zero mass of double spin axes.doc
If all elementary particles are composites then their properties of double intrinsic spin axes are relatively orientable with respect to each other. Moreover, these orientations in abstract multidimensional spacetime can be used to define the mass of each elementary particle. In view of other physical theories concerning the origin of mass, for example the Higgs mechanism, mass values derived from orientations of double intrinsic spin axes give a more plausible and completely different explanation but without the necessity of invoking the existence of scalar spin zero Higgs boson. The same idea provide an alternative description of the isotopic spin of both proton and neutron using a commutative Abelian formalism in contradistinction to the non-Abelian Yang-Mills formalism of quantum field theories using concepts of local gauge invariance.
Traditionally, the one dimensional time independent wave function (x) of every elementary particle is given as the product of its eigenvector (x) and the phase factor exp(i): (x)= (x) exp(i). However, for a theory of double intrinsic spin axes, (x) is given as (x) (x)= (x) exp(i)exp(i) where exp(i) represents one spin axis and exp(i) represents the other axis and and are angular displacements in abstract multidimensional spacetime. For mass to be zero simply means that += or 180° and satisfies Euler’s formula exp(+i)=exp(-i)= -1. In fact, infinitely many phase factors can be multiplied by the eigenvector and if the sum of all angular displacements adds up to exactly 180° the result is zero mass of the represented composite particle.


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