  A local interpretation of quantum mechanics is presented. Its main
ingredients are: first, a label attached to one of the virtual paths in the
path integral formalism, determining the output for measurement of position or
momentum; second, a mathematical model for spin states, equivalent to the path
integral formalism for point particles in space time, with the corresponding
label. The mathematical machinery of orthodox quantum mechanics is maintained,
in particular amplitudes of probability and Born's rule; therefore, Bell's type
inequalities theorems do not apply. It is shown that statistical correlations
for pairs of particles with entangled spins have a description completely
equivalent to the two slit experiment, that is, interference (wave like
behaviour) instead of non locality gives account of the process. The
interpretation is grounded in the experimental evidence of a point like
character of electrons, and in the hypothetical existence of a wave like, the
de Broglie, companion system. A correspondence between the extended Hilbert
spaces of hidden physical states and the orthodox quantum mechanical Hilbert
space shows the mathematical equivalence of both theories. Paradoxical
behaviour with respect to the action reaction principle is analysed, and an
experimental set up, modified two slit experiment, proposed to look for the
companion system.
