Particle Regime

The Particle Regime is the range of the Duality Parameter, D << 1, in which an object's de Broglie wavelength is much smaller than its characteristic form length, so localized form behavior dominates over extended wave behavior. The book classifies wave-particle behavior by this single ratio: the Wave Regime at D >> 1 shows extended field behavior, the Transition Regime at D ≈ 1 shows coexistence, and the Particle Regime shows localized form. In the limit of infinite recursion depth, forms persist without end and their length scale L▢ approaches the Planck length, with recursive density approaching the Planck density, the asymptotic end of the particle side. Among the Chapter 7.6 predictions, such transitions are to be measured through fringe visibility in matter-wave interferometry. The condition is D << 1 with D = λ_dB/L▢, where D is the Duality Parameter, λ_dB the de Broglie wavelength and L▢ the characteristic form length scale. Dimensions: D [∅], λ_dB [𝕃], L▢ [𝕃]. It connects to the Duality Parameter, Wave Regime, Transition Regime, Characteristic Form Length Scale and Field-to-Form Transition.