much stronger than the CSL collapse effect, these spontaneous collapse effects cannot be observed experimentally, even if the technology were sophisticated enough to reach such sensitivities. They would anyhow be masked by decoherence effects. Moreover, decoherence effects are not far away from the collapse effect predicted in [@Ch], which—as we argued—is anyhow overestimated. Therefore, also gravity-induced collapse effects cannot be detected via neutrino oscillations.

The rest of the paper is devoted to deriving Eqs.  and . The calculation is lengthy but instructive because it shows, as already stressed in the introduction, how the collapse, which acts on the spatial part of the wave function, as a byproduct also affects the flavour degrees of freedom. Moreover, a precise calculation clears any possible misunderstanding about the effect of collapse models on neutrino oscillations.

Mathematical setup
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Working with non-linear equations such as the CSL equation is notoriously difficult. As shown e.g. in [@Im], the experimentally testable predictions of the model—when averaged over the noise—do not change if the real noise $W_{t}\left(\mathbf{x}\right)$ is replaced by an imaginary noise $i W_{t}\left(\mathbf{x}\right)$. In this way, one loses the collapse properties of the equation. However, the advantage of having an imaginary noise is that the evolution 