# Strings '99 - in search of the theory of everything

The program of the conference provided a host of offerings. The 46 lectures focused on topics such as:

• Quantum physics of black holes (especially Hawking radiation)

• Black holes and their "microscopic" explanation in string theory

• Quantum cosmology

• Higher dimensions of space and time

• Generalizations of string theories, as e.g. relativistic membranes, "p-branes” and matrix models

• Models of non-commutative geometries of space and time

• Newly observable effects of string theory in astrophysics and elementary particle physics

• String theory and conformal quantum field theory

• Mathematics and string theory

The conference made important progress in all of these areas. In particular, the new results on the relationship between non-communicative geometry and string theory, which were presented for the first time at this conference, could prove to be ground-breaking for future developments in string theory. Hermann Nicolai emphasized: "This would enable us to understand how string theory dissolves the space-time continuum at very small distances and replaces it with 'quantum space-time'.”

The Albert Einstein Institute, headquartered in Golm near Potsdam, was instrumental in organizing the conference. Founded just four years ago, it is already one of the most important research centres in the field of gravitational physics. However, the success of the conference was also due to the special dedication and commitment of the other members of the local organizing committee: Prof. Olaf Lechtenfeld (University of Hannover), Prof. Jan Louis (University of Halle), Prof. Dieter Lüst (Humboldt University Berlin), who is also a Scientific Member of the Albert Einstein Institute and Dr. Kurt Miesel (University of Potsdam), as well as a large number of helpers from the participating institutions.

The public highlight of the conference was an event on Saturday afternoon, where the Albert Einstein Institute and the Einstein Forum in Potsdam had been invited to the Auditorium Maximum of Potsdam University. The public showed an overwhelming interest in hearing first-hand about the current state of research in this area. Well over a thousand people turned out to experience in person the world-famous physicist Stephen Hawking, the leading string theorist Edward Witten, as well as the expert on relativistic astrophysics and Managing Director of the Albert Einstein Institute, Prof. Bernard F. Schutz. In addition to the Auditorium Maximum, which accommodates 420 people, the university transferred the event via video to five other lecture halls, so that more than a thousand people could follow the lectures. Another three hundred people gathered on the meadow in front of the Auditorium Maximum and listened spellbound and still to the words of the physicists, which were transmitted outside with loudspeakers.

## The history of string conferences

Strings '99 in Potsdam was the eleventh in the series of "Strings" conferences. The tradition of string theorists of meeting annually at an international "Strings" conference in order to exchange new ideas and results began in 1985 in Argonne, USA. During the previous year, the physicists John Schwarz and Michael Green initiated the first revolution in string theory that created hopes of using string theory to combine quantum and gravitational theory with one another. The 1995 Strings conference in Los Angeles was in the showplace of the second revolution: Ed Witten showed that all string theories could be combined into one intellectual structure. In 1997 the Strings Conference took place in Amsterdam and thereby for the first time in Europe. In 1999, Germany was the host and thus established itself as a significant participant in the search for the theory of everything.

## String theory and its developments

*Summary*

For the scientific layman, physics appears to deal with seemingly completely different topics. Mechanics, thermodynamics, optics, electricity, magnetism, atomic physics and nuclear physics are examples thereof. Yet the British physicist Maxwell, in 1873, was able to describe electrical, magnetic, and optical phenomena of physics in a uniform manner. At the end of the twentieth century, with Einstein’s general theory of relativity and the standard model of particle physics we now have physical theories that describe natural processes over a vast range of distances, from the diameter of a proton to the diameter of the visible universe. And all by using mathematical formulas that fit on a piece of paper!

However, the search of physicists for a comprehensive, unified theory encounters a hard mathematical limit in an attempt to reconcile gravity and quantum theory. String theory seeks to overcome this. It no longer interprets elementary particles as point-shaped but rather as threadlike structures. This has given rise to the hope that string theory can also be used to explain the origin of matter.

The search of physicists for a unified theory also borders on metaphysics. There is a continuing fascination with this Holy Grail of physics – and not just for researchers. With the enormous ranges in size that physics spans, it reaches the limits of what the human mind can comprehend.

*Basic information*

The terms "matter" and "force" play a fundamental role in physics.

Matter

All matter is made up of building blocks, leptons and quarks.

Force

According to modern knowledge, four fundamental forces exist, which act upon the building blocks of matter (in modern physics the term "interaction" has generally replaced that of “force.”)

