Despite Maitra's observations on the difficulties in capturing correctly the photon dynamics using classical Ehrenfest trajectories, the exact factorization has the potential to shed light into alternative approximations of the PEN quantum dynamics where the photon displacements and momenta are treated with trajectories, perhaps within a CTMQC-like scheme. In the presence of many cavity modes 140 or even when envisaging to employ the formalism of the exact factorization to study the vibrational strong-coupling regime , such a treatment might represent the only valuable route for efficient and accurate simulations, at the cost of rethinking the underlying approximations of CTMQC and similar algorithms. Developments in this direction are currently ongoing in our group and will be reported elsewhere 295 .