Nonlinear relativity and the quantum ether

The orthodox approach to relativistic quantum field theory axiomatically postulates Lorentz invariance, followed by the axioms of quantum mechanics. Departing from this approach we have designed a heuristic procedure by which the Lorentz transformations follow from the interactions characterized by the quantum mechanical commutation rules, rather than being postulated a priori. The most general operator representation of the quantum mechanical commutation rules that involve a length constant, have in the past been rejected on the ground that they violate Lorentz invariance. We therefore have applied our heuristic principle to derive the corresponding transformation equations that take into account the length constant appearing in this most general representation. We find a nonlinear generalization of the Lorentz transformations, departing from special relativity at very high energies and establishing the observable existence of a substratum (ether). The principle that the velocity of light is the same in all reference system still holds, but the theory gives a finite zero point vacuum energy. Furthermore, a non-Lorentz invariant behavior of cross sections at very high energy is predicted. In the limiting case where the length constant is set equal to zero, the zero point energy diverges and special relativity is recovered. The theory satisfies the philosophical principle by Leibniz, that the space-time structure should be determined from the interactions instead of being postulated a priori