  Matter-wave interferometry is susceptible to non-inertial noise sources,
which can induce dephasing and a resulting loss of interferometric visibility.
Here, we focus on inertial torsion noise (ITN), which arises from the
rotational motion of the experimental apparatus suspended by a thin wire and
subject to random external torques. We provide analytical expressions for the
ITN noise starting from Langevin equations describing the experimental box in a
thermal environment which can then be used together with the transfer function
to obtain the dephasing factor. We verify the theoretical modelling and the
validity of the approximations using Monte Carlo simulations obtaining good
agreement between theory and numerics. As an application we estimate the size
of the effects for the next-generation of interferometery experiments with
femtogram particles, which could be used as the building block for
entanglement-based tests of the quantum nature of gravity. We find that the
ambient gas is a weak source of ITN, posing mild restrictions on the ambient
pressure and temperature, and conclude with a discussion about the general ITN
constrains by assuming a Langevin equation parameterized by three
phenomenological parameters.
