Natural Science Forum / Physics / Particle Physics / April 2004

In relativistic mechanics the relativistic mass, M, of a particle,
defined by M^2 = (p/v)^2 = m^2 + (p/c)^2, is equal to E/c^2 only in
the limit as its (interaction) potential energy, U, goes to zero.  If
we have an isolated  electron-positron pair on a collision course that
ends in annihilation that produces two photons it seems to be
universally accepted that: the total energy, S(E), of the system is
constant throughout, reading S as "Sigma"; the total relativistic mass
of the two photons, S(M) = S(E/c^2) is constant from the end of the
quantum transition that produces them; the total relativistic mass of
the electron-positron pair varies as S(Mp) = S(M) + Mi (a/R) down to R
of order 10^-18 m, where Mi = e^2/(a c^2).

Classical models and QED both seem to assume that, as R goes to zero,
S(Mp) goes to infinity and that as a result there is discontinuous
downward jump in the total relativistic mass of the system in the
annihilation transition.  Has anyone ever explored the hypothesis that
there is no such discontinuity, ie that dS(Mp)/dt reverses in sign at
some finite R with S(Mp) going to S(M) at R = 0?

Phil Gardner