Will the String Theory Tie Them All Together?

They’re (the string theorists) trying to take the next big step by pure mathematical reasoning, and it’s extraordinarily difficult. I hope they succeed. I think they are doing the right thing in pursuing this, because now string theory offers the only hope of a really unified way of nature. (Steven Weinberg [1])

The string theorists have a theory that appears to be consistent and is very beautiful, and I don’t understand it. (Sheldon Glashow [2])

Physics without strings is roughly analogous to mathematics without complex numbers. (Ed. Witten [3])

Views on the string theory, which seems to hold the promise of unifying gravity with the other fundamental forces of nature, namely the electroweak and the strong nuclear forces, are so divergent among the top-notch physicists that they do not seem to agree if the string theory is the right approach for unification. The views expressed in the above top two quotations are from Steven Weinberg and Sheldon Glashow who won the Nobel Prize together with Abdus Salam for their work of unification of the electromagnetic and weak forces in 1979. Similar confidence in the string theory and diffidence of it, is expressed by others also. Abdus Salam like Weinberg had confidence in the string theory while Richard Feynman had nothing but bitter skepticism of it. Brian Greene, a noted physicist and the author of the book “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory”, stated gingerly, “…it is a very strange research career, in a way. So far I’ve spent something like 17 years working on a theory for which there is essentially no direct experimental support. It’s a very precarious way to live and to work,” [4]. He is not alone in this uncertain quest, there is a host of other mathematicians and theoretical physicists who have staked their careers in the string theory.

The quest of unification of the fundamental forces began with Einstein in the early part of the twentieth century. At that time, gravity and the electromagnetism were the only known forces. He worked for nearly thirty years but failed to achieve his coveted goal.

With the development of the theory of quantum mechanics in the beginning of the twentieth century, two other fundamental forces were discovered namely the weak and strong nuclear forces. In due time, other physicists also got engaged in search of the Holy Grail of unification. In the late 1960s, Steven Weinberg and Abdus Salam working independently were able to unify the electromagnetic and weak forces as already mentioned above.

In the 1970s, it was shown that the strong nuclear force can also be tamed and unified with the electroweak force but theories, which provided the unification, the Grand Unified Theories (GUTs), were many. None of them was unique by itself and the force of gravitation defied unification with any of them.

Such was the state of affairs when the concept of the string theory came into existence quite accidentally. Gabrielle Veneziano, in 1968, “ ..realized that an esoteric formula concocted for purely mathematical pursuits by the renowned Swiss mathematician Leonard Euler some two hundred years earlier – the so-called Euler beta function – seemed to describe numerous properties of strongly interacting particles in one fell swoop. Veneziano’s observation provided a powerful mathematical encapsulation of many features of the strong force and it launched an intense flurry of research aimed at using Euler’s beta function…” [5]. It was brought to the attention of Leonard Susskind who “began to realize that it was describing what happens when two little loops of string come together, join, oscillate a little bit, and then go flying off,” [6]. According to Susskind, “I..found that Yoichiro Nambu, a physicist at Chicago University, had exactly the same idea, and that we had more or less by accident come on exactly the same idea on practically the same day. There was no string theory at that time. In fact, I didn’t call them strings – I called them rubber bands,” [6]. The discovery of string theory is thus usually credited to Susskind and Nambu.

The theory was plagued with several problems. One of them was the number of dimensions that it needed to make any sense. Originally, it needed twenty six dimensions and it repelled many physicists because it was so unreal. It also predicted an elementary particle called “tachyon” which had imaginary mass and superluminal velocity. Later versions worked upon by John Schwarz and Michael Green, and others reduced the number of dimensions to ten and got rid of tachyon.

The most attractive feature of the theory was that it included force of gravitation within its framework quite naturally. String theory is the only theory, which brings all the fundamental forces under one umbrella. By virtue of this feature, it should unify all the fundamental forces, if unification is at all possible.

But the difficulties are enormous and nobody can still predict with any confidence when it will deliver the unified theory, if it ever will. Einstein was fortunate in a way that he had all the mathematics required for his theory of general relativity, readily available to him. He built the edifice of his theory on the mathematics developed by Georg Riemann (1826-1866) nearly half a century before Einstein used it. The string theorists have to develop all the needed complicated mathematics with the progression of their work.

With the introduction of supersymmetry into the mathematical framework of the theory, there was a fresh resurgence of interest in the string theory. The ultimate goal of unification appeared within reach. The new optimism led Stephen Hawking to declare in his Lucasian lecture on April 29, 1980, that the unified theory of quantum gravity will be developed before the end of the twentieth century. This however did not occur and as it happens so very often in scientific research, by the time one irksome problem is tamed, some others pop up inevitably.

The new problem with the string theory or the superstring theory as it was called to distinguish it from the older version, was that it had five different versions and no body knew how to deal with them. In due time, in 1995, Ed Witten argued on the basis of duality (two apparently different theories are different version of the same theory) that the five versions were not fundamentally different from each other; they were in reality the reflections of the same physical reality. For this purpose, he had to add one more dimension to the other ten thus increasing the number of dimensions in which the new theory would work, to eleven.

