Inertia as the “Threshold of Elasticity” of Quantum States

Abstract

The principle of general relativity (GR) of Einstein is based on the possiblity “to create” or “to compensate” locally the gravitation field by a choice of the accelerated frame in spacetime. In quantum field theory there do not exist pointwise particles (material points); we have, rather, extended wave packets (quantum particles) with “polarizations” of different kinds that correspond, in principle, to indefinite number of internal degrees of freedom. Therefore, in attempts to unify relativity and quantum theory the creation and annihilation of the fields of quantum particles are desirable. In this case the spacetime manifold is inadequate for such description. We should deal instead with a quantum state space. It is natural to think that creation and compensation (annihilation) of the quantum field may be related to the choice of the local frame in the state space and that there must be some new principle of classification of quantum motions. This hypothesis has been called “superrelativity.” This leads to a new gauge theory of the geometric type in the projective Hilbert space. Here I try to connect the inertial property of “elementary” quantum particles with the deformation of quantum states.