### Re: How is String Theory and Chaos Theory related?

Date: Fri Mar 19 09:55:14 1999
Posted By: Georg Hager, Grad student, Theoretical Particle Physics
Area of science: Physics
ID: 921380811.Ph
Message:

Dear Wesley!

You ask how string theory and chaos theory are related. The problem is that in asking this question you show that you lack some understanding of at least one of those theories. So I will first try to elaborate on string theory and chaos a bit, and finally conclude with an answer to your question.

String theory is an attempt of theoretical physicists to unite the very successful, but separate theories about elementary particles and gravity. Physicists are of the KISS type - `Keep It Simple, Stupid' -, they always want to base their view of nature on principles which are as simple as possible. While the present theories of elementary particles are able to describe experiments (performed in high energy accelerators, for instance) quite well, they lack an essential property: They are not easily brought into accord with Einstein's General Theory of Relativity, which describes gravitation. String theory (in its flavour of `Superstring theory') might prove to be a solution to this problem; in string theory, all the elementary particles we know are represented as vibrations (to be more exact, vibrational modes) of tiny strings. From a mathematical point of view, this concept is very appealing, and it might be possible to derive our present theories of gravitation and elementary particles as only special cases, or limits, of some `greater' and simpler construction. To wrap it up, string theory might present us with a unified approach to a consistent description of matter and forces.

Chaos theory, on the other hand, deals with the description of certain physical systems which are extremely sensitive to initial conditions. The global weather system is of such a type: mathematical models have shown that minor variations of temperature, wind velocity etc.can make a tremendous difference when one wants to extrapolate atmospheric behaviour over some period of time. Apart from that, typical phenomena connected with chaotic systems are intermittency (short `flashes' of ordered, non-chaotic behaviour, like e.g. tornados) and non-analyticity (the inability to describe the motion of a chaotic system in closed mathematical form). Chaotic systems are also typically nonlinear systems. This means that several independent ways in which the system might behave cannot be accomodated at the same time - they would disturb each other (e.g., electromagnetic waves are described by linear equations, which means that waves which take up the same region of space at the same time do not disturb each other).

Now you will understand that chaos theory and string theory are not fundamentally related. Not only do they deal with completely different phenomena, they also have different aims. A wild guess would be that present theories about particles are of the nonlinear type and thus might show chaotic behaviour. On the other hand one also has to take the quantum nature of strings into account, and this is something that chaos theory is just beginning to incorporate.

Hope that helps,
Georg.

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