  We study compatibility of the Standard Model of particle physics and General
Relativity by means of gravitational positivity bounds, which provide a
necessary condition for a low-energy gravitational theory to be UV completable
within the weakly coupled regime of gravity. In particular, we identify the
cutoff scale of the Standard Model coupled to gravity by studying consistency
of light-by-light scattering. While the precise value depends on details of the
Pomeron effects in QCD, the cutoff scale reads $10^{16}$GeV if the
single-Pomeron exchange picture works well up to this scale. We also
demonstrate that the cutoff scale is lowered to $10^{13}$GeV if we consider the
electroweak theory without the QCD sector.
