many-worlds interpretation (MWI) is sometimes presented as a waves-only theory, including by its originator, Hugh Everett who referred to MWI as "the wave interpretation". The of R. Horodecki relates the particle to wave. The hypothesis implies that a massive particle is an intrinsically spatially, as well as temporally extended, wave phenomenon by a nonlinear law. The considers collapse and measurement as two independent physical processes. Collapse occurs when two wavepackets spatially overlap and satisfy a mathematical criterion, which depends on the parameters of both wavepackets. It is a contraction to the overlap volume. In a measurement apparatus one of the two wavepackets is one of the atomic clusters, which constitute the apparatus, and the wavepackets collapse to at most the volume of such a cluster. This mimics the action of a point particle. Hegerfeldt's theorem, which appears to demonstrates the incompatibility of the existence of localized discrete particles with the combination of the principles of quantum mechanics and special relativity, has also been used to support the conclusion that reality must be described solely in terms of field-based formulations. Particle-only view Still in the days of the old quantum theory, a pre-quantum-mechanical version of wave–particle duality was pioneered by William Duane, and developed by others including Alfred Landé. Duane explained diffraction of x-rays by a crystal in terms solely of their particle aspect. The deflection of the trajectory of each diffracted photon was explained as due to quantized momentum transfer from the spatially regular structure of the diffracting crystal. Neither-wave-nor-particle view It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. For this reason, in 1928 Arthur Eddington coined the name "wavicle" to describe the objects although it is not regularly used today. One consideration is that zero-dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Dirac delta function is unphysical, because it cannot be normalized. Parallel arguments apply to single-frequency wave states. Roger Penrose states: Such 'position states' are idealized wavefunctions in the opposite sense from the momentum states. Whereas the momentum states are infinitely spread out, the position states are infinitely concentrated. Neither is normalizable [...]. Uses Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea. Wave–particle duality is exploited in