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 nλ = 2dsin(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.

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

“…Meanwhile, the momentum quanta in diffraction from crystals and dual harmonic quasicrystals likewise depend on original harmonic states [5]. De Broglie's hypothesis is that the quantum of momentum p is inversely related particle wavelength, so that:…”

“…The natural part expresses conservation of mass, energy, momentum, charge, spin etc. ; the complex part expresses interference, annihilation, creation, entanglement 5 , etc.…”

“…The new discovery of reduction by resonant response that has been briefly described [5] before is here derived in greater detail and expanded with wider scope. The logic and significance of the following sections is outlined here for clarity.…”

Quantum Mechanics: Internal Motion in Theory and Experiment

“…The wave group is generally understood in frequency modulated and amplitude modulated communication theory. The group can be used to explain many properties in quantum physics including diffraction in general; but also intrinsic spin [4], dual diffraction in logarithmic structures [5], reduction of the wave packet by resonance [6], etc. Further possible explanations may well be available for structures of elementary particles.…”