g−2Experiments as a Test of Special Relativity

An analysis of g — 2 and lifetime measurements for electrons and muons at various velocities is used to compare the transformation of time, electromagnetic field, and mass in moving coordinate systems and to check the Thomas precession. The data are in good agreement with the special theory of relativity. The gyromagnetic ratios g of the electron and muon are among the most accurately known physical quantities, and consistent results have been obtained' ' for various particle velocities; y =(1 — v'/c') '~'=1-1. 2 for the electron, and 1. 2-30 for the muon. It is possible, therefore, that the results imply an accurate verification of special relativity, and this has indeed been claimed by Newman et al. ' As special relativity enters at many points in the interpretation of the experiments , a careful analysis is needed in order to establish the level at which the theory is tested. The quantity measured in all g — 2 experiments is the difference between the spin precession frequency f, and the orbit frequency f, for a particle turning in a uniform field B: f, =f, f, = (a/2v)(e/mc)B. — With knowledge of e/mc, the value of a-=-, '(g-2) can be deduced. Equation (1) is independent of the velocity of the particle (or of y), and is equally valid in Newtonian mechanics or in relativity. It is therefore a prio irnot surprising to find that the observed precession frequency is independent of y, to turn this observation into a test of rela-tivity therefore requires a sophisticated argument. Newman et a/. remark that, in relativity theory, Eq. (1) results from the happy cancellation of several y-dependent terms. These terms represent physically separable effects, and they conclude that the equality of these various y's is verified to an accuracy of 5 X10 ', while the values of f, are equal only to 3X10 '. We wish to point out that this conclusion is very much dependent upon the model adopted for the breakdown of special relativity, and to present one of the possible alternative assumptions which lead to somewhat different results. If the y factors in relativity theory may be of different types, one could in principle distinguish 1979 The American Physical Society 1383