Reasoning:
- A vacuum transition propagates at light speed, so any trigger event in our past light cone would have reached and destroyed us: the relevant natural experiment count is the full past-light-cone integral, 1e47 comparable Fe-Fe collisions (Hut-Rees 1983, updated here with confirmed flux data; iron measured to 2 TeV/nucleon agrees with their inputs).
- p-bar x 1e47 < 1 (no transition) and RHIC performs 2e11 collisions → P(RHIC triggers) < 2e11/1e47 = 2e-36. Insisting the trigger needs nuclei as heavy as gold costs the 1e-5 abundance factor: < 2e-26. Hut-Rees also showed pp collisions up to CM energies of 1e8 TeV are similarly excluded by proton cosmic rays.
- Frame-independence: like bubble expansion itself, nucleation probability depends on the collision’s CM conditions, not the lab velocity of the products, so the cosmic-ray/collider disanalogy (product velocities) has no purchase here. Theory alone could not deliver an unequivocal bound (electroweak-scale vacuum structure is not known well enough); the empirical bound does not need it.
Step 6 verdict
Verdict: corrected (checked). The frequency step is valid as traced: if p-bar x 1e47 >~ 1 a past trigger is near-certain, and RHIC’s 2e11 trials give the ratio 2e-36 (2e-26 with the Z > 70 abundance penalty); the frame-independence point (nucleation depends on CM conditions) is likewise valid and consistent with A-63. Surviving undercutting defeater: observation selection. Vacuum decay destroys every observer in its future light cone, so every possible observer sees O-40 (“no transition in our past light cone”) regardless of p-bar - P(O-40 | p-bar large, we observe at all) = 1 - which breaks the link from observation to bound without denying any premise (the Cirkovic / Tegmark-Bostrom anthropic-shadow objection). A weaker conclusion is immune: conditional on treating past-light-cone survival as an unbiased observation the 2e-36 bound follows, and selection-aware timing arguments (Tegmark & Bostrom 2005, from the lateness of planet formation and our evolution) still bound generic catastrophe rates, though far more weakly (~1e-9/yr scale). Statement corrected to carry that conditionalization; step 8 must price the selection effect when using O-40. Checked: elementary probability plus light-cone geometry.
Original
If heavy-ion collisions at RHIC energies could trigger vacuum decay with probability p-bar per collision, the ~1e47 iron-iron collisions above 100 GeV/nucleon in our past light cone would have triggered it long ago; our existence therefore bounds the probability of a vacuum transition during RHIC’s ~2e11-collision lifetime below 2e-36 (iron), or 2e-26 conservatively demanding Z > 70 projectiles at abundance 1e-5 — margins so vast that no plausible error in the estimates matters.