  Leggett and Garg derived inequalities that probe the boundaries of classical
and quantum physics by putting limits on the properties that classical objects
can have. Historically, it has been suggested that Leggett-Garg inequalities
are easily violated by quantum systems undergoing sequences of strong
measurements, casting doubt on whether quantum mechanics correctly describes
macroscopic objects. Here I show that Leggett-Garg inequalities cannot be
violated by any projective measurement. The perceived violation of the
inequalities found previously can be traced back to an inappropriate assumption
of non-invasive measurability. Surprisingly, weak projective measurements
cannot violate the Leggett-Garg inequalities either because even though the
quantum system itself is not fully projected via weak measurements, the
measurement devices are.