Gravity (gravitation)

It is known from everyday life, holds us on the ground of our home planet and is responsible for the large-scale structure of the universe, as well as the distribution of matter (stars and galaxies) therein.

Electromagnetism

Electromagnetic interactions are also known from everyday life. They play the decisive role “in miniature," i.e. at molecular and atomic distances. Thus, with the aid of quantum theory, almost all the phenomena of atomic and molecular physics, as well as of chemistry, can be traced back to it.

Weak interaction

Weak interaction causes radioactive decay and is important for the processes that occur in the interior of the sun.

Strong interaction (nuclear force)

Strong interaction only takes place in the nucleus. Nevertheless, it is decisive for our existence, because it overcomes the powerful electrical forces of repulsion that act between the protons in the nucleus due to the fact that they have the same charge. It keeps the core building blocks - and thereby us - together.

There may be other undetected interactions. However, the search for a "fifth force" has been unsuccessful up to now.

The first steps towards unification

The decisive step towards unification was the development of the standard model of elementary particle physics, in the framework of which the aforementioned distinction between force and matter lost its significance. This is because it assigns an elementary particle (so-called vector bosons) to the strong, weak and electromagnetic forces as carriers. For example, electromagnetic interaction is caused by the exchange of photons.

The standard model of particle physics is the most comprehensive description of physical phenomena among all known theories. However, since it still leaves central questions unanswered, it is probably not a definitive theory.

Moreover, difficulties arise in the treatment of the standard model within the framework of quantum theory, since the calculation of elementary processes gives rise to infinities (divergences) in the mathematical expressions. For example, the mass (intrinsic energy) of electrons becomes infinite based on naive calculation. This question has been solved with the renormalization method developed over the past forty years. It has led to the most accurate confirmed predictions in physics (anomalous magnetic movement of electrons) and works when applied to quantum electrodynamics as well as in the case of strong and weak interactions.

However, when applied to gravitation, it fails completely. This gives rise to new divergences, which cannot be eliminated with previous methods. The treatment of gravity in terms of quantum theory thereby loses any power of prediction. Quantum theory and gravitation do not seem to "tolerate" one another.

## Why must quantum theory and gravity be reconciled?

The effects of quantum gravity only first become effective at unimaginably small distances. This gives rise to the question as to whether a quantum theory of gravity is necessary at all. Why can’t one live with a mathematically inconsistent theory, as long as its inner contradictions are restricted to unobservably small quantities?

According to the general theory of relativity, the structure of space-time is essentially determined by the distribution of matter. As a result, it does not seem possible to avoid the idea that quantum theory ultimately affects space-time.

The (probably common) occurrence of "black holes" in the universe, at the centre of which the classical space-time ends in a singularity, also points to the inevitability of the quantum-theoretical treatment of gravity.

As a result, the only way out is to search for a new theory which contains the standard model and the general theory of relativity as borderline cases, but which overcomes their mathematical contradictions.

String theory as the approach to a solution

Superstring theory offers the most promising approach. It could reconcile quantum theory with gravity, in that it interprets elementary particles as different stimulus states of a single thread-like structure. It can be thought of as a tiny (about 10-³³ cm) vibrating string. This is fundamentally different from conventional quantum field theory, which treats elementary particles as point-shaped objects.

The advantage of assuming string-shaped elementary particles is that the contradictions described above are avoided. Superstring theory always yields finite results in arbitrary orders. The infinite number of additional "oscillation excitations" of superstrings contribute to the calculation, so that all divergences cancel out.

Is the origin of matter explained?

It is surprising that the remaining massless states that populate the "low energy field" are, in some versions of superstring theory, quite close to the observed spectrum of the elementary particles and also demonstrate their "handiness" (chirality). These successes have given rise to hopes that the theory can not only resolve the contradiction between quantum theory and gravitation, but can also explain the origin of matter.

A radical modification of space-time concepts is necessary

In spite of their incompleteness, the results achieved so far place in question the proven basic principles of quantum field theory and are likely to force a radical modification of conventional space-time concepts at extremely small distances. It is expected that, in a theory of quantum gravity the concept of the space point and thus the concept of the space-time continuum will be replaced by a superordinate concept. Just as the orbit of an electron loses meaning in quantum theory. Presumably, in such a theory the familiar distinction between space-time and matter would also be invalid. So far, however, the enormous mathematical and conceptual difficulties thereof have thwarted all attempts to understand what "really happens," where space and time loses their validity.