Heisenberg's uncertainty principle in the PTOLEMY project: a theory update

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $\beta$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised in [Cheipesh et al., Phys. Rev. D 104, 116004 (2021)], and discuss the relevant time scales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.