This may be an interesting point. Assuming a discrete space time (LQG) or
an operationally limited
minimum scale ( string / M therory) , we may need deformed lorentz
transforms and additional relativistic invariants , the Planck or string scale
parameters depending on which QG approach proves to be correct. ( if any do.)
This requires a very small CPT violation. It may well be that CPT , not CP
violation , explains the predominance of matter over anti-matter. And the
violation is fundamental and built right into the "fabric" of space time. I
also looked at the "true" negative energy states of the relativistic equations
( the ones that Pauli proved unphysical) and once again the symmetry is
between matter-negative antimatter and antimatter-negative matter.
You get
c=E_QG= 1 E =abs[E] Gamma= abs[gamma]
M_m= E/[ gamma*( 1-E) ]
M_am= -E/ -[ gamma*(1+E)]
M_nm= -E/ [ gamma*(1+E)]
M_nam= E/ - [gamma*(1-E)]
M_m <> M_am M_nm <> M_nam
M_m = - M_nam M_am= - M_nm
But the onset of CPT symmetry breaking is when conformal symmetry is broken
and particles acquire rest mass. Equivalently this is the point that
decoherence may begin , the onset of inflation.
Interesting if correct. These deformed dispersion functions should produce
measurable effects in the next few years. See links