Electron stability constrains neutrino time delays

Superluminal neutrino propagation, induced by Lorentz-invariance violation (LIV), is strongly constrained by vacuum pair emission, $\nu \to \nu + e^- + e^+$, a process ordinarily forbidden, which rapidly degrades the energy of high-energy neutrinos. Consequently, observable neutrino time delays are often preferentially associated with subluminal propagation, prompting LIV interpretations of claimed time delays between high-energy cosmic neutrinos and gamma rays. However, this expectation is at odds with the observed stability of high-energy electrons. The same Lorentz-violating correction associated with subluminal neutrino propagation opens the overlooked complementary decay channel $e^- \to e^- + \nu + \bar{\nu}$, leading to electron instability. We derive constraints on LIV from recent observations of TeV--PeV astrophysical electrons. These electron stability limits rule out LIV invoked to explain delays of high-energy cosmic neutrinos. Consequently, neutrino time delays are constrained on both the superluminal and subluminal sides. Therefore, observable delays require either purely astrophysical origins, a realization of LIV that affects all particle species equally, or physics beyond the standard effective-field-theory framework.