Uncertainty relations describing the short-term violations of Lorentz   invariance: superluminal phenomena, particles transformations
  The refinement and specifications of time-energy uncertainty relations have shown that the experimentally observed phenomena of superluminal signaling are describable by such their form: $\Delta E\Delta\tau\geq\pi\hbar$, where both standard deviations are negative. When $\Delta\tau<0$, these evanescent photons would be instantly tunneling from one light cone into another on the distance $c| \Delta\tau| $. (This assertion, previously proved via dispersion relations, is described here by the temporal parameters of process.) Special forms of these relations describe the transmutation of particles into their partners of bigger mass, in $K^{0}$ and $B^{0}$ cases and at the $\nu$'s transmutations. Thus, the violations of relativistic causality by evanescent particles can be considered as the tunneling, as an analog of the short-term violation of conservation laws at virtual transitions. The absence of Lorentz invariance at such transitions can, probably, allow violations of some other symmetries. 
M.E. Perel'man