Relativistic State Reduction Dynamics

Abstract

A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a relativistic field in which a quantized degree of freedom is associated to each point in spacetime. The purpose of this field is to mediate in the interaction between classical stochastic influences and conventional quantum fields. The equations of motion are Lorentz covariant, frame independent, and do not result in divergent behavior. It is shown that the mathematical framework permits the specification of unambiguous local properties providing a connection between the model and evidence of real world phenomena. The collapse process is demonstrated for an idealized example.

Quantum origin of the primordial fluctuation spectrum and its statistics

“…The problem is, that in the absence of a well-defined set of rules, it becomes quite unclear whether or not such "predictions" follow or not from the theory without the use of extraneous and ad hoc, but convenient hypothesis suitably introduced in connection to the particular problem at hand. Especially suspicious are, of course, those predictions that are, in fact, retrodictions, and, on this point, we should recall that, long before inflation was invented, Harrison and Zel'dovich [59] had already concluded what should be the form of the primordial spectrum, based on 22 In practice, this view is essentially indistinguishable from the so-called for all practical purposes approach to the matter [58].…”

Cosmological inflation and the quantum measurement problem

“…The straightforward relativistic generalization of the CSL model for quantum field theory, starting with the action (6) in the Tomonaga picture for instance, leads to unremovable divergences [65] (see however [69]), even more so when non linearities inherent to general relativity are taken into account.…”

Black hole evaporation: information loss but no paradox

“…We have based our treatment on a non-relativistic model of spontaneous collapse theory, while a truly satisfactory proposal to deal with the issue should be based on a fully covariant theory. Fortunately, the early studies [54,55], and the recent specific proposals for special relativistic versions of these type of theories [56][57][58][59] indicate that we should be able to address this shortcoming in near future. We just note again that in those theories the interaction picture evolution should be describable in terms of a Tomonaga-Schwinger equation where the interaction hamiltonian is replaced by the corresponding collapse theory density operator.…”

“…In this regard we note that CSL, in general, leads to small violations of energy conservation, a fact that has led to establish the most stringent bounds on the parameter λ (although modified covariant theories might evade this problems altogether. See for instance discussions in [57,58,61]). Moreover, we note that if there is a small amount of energy remaining inside the black hole region, and very close to the singularity, simply because the positive and negative energy fluxes do not precisely cancel each other, there would be no problem, at least in principle, if such energy were to be radiated after the singularity.…”