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'Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory.'
Consider a vortex in water this can behave like a string.
... .... ... missing an important fact.
pulling on a point
Many problems can be treated geometrically and I tend to explain my own thinking and decision processes in terms of mutidimensional elastic strings pulling on a point. However to get all mystical about it an look for too much is probably unwise.As to going for a theory of everything geometrically its probably quite a good approach and string theorests have worked hard on interesting geometrical ideas but I feel quite strongly that they are missing an important fact. The strings are not arbitrary and structureless but have structure. Consider a vortex in water this can behave like a string. I have always believed that the fundamental structire of the universe is based on the emergence of longlived structures in the form of vortices from a random structure of turbulent very high energy space-time. These would effectively look like strings.
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