Real Quanta and Continuous Reduction

Abstract

Previous theories of quasicrystal diffraction have called it “Bragg diffraction in Fibonacci sequence and 6 dimensions”. This is a misnomer, because quasicrystal diffraction is not in integral linear order n where n λ = 2d sin( θ ) as in all crystal diffraction; but in irrational, geometric series τ m , that are now properly indexed, simulated and verified in 3 dimensions. The diffraction is due not to mathematical axiom, but to the physical property of dual harmony of the probe, scattering on the hierarchic structure in the scattering solid. By applying this property to the postulates of quantum theory, it emerges that the 3rd postulate (continuous and definite) contradicts the 4 th (instantaneous and indefinite). The latter also contradicts Heisenberg’s “limit”. In fact, the implied postulates of probability amplitude describe hidden variables that are universally recognized, in all sensitive measurement, by records of error bars. The hidden variables include momentum quanta, in quasicrystal diffraction, that are continuous and definite. A revision of the 4 th postulate is proposed.