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In search of a final theory

Research sets out to unify the basic forces of nature

One of the greatest challenges for modern physics is to develop a theory that describes, in a unified manner, all the phenomena of the Universe. The big obstacle is the incompatibility between two of the main theories of physics of this century, general relativity and quantum mechanics. This challenge is the theme of research by Victor de Oliveira Rivelles, a professor of Ifusp, the Institute of Physics of the University of São Paulo, who has dedicated himself to the problem since the 80s.

Each of these theories performs its role perfectly, when applied in the context in which it was created. But they both fail when applied to the phenomena described by the other.  Why, then, should they be modified and not left as they stand?

The idea of unification has been the mainspring of the advances in physics since its primordial days. Until the 17th century, the movement of earthly and celestial bodies was considered separately. Earthly bodies would tend to stop after being in movement for some time, because of their earthly nature. The celestial bodies, however, like the sun, the moon, and the planets, would remain in movement eternally – which would be a sign of their divine nature.

Classical mechanics, drawn up by the English physicist Isaac Newton (1642-1727), showed that earthly and celestial bodies obeyed the same laws of movement, by giving a unified description for them both. His ideas caused a profound philosophical and religious change, since they showed, mathematically, that the movement of bodies in the skies was purely material.

By synthesizing theories that appeared to be antagonistic, scientists succeeded in describing a larger number of phenomena with fewer hypotheses, as well foreseeing phenomena in the future. On the basis of his theory, for example, Newton was able to foresee the exact date of the return of Halley’s Comet.

The German physicist Albert Einstein (1879-1955), according to his biographer Abraham Pais (in Subtle is the Lord- the Science and Life of Einstein),  said that the theory of physics has two aspirations:  “Comprising the most phenomena and their connections possible” and “achieving this based on the smallest possible number of independent concepts and arbitrarily presupposed relations”.

The fundamental objective of the unification of theories of physics is, therefore, to obtain more effective models to explain and to control nature. This was what Einstein achieved in 1915, when he conceived general relativity: a theory of gravity more comprehensive than Newton’s.

In the Department of Physical Mathematics at USP’s Institute of Physics, Rivelles and another eight physicists (post-doctorate and post-graduate) have been working for three and a half years on the Quantum Gravity project, with finance of R$ 3,400 from FAPESP.  Besides USP, there are studies in this area at the state universities of São Paulo (Unesp) and Rio de Janeiro (UERF), and at the federal universities of Rio de Janeiro (UFRJ) and Rio Grande do Sul (UFRGS) and at the CBPF, the Brazilian Center for Research in Physics.

They have no doubts: the result may revolutionize Physics. But it is not easy getting there. After all, the two extremes of this conciliation are the main pillars if modern Physics.

Micro versus macro
Quantum mechanics may seem to the laymen to be a jumble of concepts that defy common sense: what now seems to be a particle behaves like a wave, and vice versa. Besides this apparent contradiction, there is the permanent loss of what was left of classical physics. After centuries of tranquility, with the determinist equations of movement, scientists had to face up to the terrible principle of uncertainty, drawn up by the German physicist Werner Heisenberg (1901-1976), according to which it is impossible to determine simultaneously the position and the velocity of a particle.  “When we try to apply the concepts of quantum mechanics to general relativity, we are led to absurd results, which contradict the very foundations of these theories”, says Rivelles.

Does God play dice?
In spite of having contributed towards the birth of quantum mechanics, Einstein never accepted its probabilistic interpretation. In classical physics, every physical quantity has a determinate value. In the quantum world, however, probability took over. “God does not play dice with the Universe”, said Einstein. The British physicist Stephen Hawking (1942-), who occupies the same post as Newton at Cambridge University, rebuts Einstein: “Yes, God does play dice!”

