Abstract
It is a starting point in string theory to assume that elementary particles are in fact rotating strings, and the final goal of the theory is a complete description of fundamental physics, including general relativity. This paper is instead concerned with the reversed question: starting from general relativity, is there a good way to motivate why rotating strings should be more natural models for elementary particles than, say, spherical particles or point-particles? Also, the purpose here is not to motivate full string theory. For example, no hidden dimensions come into play, only the four usual ones, and strings are defined in a very simple geometric way. Rather, the focus is on investigating an interesting mathematical property, which implies that strings may have special features with respect to rotation which spherically symmetric particles have not. In particular, it turns out that in a certain sense rotating strings are simpler than non-rotating ones. This is a consequence of the indefinite metric, and the main result states that the curvature of a non-rotating string, as measured by the square of the scalar curvature, may be reduced by letting it rotate in an appropriate way. The calculations underlying this theorem are heavy and have partly been car-ried out using Mathematica, although in principle the essential theorem may not require super-human labour.
Highlights
It is a starting point in string theory to assume that elementary particles are rotating strings, and the final goal of the theory is a complete description of fundamental physics, including general relativity
String Theory is an ambitious project which starts from the assumption that elementary particles can be understood as rotating strings, and it aims at a complete description of fundamental physics, including general relativity
The calculations in this paper are obviously only a first step towards understanding why curvature is diminished by rotations in Lorentz geometry
Summary
String Theory is an ambitious project which starts from the assumption (among other things) that elementary particles can be understood as rotating strings, and it aims at a complete description of fundamental physics, including general relativity. I proceed in Section 3 to give a few numerical examples computed by Mathematica to give a feeling for what may happen In this case, I consider high-speed rotations, even if this means that one should be careful when drawing conclusions. I consider high-speed rotations, even if this means that one should be careful when drawing conclusions As it seems, the general behavior is rather independent of the exact form of the metric inside the string; all examples indicate a similar behavior where the minimum of the curvature is assumed when the ends of the string rotate with (approximately) the speed of light. I do think that the topic of this paper has got something important to say about Lorentz geometry on the microscopic level and, as a consequence, may contribute to our understanding of the connection between general relativity and quantum mechanics
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