  Various Bell inequalities are trivial algebraic properties satisfied by each
line of particular data spreadsheets.It is surprising that their violation in
some experiments, allows to speculate about the existence of nonlocal
influences in Nature and to doubt the existence of the objective external
physical reality. Such speculations are rooted in incorrect interpretations of
quantum mechanics and in a failure of local realistic hidden variable models to
reproduce quantum predictions for spin polarisation correlation experiments.
These hidden variable models use counterfactual joint probability distributions
of only pairwise measurable random variables to prove the inequalities. In real
experiments Alice and Bob, using 4 incompatible pairs of experimental settings,
estimate imperfect correlations between clicks, registered by their detectors.
Clicks announce detection of photons and are coded by 1 or -1. Expectations of
corresponding ,only pairwise measurable, random variables are estimated and
compared with quantum predictions. These estimates violate significantly the
inequalities. Since all these random variables cannot be jointly measured , a
joint probability distribution of them does not exist and various Bell
inequalities may not be derived. Thus it is not surprising that they are
violated. Moreover,if contextual setting dependent parameters describing
measuring instruments are correctly included in the description, then imperfect
correlations between the clicks may be explained in a locally causal way. In
this paper we review and rephrase several arguments proving that the violation
of various Bell inequalities may neither justify the quantum nonlocality nor
allow for doubt regarding the existence of atoms, electrons and other invisible
elementary particles which are building blocks of the visible world around us
including ourselves.
