Recent evidence for neutrinos moving faster than light in free space is consistent
with earlier measurements of the speed of light in condensed media in wavelength
regions of anomalous dispersion. Both findings are widely assumed to be ruled
out theoretically because they would violate Einstein causality, that is, the
principle that the time-order of events must be the same for all observers. The
latter conclusion is based on the Lorentz transformation (LT) of special relativity
(SR). A review of the assumptions made in Einstein s original derivation of the
LT in 1905 shows that it is possible to avoid this conflict between theory and
experiment while still satisfying his two postulates of relativity. An amended
version of relativity theory is presented which is based on an alternative Lorentz
transformation (ALT) that remains consistent with Einstein’s velocity addition
theorem (VT), which is compatible with super-luminal motion. At the same time,
it is argued that faster-than-c neutrinos must have null rest mass, the same as
photons, in order to satisfy other requirements of the original theory.