After considering Heisenberg's uncertainty principle, the mass-speed relationship of special relativity i.e. the Einstein-Lorentz mass formula can be extended to a more complete equation, which predicts that abnormal ultra-high energy electrons will be generated with a small probability when the electron beam passes through an accelerating electric field. The author used the accumulating detection method of a large number of events to test at the electron storage ring of BEPCII, of which results show that under the beam energy of 2GeV there is emission of abnormal ultra-high energy electrons with the highest energy reaching 400TeV at downstream of the RF cavity. For this reason, it is recommended that particle physicists conduct more experiments to fully verify this previously unknown phenomenon and further discover new physics.