For over a decade several workers have argued for the existence of quantum
deviations from the classical, Einstein dilation of the decay evolution of
moving or Lorentz boosted unstable particles. While the general claim is
correct, the discussions have been incomplete and, sometimes, misleading. The
discussions have been of three kinds. Type 1 examines the time dependence of
the survival probability for 3-momentum eigenstates of the unstable quanton
(Khalfin). Type 2 does the same for velocity eigenstates, obtaining an
outrageous result which then discredits velocity eigenstates (Shirokov /
Hegerfeldt). Type 3 examines arbitrary boosts of 3-momentum eigenstates
(Stefanovich). Type 1 is incomplete since the momentum eigenstates are not the
boosts of one another. Type 2 is misleading since the outrageous result is due
to misinterpreting the initial conditions of the velocity eigenstates (as I
have previously argued). Type 3 is the most satisfactory, but has failed to
recognize and implement the unification of all three types of discussion that
can be achieved. In this paper I will provide that unified treatment, beginning
with a recapitulation of Type 1 and offering further clarification of Type 2 in
the process. The unified treatment fully reinstates velocity eigenstates as
essential contributors to unstable quanton states. Besides discussing the time
evolution of survival probabilities I also focus on the concept of lifetime
defined as the average time of decay. This quantity is helpful in order to
display the inequivalent dependence of dilation on momentum and boosts most
sharply and the deviation from Einstein dilation most cleanly.Comment: 40 pages, 2 figure
