In a new version of special relativity that incorporates the uncertainty principle, the Einstein-Lorentz mass formula is extended more completely. The new formula shows that there is a weak "high-speed but low-mass" effect in particles movement, which will cause the generation of abnormal ultra-high energy electrons with a computable small probability when the electron beam passes through an accelerating electric field. This previously unknown anomaly was tested on the electron storage ring of BEPCII by the author with a cumulative detection method, and results show that there is indeed the emission of electrons with energy up to 790TeV at downstream of the RF cavity, which is consistent with the theoretical expectation. On this basis, it is suggested that particle physicists do more experimental detection, so as to further fully verify the extended Einstein-Lorentz mass formula.