Gribbin (1989: xvi):
In this new world of particle physics it turned out that particles and waves are two aspects of the same thing. Light, which was thought of as an electromagnetic wave, had now to be thought of as a stream of particles, called photons; and electrons, previously regarded as particles, like little hard billiard balls, now had to thought of as smeared-out waves. Worse still, when they tried to apply their new understanding of quantum physics to predicting the behaviour of electrons, or other objects, in an experimental setup, the physicists of the 1920s found that it was impossible, except on a statistical basis.
From the perspective of Systemic Functional Linguistic theory, 'wave' and 'particle' are meanings construed of experience. In the field of quantum physics, the wave aspect models the quantum in terms of potential, whereas the particle aspect models it as an instance of that potential. The wave aspect is concerned with system probabilities, since probability is a quantification of potential, whereas the particle aspect is concerned with the statistical distribution of its instances, since frequency is a quantification of instances. This is why prediction is probabilistic/statistical.