  We propose a novel method to measure the neutron-neutron scattering length
using the $^{6}$He$(p,p\alpha)nn$ reaction in inverse kinematics at high
energies. The method is based on the final state interaction (FSI) between the
neutrons after the sudden knockout of the $\alpha$ particle. We show that the
details of the neutron-neutron relative energy distribution allow for a precise
extraction of the $s$-wave scattering length. We present the state-of-the-art
in regard to the theory of this distribution. The distribution is calculated in
two steps. First, we calculate the ground-state wave function of $^6$He as a
$\alpha n n$ three-body system. For this purpose we use Halo effective field
theory (Halo EFT), which also provides uncertainty estimates for the results.
We compare our results at this stage to model calculations done with the
computer code FaCE. In a second step we determine the effects of the $nn$ FSI
using the $nn$ t-matrix. We compare these FSI results to approximate FSI
approaches based on standard FSI enhancement factors. While the final
distribution is sensitive to the $nn$ scattering length, it depends only weakly
on the effective range. Throughout we emphasize the impact of theoretical
uncertainties on the neutron-neutron relative energy distribution, and discuss
the extent to which those uncertainties limit the extraction of the
neutron-neutron scattering length from the reaction $^{6}$He$(p,p\alpha)nn$.
