  Whether the quantum mechanics (QM) is non-local is an issue disputed for a
long time. The violation of the Bell-type inequalities was considered as
proving this non-locality. However, these inequalities are constructed on a
class of local hidden variables, which obey the calculus with positive
probabilities. Such a calculus is rather suitable for billiard balls while the
QM deals with wave-packets of complex amplitudes. There is no wonder that a
calculus with positive numbers does not match a calculus with complex numbers.
The present text describes a different model of hidden variables for
entanglements, model that reproduces the quantum predictions in different
experiments, and also explains why the QM is nonlocal. The model deals with
waves, some of them full and the others empty, and the hidden variables mark
which waves are full. The basic physical concept with which the model operates
is joint amplitudes of probability, and not probabilities. The latter are a
secondary concept, the probability of a combination of results being equal to
the absolute square of sum of all the contributing joint amplitudes. Thus the
non-locality appears: a) a joint amplitude ignores distance, it handles distant
particles as if they were one single particle at one single place, b) joint
amplitudes are complex numbers and the sum of several contributions may vanish,
blocking the respective combination of wave-packets and therefore of results.
Although showing the success of the model, this text does not advocate for
full/empty waves. It is shown that this hypothesis works only as long as one
does not consider moving observers, and does not compare their conclusions. The
real purpose here is to point to a severe impasse: assuming the existence of a
preferred frame contradicts the theory of relativity, while refuting the
full/empty waves idea one runs into other insurmountable difficulties.
