where m e is the mass of the electron, c is the speed of light in vacuum, q e is the elementary charge, and ħ is the reduced Planck constant. These are enormous field strengths. Such an electric field is capable of accelerating a proton from rest to the maximum energy attained by protons at the Large Hadron Collider in only approximately 5 micrometers. The magnetic field is associated with birefringence of the vacuum and is exceeded on magnetars.