  Relativistic invariance is a physical law verified in several domains of
physics. The impossibility of faster than light influences is not questioned by
quantum theory. In quantum electrodynamics, in quantum field theory and in the
standard model relativistic invariance is incorporated by construction. Quantum
mechanics predicts strong long range correlations between outcomes of spin
projection measurements performed in distant laboratories. In spite of these
strong correlations marginal probability distributions should not depend on
what was measured in the other laboratory what is called shortly:
non-signalling. In several experiments, performed to test various Bell-type
inequalities, some unexplained dependence of empirical marginal probability
distributions on distant settings was observed . In this paper we demonstrate
how a particular identification and selection procedure of paired distant
outcomes is the most probable cause for this apparent violation of
no-signalling principle. Thus this unexpected setting dependence does not prove
the existence of superluminal influences and Einsteinian no-signalling
principle has to be tested differently in dedicated experiments. We propose a
detailed protocol telling how such experiments should be designed in order to
be conclusive. We also explain how magical quantum correlations may be
explained in a locally causal way.