And so the conflict between quantum mechanics and general relativity was instituted.  Many physicists followed the steps of Einstein and proposed changes to quantum mechanics. Hawking himself took the first few steps in this direction.  Holland’s Gerard’t Hooft (1946-) – 1999 Nobel Physics prize for his work on the unification of weak and electromagnetic forces – and the American Leonard Susskind (1940-) – whose birthday was commemorated at the end of May at Stanford University, where he lectures, with a seminar on quantum gravity – propose to maintain quantum mechanics and to make some changes in general relativity. The first signs that it really is general relativity that should be changed came with the proposal of superstrings, in the mid-80s.

The motivation for the superstrings is based on the discovery that the concept of a particle idealized as a point of matter is unsuitable to bring quanta to general relativity. The theories of strings are radically different from the usual theories.  The fundamental objects are no longer particle points, but extended, unidimensional objects, which are called strings”, says Rivelles. “As they are very small in size, they seem to behave like particles”.  The theory of strings is a matter for study, in São Paulo, by researchers Nathan Berkovits, from Unesp’s Institute of Theoretical Physics, and Élcio Abdalla, from USP’s Institute of Physics.

The theories of strings, however, need to be drawn up so as to describe all the known types of elementary particles. One of the theories of strings considers the existence of a particle with all the properties of the graviton, and which, although still not proven in experiments, would be capable of carrying the force of gravity. It is a result that Rivelles regards as surprising. Another particle provided for in the theory of strings has the property of moving at a speed faster than light. The existence of this particle, the tachion, is ruled out by Einstein’s special relativity.

That is where the concept of supersymmetry comes in, solving the problem by eliminating the undesirable particle. Supersymmetry – a theme that Rivelles covered in the thesis for his doctorate in 1982, at King’s College in London, United Kingdom – is a theoretic artifice that unifies all the particles and forces of nature, simply by regarding two kinds of very distinct particles, the bosons and the fermions, as being on an equal footing.

By applying supersymmetry, the theories of strings are transformed into theories of superstrings, unifying in a suitable way all the kinds of fundamental particles. One of the surprises of the theory of superstrings, according to Rivelles, is that it presupposes ten dimensional space, of which nine dimensions are of space and one of time. The explanation for the fact that our space-time only shows four dimensions is that at the beginning of the formation of the Universe, straight after the Big Bang, six of these dimensions became extremely small.

This is an area in which practical proof is regarded as virtually impossible, as tiny distances are involved, billions and billions of times smaller than the distances investigated in the most modern particle accelerators in use (and these go down to distances of a billionth of a billionth of a centimeter).  It is a situation analogous to that of the Big Bang, the explosion said to have originated the Universe and which is equally impossible to prove.

The theory of superstrings, according to Rivelles, may be able to foresee unknown relations between particles, and even the existence of new particles, and, therefore, of forces still not detected.  As the theory of superstrings becomes consolidated, it may even solve questions that intrigue physicists and philosophers, such as: why does the Universe exist in four dimensions (the three dimensions of space, length, breadth and height, plus the dimension of time), and not in more or less dimensions?  Why does matter appear only in the form of quarks and leptons?

Rivelles does not lose heart when he remembers that only a few bits of the theory of superstrings are known. Doubts are piling up, but this theory, which ought to describe all the forces of the Universe, is still in its infancy, and drawing it up completely will take a long time, the researcher observes. Einstein himself took ten years to draw up the theory of general relativity, which just describes gravity. Years ago, the American physicist Edward Witten commented – and colleagues all over the world agree – that the theory of superstrings is a 21st century theory that was discovered by chance at the end of the 20th century.

• Victor de Oliveira Rivelles, 48 years old, graduated in 1974 from the Institute of Physics of the University of São Paulo, with a master’s degree in 1977 from the Federal University of Paraiba (UFPB), doctorate in 1982 from King’s College, of London, has been a professor with the Institute of Physics since 1987.
Project: Quantum Gravity
Investment: R$ 3,452.00


Two incompatible theories
Quantum mechanics was born in 1900, with the theory of Max Planck (1858-1947), according to which energy does not propagate itself in a continuous flow, but through small packets of energy, the quanta.  This made two advances possible: Albert Einstein’s proposition of 1905 that light is also propagated by means of packets of energy, and the atomic model of Denmark’s Niels Bohr (1892-1987).

