In a new version of special relativity that absorbed the uncertainty principle, the Einstein-Lorentz mass formula proved to be a special case of a more universal equation. The new equation indicates that there is a “high speed but low mass” weak effect in particle motion, which will cause the generation of abnormal ultra-high energy electrons with a small probability when an electron beam passes through an accelerating electric field. The author used the method of long-times accumulation detection to test it on the BEPCII, which results show that there is indeed emission of abnormal electrons with energy up to 105 times of the beam energy at the downstream of the RF cavity of the electron storage ring. Therefor, it is suggested to use the detector with an online real-time display function, such as the “Shashlyk calorimeter”, to detect the single event of ultra-high energy electron, so to fully verify this previously unknown phenomenon and further discover new physics.