It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. One consideration is that zero dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Kronecker delta function is unphysical, because it cannot be renormalized. Parallel arguments apply to pure wave states.

    “Such positions states are idealised wavefunctions [..] Whereas the momentum states are infinitely spread out, the position states are infinitely concentrated. Neither is normaliseable[..]”

— R Penrose, Road to Reality p.521 s21.11
   
— Wikipedia on Wave–particle duality

Particle is a single pulse. Wave is a train of infinite pulses. Both are physically impossible.

— Me@2011.11.29

2011.11.30 Wednesday (c) All rights reserved by ACHK