- #36
ChrisVer
Gold Member
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- 464
Well, you can also have imaginary mass without having superluminal propagation...http://en.wikipedia.org/wiki/Tachyon#Fields_with_imaginary_mass
You actually need an 11th degree of freedom to define the Galilei
limit. The 11th parameter (in Galilei) is the "central charge"
associated with mass. To make Poincare' suitable for taking the limit
to Galilei (that is: to implement the correspondence principle with
respect to non-relativistic physics!), one needs to split the energy
generator E into two parameters -- kinetic energy H and "relativistic
mass" M. E does not have a Galilean limit. The mass shell condition (E/
c)^2 - P^2 = (mc)^2 (where P is the momentum and m the rest mass)
needs to be generalized to P^2 - 2MH + (1/c)^2 H^2 = constant. An
additional invariant emerges: M - (1/c)^2 H = constant.