On 10/24/2012 11:25 PM, Richard Ruquist wrote:

The compactified dimensions curl-up into particles
that resemble a crystalline structure
with some peculiar properties
compared to ordinary particles,
but nevertheless just particles.

What about that do you not understand?

Dear Richard,

That picture is not consistent with the mathematics as I understand them, they do not "curl up into particles". The explanations for laymen books like to invoke such ideas, but the math tells a different tale. The compactified dimensions exhibit the properties of particles, yes, but they are not free floating. The string picture is very much like a cellular automata on a 3d lattice. This looks like a crystalline structure, yes. One of the problems of string theory is that there is no explanation as to what prevents the compactified manifolds from "uncurling" if we relax the strict orthogonality condition. The Kaluza-Klein theory that inspired string theory has the same problem. There does not seem to be a way to prevent the uncertainty principle from being universal such that the "size" of the compact manifold's radius is not subject to uncertainty. We can try to hand wave this away with the T-duality <http://en.wikipedia.org/wiki/T-duality>, but that just pushes the problem somewhere else. I have tried hard to make string theory "work" for me. I appreciate your enthusiasm for them, but the theory seems too dependent on the assumption of a fundamental substance (in this case an a priori existing lattice of manifolds) and on the vicissitudes of scalar fields. I hope you can appreciate that I simply see string theories as very elegant examples of "pure math" <http://en.wikipedia.org/wiki/Pure_mathematics>.



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