**Authors:** Carl Brannen

This paper eshes out the arguments given in a 20 minute talk at the Phenomenology 2005 meeting at the University of Wisconsin at Madison, Wisconsin on Monday, May 2, 2005. The argument goes as follow: A hidden dimension is useful for explaining the phase velocity of quantum waves. The hidden dimension corresponds to the proper time parameter of standard relativity. This theory has been developed into a full gravitational theory, "Euclidean Relativity" by other authors. Euclidean relativity matches the results of Einstein's gravitation theory. This article outlines a compatible theory for elementary particles. The massless Dirac equation can be generalized from an equation of matrix operators operating on vectors to an equation of matrix operators operating on matrices. This allows the Dirac equation to model four particles simultaneously. We then examine the natural quantum numbers of the gamma matrices of the Dirac equation, and generalize this result to arbitrary complexified Clifford algebras. Fitting this "spectral decomposition" to the usual elementary particles, we find that one hidden dimension is needed as was similarly needed by Euclidean relativity, and that we need a set of eight subparticles to make up the elementary fermions. These elementary particles will be called \binons", and each comes in three possible subcolors. The details of the binding force between binons will be given as a paper associated with a talk by the author at the APSNW 2005 meeting at the University of Victoria, at British Columbia, Canada on May 15, 2005. After an abbreviated introduction, this paper will concentrate on the phenomenological aspects of the binons, particularly as applied to the Centauro type cosmic rays, and gamma-ray bursts.

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[v1] 25 Mar 2007

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