correct description of nature. In this case the forces are derived, not put in by hand.
Now let's look at each of these cases in somewhat more detail.
These theories are based on theories that are conceptually identical to the electroweak theory. The only difference is that the dimension of the quantum wave space is larger. It turns out that the smallest dimension quantum wave space that fits both the electroweak force and QCD has 5 complex (10 normal) dimensions (see gauge theories section of handout 3). Three of these complex dimensions correspond to the three colors of a quark of QCD and the other two correspond to the electron and neutrino directions (as in the electroweak theory). This is called the minimal SU(5) theory. It relies on a spontaneous symmetry breaking mechanism much like the electroweak theory. It is really just a bigger copy of the electroweak theory. It predicts that there are 24 force carrying bosons, 8 of which are gluons, 3 the W and Z particles of the electroweak theory, and one photon. The remaining 12 particles (called X and Y particles) are supermassive (a hundred trillion times the mass of a proton) bosons that carry the new unified force.
The predictions of the minimal SU(5) model include that a 5 complex dimensional quantum wave pointing in one of the quark color directions can rotate into an electron or a neutrino direction by emitting an X or Y particle (much like the muon can rotate into a muon neutrino by emitting a W particle). This would cause hadrons (particles made of quarks) to decay into new hadrons and leptons. Thus a particular prediction is that the proton may decay into a pion and a positron. This is the infamous proton decay, and should take place, on the average, in about 1032 years. We can observe this by getting 1032 protons in one place (like a tank of water) and then one proton should decay in about a year. This has been done, but no proton decay has been seen. While the final judgment is not in, it currently looks bad for the minimal SU(5) model.
There are other predictions of the minimal SU(5) model that are in striking agreement with observation, including the prediction that the electrical charge of some quarks should be one third the charge of the electron. There are others, but they are too technical to mention here.
There are many other grand unified models (using quantum wave spaces of greater than 5 complex dimensions) that may give correct unifications of QCD and the electroweak theories. The difficulty is that we have no way of determining via observation which of these theories may be right.
Inspired by the prevalence of gauge symmetries in quantum field theory, some physicists have postulated that there is a symmetry between the fermion type particles and the boson type particles. In other words the physics should be the same if we interchanged, for example, electrons with photons. This would make the relationship between fermions and bosons much like the relationship between particles and antiparticles: the existence of a fermion would automatically imply the existence of a boson (called the fermion's supersymmetric partner). As this is obviously not the case, these physicists say that this fermion-boson symmetry (called supersymmetry) is 'badly broken'. Then as under this symmetry one can generate lots of theoretical particles and forces, one hopes that by simply assuming supersymmetry one can explain all the known particles and forces.
The original motivation for postulating supersymmetry are many fold. They include: the rather metaphysical idea that "nature likes symmetry and would not pass up an opportunity like this"; the hope that known bosons would turn out to be the supersymmetric rotations of known fermions, thus cutting the number of fundamental particles in half; also some technical motivations involved in the fact that at least one type of supersymmetric theory is completely finite (thus not requiring big bad renormalization theory); Supersymmetry automatically predicts a force that acts like gravity (this has been referred to as supergravity). There are some other more technical motivations.
The current status of supersymmetry is: none of the known bosons can be partners of any of the known fermions, thus predicting twice as many particles as are currently known--in other words this motivation backfired; one (out of eight) type of supersymmetric theory (known as N=4 supersymmetry) has been solved exactly (by Stanley Mandelstam) making it the only quantum field theory ever to be exactly solved but it turned out not to contain the real world; Other types of supersymmetry may not be completely finite after all.
It is now generally felt that supersymmetry by itself is not the answer.
These theories take the ideas of supersymmetry and postulate the spacetime is bigger than we thought. They postulate that spacetime actually has more than 4 dimensions. The most popular model gives spacetime 11 dimensions (not to be confused with quantum wave space dimensions), 10 of space and 1 of time. Then the reason that the universe looks 4 dimensional (three space and one time) is that the other 7 space dimensions are rolled up very tightly into little circles. These circles are so small that (to quote Prof. Mary Galliard) "when you go in those seven directions you get back where you started so quickly that you never realize that you went anywhere" so that you never notice those seven dimensions.
The motivation for postulating those seven extra dimensions is that quantum field theory in general and supersymmetry in particular are better behaved in these 11 dimensional spacetimes than in 4 dimensions. Also, it is hoped that the gauge symmetries of the quantum wave functions could be understood as something like rotational symmetries in the 11 dimensional space.
While Kaluza-Klein theories made for some interesting models with very interesting mathematics, no new physics came out of them.
(These theories are not to be confused with something called 'cosmic strings' which are something else entirely.)
The basic postulate of superstring theories is that elementary particles are really very short (10-30 cm) strings which wiggle. The different observed particles are different wiggles in otherwise identical strings. When supersymmetry is included in the description of the strings, one discovers that one can describe just about any particle that one wishes. Further, the superstring theory is very well behaved on a technical level if the universe is really 10 dimensional (9 space and 1 time), where six of the space dimensions are rolled up into very tiny circles much like in the Kaluza-Klein theories. String theories necessarily contain forces that behave just like gravity, and they may give a quantum description of gravity that is completely finite.
It turns out that if you phrase your theory just right you find that there are only two (very large) possible gauge symmetries allowed, and both of them contain the observed symmetries of QCD and the electroweak theory. Thus in some sense you have actually derived the existence of QCD and the electroweak theory from the idea of strings. There are also predicted many forces that have not yet been observed as well as many as yet unseen particles. One possible prediction is that there is a whole set of particles just like the observed particle in nature except that they do not interact in any way (except perhaps gravitationally) with the observed particles. This is the so-called 'shadow matter' that may solve certain problems in astronomy.
From 1983, when the first major technical successes were demonstrated, until about 1990 superstrings have been the vogue in the physics community. Lately, however, many physicists have become disenchanted with string theory. In any case, superstring theory is far from mature enough to make any actual quantitative predictions that can be tested by experiment.
I think it is fair to say that there is quite a lot of turmoil and uncertainty of direction in the theoretical particle physics community. One of the main problems is that the standard model, with all of the uncertainties and arbitrary structures that it contains, accurately accounts for just about every major observation in particle physics. For technical reasons, however, we can expect something new at the very next generation of particle accelerators currently coming on line at Fermilab in Illinois, SLAC in Palo Alto, and CERN in France/Switzerland. We eagerly await the result from these new accelerators.