  Experiments showing the violation of Bell inequalities have formed our belief
that the world at its smallest is genuinely non-local. While many non-locality
experiments use the first quantised picture, the physics of fields of
indistinguishable particles, such as bosonic gases, is captured most
conveniently by second quantisation. This implies the possibility of non-local
correlations, such as entanglement, between modes of the field. In this paper
we propose an experimental scheme that tests the theoretically predicted
entanglement between modes in space occupied by massive bosons. Moreover, the
implementation of the proposed scheme is capable of proving that the particle
number superselection rule is not a fundamental necessity of quantum theory but
a consequence of not possessing a distinguished reference frame.
