Causal Consistency of Diósi–Penrose Reduction and a Profile-Independent Mass Scale M_P/√2

The Diósi–Penrose (DP) model assigns a spatial superposition the lifetime τ_DP = ħ/ΔE_G, computed from the instantaneous Newtonian self-energy difference of its branches. We ask what local relativistic causality adds to this picture. First, in a relativistic scalar-field model of the branch difference, a finite protocol duration T replaces the logarithmic infrared dependence ln(ξ/σ_eff) of static configurations by ln[min(ξ, cT)/σ_eff]; the result is independent of the branch separation ξ only for ξ > cT, whereas laboratory protocols satisfy cT ≫ ξ. Second, defining the causal self-crossing time ⟨t⟩ of a branch from the retarded Green function, we prove that E_self⟨t⟩ = Gm²/c for every regular mass profile. Consequently τ_DP/⟨t⟩ = (m_H/m)² with m_H = M_P/√2 ≈ 15.39 μg, independently of the profile and of the regularization width: above m_H the DP reduction would be completed before the self-energy that drives it is causally established across the branch. We also show that the switch-on action deficit of the branch difference vanishes identically by mass conservation. What happens at m_H depends on whether the branch phase keeps accumulating beyond ⟨t⟩. If it does (H1), the decoherence time crosses over from the DP law ∝ m⁻² to a causally limited ∝ m^(−2/3) at m_H, for every profile. If it does not (H2), the phase acquired per causal interval is exactly (m/m_H)², and m_H acts as a Heisenberg cut. Both hypotheses predict that a superposition with m ≥ m_H and ξ ≫ σ_eff loses coherence within about 2⟨t⟩, while their predictions below m_H differ. All results are reproduced by openly available code (doi:10.5281/zenodo.23064101).