Quantum Gravity 367.7: Strong Interaction/Force as Combinatorial Catalan Number Elasticity Unrelated to Quantum Theory
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From: OsherD on 30 Apr 2010 22:04 From Osher Doctorow The Catalan Numbers which I discussed somewhat in a very recent post here have a remarkable ability to "mimic" the Strong Interaction/ Force. See Wikipedia's online "Catalan Number". The nth Catalan Number C_n or Cn is defined as: 1) Cn = (definition) (1/(n+1)) C(2n, n) where C(2n, n) the number of ways of choosing n things without order (n unordered things) from 2n things. The most interesting characterization of Catalan Numbers for our purposes is: 2) Cn = number of ways of cutting a convex polygon with n + 2 sides into triangles by connecting any two non-adjacent vertices by a straight line segment. Triangles (and the 3 vertices and 3 sides) should immediately conjure up a picture of quark triples in hadrons. The Strong Interaction's almost non-effect at close proximity of quarks would correspond to a "collapsing" triangle where the vertices approach each other, while the pull-back of quarks trying to leave each other comes from elastic stretching of the edges as the vertices try to move away (presumably due to external forces, etc.). The elastic material remains to be found, but it is no more unusual than the idea of Chaplygin Gas in cosmology. In fact, in "Repulsion" in cosmology, the elastic material may rupture. So what makes this an alternative to Quantum Theory? Both Catalan Number Elasticity and Quantum Theory deal with the "microscopic" level, but the former merely introduces a particular elastic material or medium at the very small level, while the latter introduces too many complications and too few results at least for the Strong Interaction and Gravitation, and also largely for the Weak Interaction. Osher Doctorow |