Consider the interaction of point-like photons and electrons (Compton scattering). This is a disaster for quantum gravity since we have infinite energy at the point of interaction.
Consider a loop (closed string) evolving in time. It will span out a world-sheet in spacetime.
The instants t1 and t2 at which the fission and fusion take place have no physical significance since they are not frame invariant.
However, the string interaction is independent of the geometry of the world sheet and depends only on its topology. Topology is a global property of a space and does not depend on the local geometrical structure. For eg., a cube and sphere have the same topology but vastly different geometry (all structures which can be smoothly transformed to each other are topologically equivalent which is why topology is sometimes called "rubber-sheet mathematics").
For eg., Compton scattering from the string theoretic point of view would look as follows.
This string interpretation of Compton scattering in fact does solve the problem of infinities as the interaction is no longer happening at an exact point in spacetime.
The independence of strings from the local properties of spacetime for its interaction is a fundamental new symmetry in theoretical physics.
Last updated: 03 March, 2000
