Some deviations from special relativity—especially isotropic effects—are most efficiently constrained using particles with velocities very close to 1. While there are extremely tight bounds on some of the relevant parameters coming from astrophysical observations, many of these rely on our having an accurate understanding of the dynamics of these high-energy sources. It is desirable to have reliable laboratory constraints on these same parameters. The fastest-moving particles in a laboratory were electrons and positrons at LEP. The energetics of the LEP beams were extremely well understood, and measurements of the synchrotron emission rate indicate that the isotropic Lorentz violation coefficient $|{\tilde{\kappa }}_{\mathrm{tr}}-\frac{4}{3}{c}_{00}|$ must be smaller than $5\times {10}^{-15}$.

• Received 28 May 2009

DOI:https://doi.org/10.1103/PhysRevD.80.091901