Causal restriction is not spectral truncation: a no-go result for the Rindler–Casimir mechanism of Quantised Inertia (QI)

Quantised inertia proposes that acceleration-dependent causal horizons modify inertia, in one formulation through an asymmetry in the momentum flux attributed to Unruh radiation. We test that mechanism at the quantum-field-theoretic step on which it depends. In algebraic quantum field theory an acceleration horizon imposes no reflecting or Casimir boundary condition: the Minkowski vacuum is restricted to the Rindler-wedge algebra, where it is a KMS state under boost modular flow. Restricting a state to a subalgebra leaves unchanged the expectation value of every local observable supported there, so the renormalised vacuum stress tensor is unaltered. Poincaré invariance fixes that tensor to be isotropic, and conventionally zero, and isotropy is a tensor statement that survives passage to an accelerated frame. The one-sided mean radiation-pressure deficit the mechanism requires is therefore not generated by the horizon. The natural replies, including the Fulling–Rindler vacuum, detector back-reaction and a horizon-limited uncertainty relation, do not restore it without further physical input. We further note that the cosmological scale Θ denotes inequivalent geometrical objects in this literature, implying different critical-acceleration histories not, to our knowledge, tested in common. An appendix corrects the discrete mode count in Renda’s published sceptical analysis: restoring the polarisation multiplicities of a conducting cavity removes the reported F ≃ 2.17 overshoot and the stable acceleration inferred from it, and a factor-of-two convention in the largest admissible wavelength reproduces the abscissa of the published critical point. Neither correction weakens that paper’s two principal criticisms.