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Superstrings without knots

Approach created by a Unesp researcher makes the calculations in the theory that aims to unify the forces of nature easier

A baby emits its first sounds during its first month of life, and with time begins to speak vowels and words, which at first appear to be a foreign language, until finally he says mummy or daddy. During the last three decades, the Superstrings Theory – one of the frontiers of physics, which aims to bring together all of the known forces and to look to explain extreme phenomena, from the interior of an atom to the depths of the universe – has passed through a similar evolution.

One of the most recent advances in this field was produced by a group or researchers led by the North American, naturalized Brazilian Nathan Jacob Berkovits, from the Theoretical Physics Institute (IFT) of the São Paulo State University (Unesp). It consists of a new mathematical language, destined to resolve a problem that has tormented physicists for more than twenty five years: the complexity of the calculations in the Superstrings Theory.

Berkovits, a forty-one-year-old physicist who maintains a jovial and unspoiled air about him, looked at an old difficulty through new eyes and created a short cut that allows for the manipulation with greater easiness of the Theory of Superstrings: for the first time, he has managed to carry out calculations that deal on an equal footing with two groups of subatomic particles. One of them is the bosons, force transporters: that are formed by photons, which conduct light, and the gravitons, those which carry the force of gravity.

The other group is that of the fermions, particles that go to make up matter: those are the electrons and quarks. When the bosons and fermions were viewed in a different manner, it was much more difficult to develop the equations that would look towards forecasting the behavior of subatomic particles. “The calculations involving fermions were extremely troublesome”, explains the Unesp researcher, who for some fifteen years had been chewing over these problems. “I only changed the manner of dealing with the particles.”

The new approach could have important implications. Initially, in saving time: instead of weeks, one might spend only a few days to carry out the mathematical reasoning; or say, hours instead of days. Specifically, the model simplifies the calculations that involvesuper-symmetry – a concept of the subatomic world related to the spinning of particles around themselves, as if they were little planets – and for this reason facilitates the resolution of one of the most challenging problems in physics: to include the General Theory of Relativity into the world of quantum mechanics – which is fundamental for the theoretical unification of all of the forces and interactions of nature.

Besides simplifying the calculations that involve super-symmetry, the model allows one to formulate in the Superstrings Theory some calculations that previously were impractical. According to Berkovits, the new calculations could be used, for example, to test the recent conjecture by Juan Maldacena, a talented young Argentinean physicist of only thirty three years of age, which explains the interaction between quarks – particles that make up the protons and the neutrons of an atomic nucleus.

Published in April of 2000 in the Journal of High Energy Physics and presented in July of the same year at Strings 2000, a congress of specialists in superstrings who met at Michigan University, in the United States – and since then has been improved through dozens of scientific articles in specialist magazines -, the Berkovits model has generated admiration and surprise. “It is impressive that a physicist working almost alone has developed this model”, comments one of the pioneers of the Superstrings Theory, the American physicist John Schwarz, from the Californian Technology Institute (Caltech), in the United States. “This piece of work shows great talent and determination.”

It was not a piece of work so lonely. In 1994, Berkovits traded Kings College in London for the IFT, a place with a shortage of specialists in his area. The work that solved the problem of the treatment of the bosons and the fermions included collaborators such as Cumrun Vafa, from the University of Harvard, Warren Siegel, from New York State University in Stony Brook, both in the United States, and undergraduate and post-doctorate students at the IFT such as Brenno Carlini Vallilo, Carlos Tello Echevarria, Marcelo Leite, Osvaldo Chandía and Vladimir Pershin.

Berkovits continues to research his model, given the name of Pure Spinor Formalism (spinor is a mathematical resource used to describe the position and the behavior of subatomic particles). The researcher, who this year has already published four papers on the question, is developing applications that are more and more refined. “I was invited to present the steps in the unfolding of the original model at the Strings conference to be held this year in England”, he advised.

The understanding of the model, especially for non-specialists, demands a panoramic vision of the history, of the defects, of the qualities and the difficulties of the Superstrings Theory. It awakens sentiments that range from total discredit, when looked at from the point of view of the insurmountable difficulties, to euphoria, given its potential to solve problems that in another manner appear insoluble. Since its creation at the end of the 60s, it has shown itself to be a revolutionary concept. Revolutionary, because it changed the concept of subatomic particles: they are no longer seen as points, but small chords, opened or closed, which vibrate like the strings of a violin, and would have dimensions calculated as 10-35 meters (the number 1 preceded by 35 zeros after the point). The approximately two hundred particles known today would be no more than different forms of vibration of these microstrings, somewhat similar to musical notes.

The theory, considered elegant by the very physicists themselves, has intriguing implications. Strings could vibrate in incalculable manners, which would create the possibility of the existence of an infinite number of particles in the universe. The Austrian physicist Isidor Isaac Rabi (1898-1988, Nobel Prize winner of 1944) would have enjoyed himself nowadays with the question which he made when he related that one more particle, the muon, had been discovered: “Who asked for this particle?” Detail: he said this in 1936 and shortly afterwards dozens of other particles were discovered.

The Superstrings Theory suggests that both the behavior and the basic characteristics of particles, such as mass and electrical charge, are defined by the vibration kind of the strings. Probably the strings will never be seen: tunnel microscopes are capable of examining atoms – in a recent achievement, a group of IBM researchers wrote the name of the company using thirty five atoms of xenon -, but there is no way of visualizing the chords, so small that, if one atom was the size of the Earth, they would be the size of an atom. The concept is absolute: the entire Universe – including ourselves, human beings – is nothing more than vibrating strings.

