Ultrafast visualization of an electric field under the Lorentz transformation

Abstract In special relativity, four-vectors, such as space–time, energy–momentum and electromagnetic potential vectors, follow the Lorentz transformation. The transformations of space–time vectors have been tested by time dilation rest mass energy experiments, respectively. However, transformation potentials has never directly demonstrated in experiments due to limitations diagnostics. Here we show spatiotemporal electric-field profiles around a highly energetic electron beam with subpicosecond temporal resolution obtained terahertz technique based on electro-optic sampling. We observe Coulomb field contraction propagation direction under After passing through metallic plate, investigate birth it evolution spherical wavefront, which is derived Liénard–Wiechert potentials. measured profile far distance experimentally confirmed coincide calculation Our ultrafast measurement relativistic electric provides both additional experimental evidence relativity platform for detailed research charged particle beams radiation physics.