  Is the wave function a physical reality traveling through our apparatus? Is
it a real wave, or it is only a mathematical tool for calculating probabilities
of results of measurements? Different interpretations of the quantum mechanics
(QM) assume different answers to this question. It is shown in this article
that the assumption that the wave function is a real wave entails a
contradiction with the predictions of the QM, when the special relativity is
invoked. Therefore, this text concentrates on interpretations which conjecture
that the reality that moves in our apparatuses is particles, and they move
under the constraints of the wave function. The de Broglie Bohm interpretation,
which matches this picture, assumes that the particle travels along a
continuous trajectory. However, the idea of continuous trajectories was proved
to lead to a contradiction with the quantum predictions. Therefore this
interpretation is not considered here. S. Gao conjectured that the particle is
in a permanent random and discontinuous motion (RDM). As it jumps all the time
from place to place, the total set of occupied positions at a certain time is
given by the absolute square of the wave function. As motivation for his idea,
Gao argued that if a charged particle were simultaneously in two or more
locations at the same time, the copies of the particle would repel one another,
destroying the wave function. It is proved here that the quantum formalism
renders this motivation wrong. Although refuting this motivation, the RDM
interpretation is examined here. A couple of problems of this interpretation
are examined and it is proved that they do not lead to any observable
contradictions with the QM predictions, except one problem which seems to have
no solution. In all, it appears that none of the wide-spread interpretations of
the QM is free of contradictions.
