It has been demonstrated recently by the authors that the non-relativistic quantum state diffusion model can be generalized to yield a consistent, relativistically covariant theory. It is shown here that the `counterexample' constructed by Diósi can easily be disproven.
A relativistic generalization of the quantum-state diffusion model is developed. The model describes a Dirac electron which is coupled to an external electromagnetic field and a dissipative environment. A relativistically covariant stochastic Dirac equation is obtained by regarding the state vector as a functional on a certain set of spacelike hypersurfaces in Minkowski space and by the definition of an appropriate Hilbert bundle on this set. The integrability condition of the stochastic process and the corresponding covariant density matrix equation are derived. Further, the relativistic equations governing the dynamical state-vector localization are deduced.
We offer a new look on multiparticle theory which was initiated in a recent philosophical paper [1] of the author. To accomplish such feature, we start by a revision and extension of the single particle theory as well relativistically as nonrelativistically. Standard statistics gets an interpre- tation in terms of symmetry properties of the two point function and any reference towards all existing quantization schemes is dropped. As I have repeatedly stated and was also beautifully explained by Weinberg, there is no a priori rationale why quantum field theory should take the form it does in a curved spacetime; there is no reason why the straightforward generalizations of the Klein Gordon and Dirac theory should have some- thing to do with the real world. Perhaps, if we were to look differently at the flat theory, a completely satisfactory class of relativistic quantum theories would emerge. These may not have anything to do with quantum fields at all except in some limit.
Up to this point, our study of quantum mechanics has concerned itself with the behaviour of particles that inhabit a Galilean spacetime. For many purposes, in atomic, molecular and condensed matter physics, this theory is quite adequate. We saw in earlier chapters, however, that our actual spacetime has a structure which is much closer to that of the Minkowski spacetime of special relativity and that more general structures must be considered when gravitational phenomena are signicant. From a purely theoretical point of view, it is therefore important to formulate quantum theory in a way which is consistent with these more general spacetimes. The benets of constructing a relativistic quantum theory actually go far beyond the aesthetic satisfaction of making our geometrical and quantum-mechanical reasoning compatible. For one thing, we shall discover that the relativistic theory provides a deeper understanding of spin and the distinction between fermions and bosons, which in the non-relativistic theory appear simply as facts of life that we must strive to accommodate. Also, of course, there are many situations in which relativistic eects become observable, for which non-relativistic theory provides no explanation. The most obvious are high-energy scattering experiments, in which particles acquire kinetic energies comparable with or greater than their rest energies mc2, and the correct 4-momentum (3.33) must be used. There are, however, more subtle eects, such as the spin-orbit coupling that is essential for interpreting atomic spectra, which are also of relativistic origin.
Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.