  Macroscopic realism is the thesis that macroscopically observable properties
must always have definite values. The idea was introduced by Leggett and Garg
(1985), who wished to show a conflict with the predictions of quantum theory.
However, their analysis required not just the assumption of macroscopic realism
per se, but also that the observable properties could be measured
non-invasively. In recent years there has been increasing interest in
experimental tests of the violation of the Leggett-Garg inequality, but it has
remained a matter of controversy whether this second assumption is a reasonable
requirement for a macroscopic realist view of quantum theory. In a recent
critical assessment Maroney and Timpson (2017) identified three different
categories of macroscopic realism, and argued that only the simplest category
could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and
Gogioso (2016) then showed that the second of these approaches was also
incompatible with quantum theory in Hilbert spaces of dimension 4 or higher.
However, we show that the distinction introduced by Maroney and Timpson between
the second and third approaches is not noise tolerant, so unfortunately Allen's
result, as given, is not directly empirically testable. In this paper we
replace Maroney and Timpson's three categories with a parameterization of
macroscopic realist models, which can be related to experimental observations
in a noise tolerant way, and recover the original definitions in the noise-free
limit. We show how this parameterization can be used to experimentally rule out
classes of macroscopic realism in Hilbert spaces of dimension 3 or higher,
including the category tested by the Leggett-Garg inequality, without any use
of the non-invasive measurability assumption.
