  Entanglement is one of the most intriguing features of quantum mechanics. It
gives rise to peculiar correlations which cannot be reproduced by a large class
of alternative theories, the so-called hidden-variable models, that use
parameters in addition to the wave-function. This incompatibility was
quantified through the celebrated Bell inequalities, and more recently through
new inequalities due to Leggett. Experiments confirm the predictions of quantum
mechanics. However, this does not imply that quantum mechanics is the ultimate
theory, unsusceptible of improvement, nor that quantum mechanics is essentially
non-local. The theories ruled out by Bell and Leggett inequalities are required
to satisfy some hypotheses, none of which is implied by locality alone. By
dropping one or more hypotheses, it is possible not only to violate said
inequalities, but to reproduce the quantum mechanical predictions altogether.
So far, the models proposed were only mathematical constructs. In this paper we
provide a classical realization of two of these models, using local classical
resources, without recurring to any type of communication among the involved
parties. The resources consist in two baseballs, two bats, and a number of
synchronized watches. Our results demonstrate the possibility of reproducing
the quantum mechanical correlations, and even creating stronger correlations
which provide the maximum violation of the Bell inequality, beyond the
Cirel'son bound for quantum mechanics.