For example, the Superstrings Theory was used to explain a type of radiation emitted by black holes, Hawking radiation, a name given to it in recognition of the English physicist Stephen Hawking. The theory is also one of the means by which physicists are looking to understand the explosion that gave origin to the Universe, the Big Bang, and even the possibility of having twin universes, one giving origin to the other.

From an atom to planets
The major objective of the Superchord Theory, which the Unesp group is helping to put together, is the unification of the equations – or to make them interchangeable – for the four forces of nature: strong, weak, electromagnetic and gravitational. The first two act essentially within the interior of the atom: the strong force (or interaction) makes the quarks of the nucleus remain close to each other and the weak force is responsible for their radioactivity. Then on a more observable plane, the electromagnetic force allows for the use of electricity and makes motors work, while the gravitational force makes the bodies of the universe attract each other – and is the weakest of all but is that which maintains the planets in orbit.

The strings could bind together the microscopic world of quantum mechanics – which integrated the three first forces – with the macroscopic world of general relativity, sustained by gravity. This is not easy because of the very definition of gravitational force: it is the result of the multiplication of the value of each mass involved, divided by the square of their distance. In the subatomic world, when a particle is close to another, the distance is so minimum, which, mathematically, has the gravity force tending to infinity – a result that perturbs the quantum world and makes impossible the integration of gravity with the other forces.

The search for the unification of the forces was too much for the creator of the two Theories of Relativity, specific and general, the Jewish German Albert Einstein (1879-1955), and persists as a challenge for the greatest intelligences in science. Right from its birth, in the 70s, the Superstrings Theory aims to explain everything that occurred with forces and interactions in nature. But the first version, put together by three physicist – John Schwarz of Caltech, Pierre Ramond from Florida University, in the United States, and André Neveu, from the Montpellier II University, in France – had a problem: its mathematical tools, that is to say its vocabulary, were inadequate to describe a key concept of Superstrings Theory, super-symmetry.

The Superstrings Theory forecasts that nature has another symmetry, as well as those already known, the symmetry of space-time – according to which the laws of physics are the same, whether on Earth, on Mars or at any other point of the Universe. This new form of organization of nature, called super-symmetry, is related to the rotation of particles about their own axis, in the same manner that the Earth spins about its own axis once every 24 hours, – and the so called spin, a characteristic as important for the subatomic particles as their mass and charge.

However, while the Earth only manages to rotate around itself in one only form, nature has divided particles into two distinct groups, each one rotating in a different form- the bosons and the fermions. Super-symmetry implies that for each boson there is a corresponding fermion. For example, the electron, which is a fermion, will have a super-symmetrical partner, the seletron (s for super), which is a boson. The physicists themselves have doubts about the existence of these twin-particles, called super-partners, since none of them have yet been found.

Schwarz, who was part of the first team of formulators of the theory, did not give up trying to find a more adequate manner of dealing with super-symmetry. In 1984, along with the English physicist Michael Green, he finally found the necessary tools. It was a moment of euphoria, that became known as the First revolution of the Superstrings Theory and attracted hundreds of physicists to the area. But the blanket was short. On covering the head, creating a vocabulary to describe super-symmetry, the symmetries that deal with space and time began to behave in a strange fashion and did not fit in directly to the new model. The feet stuck out at the end.

Possible accounts
Berkovits’ model fixes this problem, just like a baby that, after learning some single words, manages sufficient vocabulary to put a phrase together – the vocabulary that Berkovits created allows one to study superstrings in a new manner, up until that moment impossible as previously described. A group that includes Berkovits, physicists from the Massachusetts Institute of Technology (MIT) and from the Universities of Harvard and North Carolina in the United States, as well as Witten, Vafa and post-doctorate students at the IFT, applied this approach in the analysis of the properties of Maldacena conjecture, which opens the door to understanding, in detail, the behavior of the particles in the atomic nucleus – and the work went ahead.

“Before, it was impossible to carry out any calculations concerning Maldacena’s conjecture”, comments Berkovits. Little by little, evidence came forward that this focus was managing to harmonize super-symmetry and the symmetry of space-time in the Superstrings Theory, simply by eliminating the differences of the mathematical treatment between bosons and fermions, seen before as distinctly different formulae and now making up part of the same equations.

Another vision of the Earth
But, in order to arrive at this solution, it was necessary to change one’s point of view, as if the problem were to find a single person on the planet. To describe their position – latitude and longitude -, we could use two types of coordinates: Cartesian or polar. The first has three perpendicular variables (height, width and depth) and deals with the Earth as if it were a cube. The polar coordinate substitutes height for latitude, width for longitude and depth for the radius of the Earth, now seen as a sphere. It was basically this that Berkovits did: used a more adequate form that that of his colleagues to describe super-symmetry, as if he had found a short-cut.

The significance of his work could be even greater. The model may perhaps manage a more uniform description of the five Superstrings Theories already known. Yes, nothing is simple in this area, but the American physicist Edward Witten, one of the most important in this field, gave a beautiful push forward by demonstrating, in 1995, that these theories are only different versions of another that he named Theory M – the letter that reminds one either of mother, membrane or matrix. Until this moment, the Superstrings Theory appeared to be an animal that had only been partially observed – either the head or the tail -, without an overall view.

Witten managed to look at the mosaic formed by these flashes and generated another moment of euphoria among physicists – it was the Second Revolution of Superstrings Theory. Witten has been accompanying the work of the Unesp group for many years. “Berkovits’model is elegant and surprising”, he comments. It could be that we are close to the Third Revolution of Superstrings Theory. Let’s wait and see.

The project
Research and Teaching in Chord Theory (nº 09/50639-2); Modality Thematic project; Coordinator Nathan Jacob Berkovits – Institute of Theoretical Physics of Unesp; Investment R$ 52,000.00