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

*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.