Also in 1905, Einstein drew up the theory of restricted relativity, based on the proposition that no body may reach a speed greater than that of light in a vacuum (300,000 km/sec).   Afterwards, he disclosed the equation E=mc2 (energy is equal to mass multiplied by speed of light squared). And, in 1915, he launched the theory of general relativity, showing that the gravity of a body deforms the space and time around it. This thesis was proved a few years later, after an eclipse of the sun at Sobral, in Ceará: comparing the positions of the stars around the sun before and during the eclipse, it was discovered that, seen from here, they seemed to be nearer, due to the passage of rays of light close to the sun’s gravitational field.

General relativity inspired other theories, like the one of expansion of the Universe, by America’s Edwin Hubble (1889-1953), in 1929, and the one of the formation of black holes, by the American of Indian origin, Subrahmanyan Chandrasekhar (1910- 1995), in 1931. In 1997, Wei Cui, of the Massachusetts Institute of Technology, and collaborators from Nasa, the space agency of the United States, announced the discovery of black holes that dragged in the space-time around them, which proved the forecasts made using general relativity, 80 years before, when there was still no incompatibility with the quantum theory.  In 1924, France’s Louis-Victor de Broglie (1892-1987) proposed wave-particle duality, which earned him the Nobel Prize for Physics, five years later: it showed that the electron can show the behavior of a wave, and that of a particle as well.

Three years later, it was the turn of Werner Heisenberg, with the principle of uncertainty.  Contrary to the whole tradition of classic mechanics, in which the position and speed of a body could always be determined precisely, Heisenberg showed that in the domain of quanta it is impossible to determine both with precision, simultaneously. Einstein never accepted this proposition.

The many concepts to explain nature

1915 – General relativity
Albert Einstein shows that the gravity of bodies deforms time and space around them, and that the theory of gravity of Isaac Newton does not explain completely phenomena involving very strong gravitational fields.

1924 – Duality
The French physicist Louis-Victor de Broglie (1892-1987) shows that the electron can show characteristics both of a corpuscle and of a wave. It was an advance that was essential for quantum mechanics to be drawn up.

1927 – Uncertainty
Werner Heisenberg puts forward his principle of uncertainty, showing that it is impossible to measure with precision, simultaneously, the position and the speed of a particle.

1928 – Quantum mechanics
A group of physicists – including Austria’s Erwin Schrodinger (1887-1961), and, next to him, Germany’s Max Born (1882-1970, Nobel Prize for Physics in 1954) – finalizes the mathematical methods for interpreting quantum mechanics, announced in 1900 by Max Planck.

1970 – The birth of the theory of strings
Physicists have reached the consensus that general relativity is not compatible with quantum mechanics. The Japanese physicist Yoichiro Nambu, today with the Enrico Fermi Institute, of the University of Chicago, puts forward the theory of strings, in the context of elementary particles. There was still no suspicion that the strings would describe gravity.

1973 – Supersymmetry
Germany’s Julius Wess, from the University of Munich (photo), and Italy’s Bruno Zumino, from the University of California, apply the concept of supersymmetry to the theory of elementary particles. Although supersymmetry was brought into the theory of strings in 1971, it was little known by physicists.

1974 – Strings and gravity
England’s John Schwarz (in the photo), now with Caltech, the California Institute of Technology, and America’s Joel Scherk (who died in the beginning of the 80s) discover that the theory of strings includes general relativity. The theories of strings, still in their primordial days, show themselves to be inconsistent and are left aside.  Few physicists continue to study them.

1984 – The first revolution: superstrings
The inconsistencies are overcome by England’s Michael Green, of Cambridge University, and J. Schwarz.  Five theories of superstrings are discovered.  This is the so-called first superstring revolution.

1995 – The second revolution: the M theory
The American physicist Edward Witten, from Caltech, proposes that the superstring theories form a small part of a more general theory, the M theory, which includes strings, membranes, and supersymmetrical gravity theories.  The membranes are one of the more simple extensions of the string concept, the equivalent to the surface of a soap bubble.