  Despite the great success of quantum mechanics, questions regarding its
application still exist and the boundary between quantum and classical
mechanics remains unclear. Based on the philosophical assumptions of
macrorealism and noninvasive measurability, Leggett and Garg devised a series
of inequalities (LG inequalities) involving a single system with a set of
measurements at different times. Introduced as the Bell inequalities in time,
the violation of LG inequalities excludes the hidden-variable description based
on the above two assumptions. We experimentally investigated the single photon
LG inequalities under decoherence simulated by birefringent media. These
generalized LG inequalities test the evolution trajectory of the photon and are
shown to be maximally violated in a coherent evolution process. The violation
of LG inequalities becomes weaker with the increase of interaction time in the
environment. The ability to violate the LG inequalities can be used to set a
boundary of the classical realistic description.
