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String Theory and the Unification of Forces
String Theory and the Unification of Forces

Sunil Mukhi

Early attempts at unification.

The urge to discover a fundamental theory underlying all natural phenomena has been expressed since the beginning of civilization. From the reduction of all matter to ``earth, air, fire, water'', we have progressed considerably. Chemistry reduces all of matter to a hundred or so types of atoms, called ``elements''. But these in turn consist of smaller particles interacting with each other. We now understand reasonably well how to reduce all of matter to a large collection of elementary particles. The interactions amongst them are ascribed to the exchange of other particles, called ``force carriers''.

The four forces.

Experimentally it is known that there are just four basic forces in nature. Two of them are very familiar: the electromagnetic force, and the gravitational force. The other two are invisible unless we probe deep inside the nucleus of the atom. They are called ``nuclear forces'' and come in two varieties, the ``weak'' and the ``strong'' force. The weak nuclear force is responsible for radioactive decay, while the strong force binds protons and neutrons together to make up the nucleus.

The Standard Model of elementary particles.

The most fundamental theory today that is substantially confirmed by experiment is the ``Standard Model'' of three interactions: electro-magnetic, weak nuclear and strong nuclear. In this model, particles like electrons, muons, neutrinos and quarks make up matter. They interact via the above forces. The force carriers are other particles, such as photons and the more recently discovered W and Z bosons and gluons.

Success of the Standard Model.

The Standard Model gives us a recipe to calculate the rates at which interactions take place. We can then measure the same rates in an accelerator or other laboratory, and compare with the theory. The result of this comparison has been very successful, and has ultimately led to several Nobel Prizes in Physics. In 1979, the prize was awarded to theorists Sheldon Glashow, Abdus Salam and Steven Weinberg, who proposed the theory of electromagnetic and weak interactions. In 1984, it went to experimentalists Carlo Rubbia and Simon van der Meer, for the detection of the W and Z particles predicted by the model. The 1976, 1988, 1990 and 1995 Nobel Prizes were given for other experiments that corroborated aspects of the Standard Model, and the 1999 prize went to theorists Gerardus 'tHooft and Martinus Veltman for elucidating the mathematical theory that underlies it.

Shortcomings of the Standard Model.

Despite all this, today it is believed that the Standard Model is approximate and incomplete. It does not incorporate the fourth and perhaps best-known force in nature: gravity. This is believed to be mediated by the exchange of gravitons, and due to problems of mathematical consistency, no one has ever been able to incorporate gravity into the Standard Model. So it is surely incomplete. Another problem with this model is that one has to assume the existence of distinct forces and their carriers. Einstein hoped that there would be a ``unified'' theory in which all known forces would emerge out of a single one in some way. Electricity and magnetism used to be thought of as two forces, but now we know they are different aspects of the same (electro-magnetic) force. Could the same type of unification hold for the four forces that are today viewed as distinct?

Unified Theories.

A unified theory would be a mathematical framework in which all the different kinds of forces and particles occur naturally. We should not have to fix the masses and charges of particles from experiment; rather the theory should fix them automatically to be the right values. Why does the electron weigh as much as it does? Why do particles interact with a given strength and not any other? In the standard model we just assume that these values are the ones measured in experiments, but in a unified theory these values should be predicted. Clearly this is an ambitious goal.

This suggests that the theory should possess a great degree of mathematical elegance and consistency. To discover the unified theory, we must look among those physical models which broadly resemble nature and in addition satisfy the above criteria. Only at a later stage -- after the detailed structure of the theory is understood -- can we check whether it describes our world.

Einstein's dream.

Einstein was among the earliest to propose that such a unified field theory must exist, and he struggled -- without success -- for most of his later life to find the right theory. Today we may be on the verge of realising Einstein's dream. String theory is currently the most promising example of a candidate unified theory. We are not yet sure that it correctly describes nature, but it broadly describes a world similar to ours, and is endowed with beauty and consistency to an astonishing degree.

The Physical Idea of String Theory.

The physical idea is utterly simple. Instead of many types of elementary point-like particles, we postulate that in nature there is a single variety of string-like object. The string is not ``made up of anything'', rather, it is basic and other things are made up of it. As with musical strings, this basic string can vibrate, and each vibrational mode can be viewed as a point-like elementary particle, just as the modes of a musical string are perceived as distinct notes!

Thus string theory certainly is a model of elementary particles. The great surprise is that mathematical equations describing strings are highly constrained by consistency. In some sense, most of the equations we would think of writing down turn out to be inconsistent, only a few appear to be allowed. Indeed, it looks most likely that (unlike particle theories) there is only one unique string theory! If so, what does it predict, and is it the promised unified theory?

Surprises from Strings.

Researchers studying the equations of string theory soon discovered a wealth of surprises. First of all, among the particles arising as vibrations of the string, we find some which are very similar to electrons, muons, neutrinos and quarks -- the known matter particles. There are others similar to photons, W and Z bosons and gluons -- the known force carriers. And there is one particle similar to the graviton, the elusive fourth force carrier.

Now since the structure of the theory is unique, we can work out (not postulate) what are the types of interaction between these particles. Astonishingly, at low energies the interactions are precisely of the type appearing in the Standard Model, and as a welcome bonus, we also get the gravitational interaction that Einstein originally discovered. So string theory predicts, roughly speaking, the right types of particles and the right types of interactions among them. The famous mathematical inconsistency -- which for decades made it impossible to incorporate quantum gravity in a theory along with the other interactions -- is conspicuous by its absence in string theory. It is almost as if gravity needs strings in order to exist!

More Surprises, and Some Hopes.

Besides these surprises, there are many others that we have stumbled upon in the last decade. In string theory, the fact that there are three space dimensions in our world might also be predicted rather than assumed. The dimension of ``space-time'' is variable in string theory, in the sense that we have to understand and solve string equations to determine it. This has not been done yet, because of the great complexity of the theory. If the answer comes out to be four (three space and one time) then we would have ``explained'' one of the most deep and abiding mysteries since the dawn of civilization: why does our world have the dimensionality that it has? If the answer is something else then string theory may be the wrong theory of nature, though we may still learn something about the right theory. Only successful comparison with experiment can give us convincing proof that string theory is correct.

Sunil Mukhi
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai, India

8 November 1995, revised 7 October 2000.
My thanks to all those who emailed me with their valuable comments and suggestions.
Click here to go to my second (and longer) non-technical article on string theory:
"The Theory of Strings: A Detailed Introduction"