Comment on "Spatiotemporal torquing of light"

The recent paper Phys. Rev. X. 14, 011031 (https://doi.org/10.48550/arXiv.2307.01019) includes an appendix that casts doubts on the validity the theory of the transverse orbital angular momentum of spatiotemporal optical vortices (STOVs) in Prog. Electromagn. Res. 177, 95 (https://doi.org/10.48550/arXiv.2301.09105). The argumentation in that appendix mixes a mechanical approach where STOVs are seen in space evolving in time with an optical approach where STOVs are seen in space-time evolving with propagation distance, which leads to wrong conclusions. We consistently carry out the analysis from the mechanical approach, and the results confirm the theory in Prog. Electromagn. Res. 177, 95 consistently performed within the optical approach.