  We study the loss of quantumness caused by time dilation [1] for a
Schr\"odinger cat state. We give a holistic view of the quantum to classical
transition by comparing the dynamics of several nonclassicality indicators,
such as the Wigner function interference fringe, the negativity of the Wigner
function, the nonclassical depth, the Vogel criterion and the Klyshko
criterion. Our results show that only two of these indicators depend critically
on the size of the cat, namely on how macroscopic the superposition is. Finally
we compare the gravitation-induced decoherence times to the typical decoherence
times due to classical noise originating from the unavoidable statistical
fluctuations in the characteristic parameters of the system [21]. We show that
the experimental observation of decoherence due to time dilation imposes severe
limitations on the allowed levels of classical noise in the experiments.