The theory also predicted that depending on the energy content, a string could expand and form a sort of membrane. This new theory is called M (membrane) theory. As Ed Witten remarked, “The richer theory has as limiting cases the five string theories studied in the last generation, (and) has come to be called M-theory, where M stands for magic, mystery, or matrix,” [3]. Many like to think that M stands for mother, that is, the M-theory is the mother of all string theories.

An expanded membrane can become as large as the whole universe and when two small branes (short for membranes) of high energy content collide with each other, an explosion like the ‘big bang’ can take place. The big bang, which created our universe was the result of collision of two such branes. The theory also predicts that our universe is situated within a megaverse, which may be enveloping numerous other universes like ours. The strings attached to these various universes may vibrate with different frequencies. Vibrations of a string define the properties of the corresponding elementary particles that the vibrating strings represent because each material particle is nothing but the vibrations of a string. The vibrations of different branes (universes) may thus assign different laws of nature to the plethora of universes. The unification that is being sought is for the unification of the fundamental forces in our universe and such a unified theory will not be applicable in other universes.

And now a word about the character of strings. Answering a question: what is string theory? Ed Witten said, “String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string. One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty….So in the case of one of these strings it can oscillate in many different forms – analogously to the overtones of a piano string. And these different forms of vibrations are interpreted as different elementary particles: quarks, electrons, photons. All are different forms of vibration of the same basic string. Unity of the different forces and particles is achieved because they all come from different kinds of vibrations of the same basic string,” [3]. So the fuzziness that is displayed by the duality of wave and the material structure of the particles, is somehow explained by the vibrating string.

These ideas are so strange and unfamiliar, even to many physicists, that they complain that string theory is a kind of philosophy and not physics. But then new ideas and new theories are always like that. The relativistic character of time embedded in the theory of relativity was not easy to comprehend in the beginning, nor a very palatable one, to many who were used to thinking in the framework of Newtonian physics.

However, one of the things that is of serious concern to many physicists like Glashow is that the string theory doesn’t look like ‘testable’ empirically. It is a theory, which cannot be ‘falsified’ and hence ‘unscientific’. However, its strong proponents like Ed Witten, Brian Green, and others believe that there are ways, although only a few at the time, in which the theory can be tested. One of these tests is via the string theory of the black holes, which was developed by Susskind, Cumrun Vafa, and others. According to Susskind, “To this day the only real physics problem that has been solved by the string theory is the problem of black holes. It led to some extremely revolutionary and strange ideas,” [5]. Other testable results might be discovered in future.

One of the most vitriolic critics of the string theory is Sheldon Glashow.
He said, “The string theorists have a theory that appears to be consistent and is very beautiful, very complex, and I don’t understand it. It gives a quantum theory of gravity that appears to be consistent but doesn’t make any other predictions. That is to say, there ain’t no experiment that could be done nor is there any observation that could be made that would say, you guys are wrong. The theory is safe, permanently safe. I ask you, is that a theory of physics or a philosophy?” [2]. At another occasion, he was asked, in 1986, to summarize the Toe in no more than seven words and “he exclaimed in mock anguish, ‘Oh, Lord, why have you forsaken me?’” [7].

This is reminiscent of the logical positivists at the turn of the twentieth century who had prohibited talking about things like atoms that could not be seen or observed. Atoms now are a fact of life.

In spite of this, Glashow’s skepticism is not totally misplaced and is not so difficult to comprehend either. Some of the new developments in the string theory appear to be too eerie and outlandish. For example, Cumrun Vafa, Physics Professor at Harvard University, has formulated a string theory in 12 dimensions, which he calls F-theory in contrast to the M-theory (if M stands for mother, F stands for father). In this theory, there are ten dimensions of space and two of time. It is difficult to perceive a two-dimensional time, hypertime, even for the dedicated string theorists.

Conclusion

The string theory appears to be the only theory so far that can unify the fundamental forces of nature. There is no clear hint so far as to when such unification will be achieved. Such a theory will probably also explain how the universe originated and whether ours is the only universe that is there. Or, there are many others also. It will probably also shed light on the dark (invisible) matter and energy and its structure and the true nature (or ontology, if you will) of the cosmological constant. The unified theory may not be literally a Theory of Everything (TOE) but it will explain many mysterious problems that are confronting the physicists.

References

1.Duncan L. Copp, “Welcome to the 11th Dimension,” Science in Space, wysiwyg://23/http:www.channel4.co…/S/science/space/stringtheory3.htm, November, 2003.
2.Sheldon Glashow, “Viewpoints on String Theory,” The Elegant Universe Homepage, Nova Science Programming, wysiwyg://http://www.pbs.org/wgbh/nova/elegant/view-glashow. htm, July, 2003.
3.Edward Witten, “Magic, Mystery, and Matrix,” Notices of the AMS, Volume 45, Number 9, October, 1998, pp. 1124-1129.
4.“A Conversation with Brian Greene,” The Elegant Universe Homepage, Nova Science Programming, wysiwyg://25/http:www.pbs.org/wgbh/nova/elegant/greene.htm, July, 2003.
5.Brian Greene, “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory”, W.W. Norton & Company, New York, 1999, p. 137.
6.Leonard Susskind, “The Third Culture,” Edge, http://www.edge.org/3rd_culture/susskind03/susskind_index.ht m.
7.“Duality Articles,” http:www.dhushara.com/book/quantcos/dual/dual.htm.