  Glashow and Cohen make the interesting observation that certain proper
subgroups of the Lorentz group like HOM(2) or SIM(2) can explain many results
of special relativity like time dilation, relativistic velocity addition and a
maximal isotropic speed of light. We show here that such SIM(2) and HOM(2)
based VSR theories predict an incorrect value for the Thomas precession and are
therefore ruled out by observations. In VSR theories the spin-orbital coupling
in atoms turn out to be too large by a factor of 2. The Thomas-BMT equation
derived from VSR predicts a precession of electrons and muons in storage rings
which is too large by a factor of $10^3$. VSR theories are therefore ruled out
by observations.
