An Attempt at Relativistic Spontaneous Localization

O. Nicrosini, A. Rimini

G. C. Ghirardi, Philip Pearle

In this part we will consider recent attempts to get a relativistic CSL theory. The problem of getting such a generalization, or at least of making plausible that it exists, is of great interest. J. Bell (1990), after having expressed his dissatisfaction with the fundamental lack of precision of the standard formulation of quantum mechanics and the opinion that the only available acceptable alternatives are the Pilot Wave and the Spontaneous Localization schemes has stated: The big question, in my opinion, is which, if either, of these two precise pictures can be redeveloped in a Lorentz invariant way. The point of view of this paper is that what is most interesting is not a detailed exposition of the formal aspects of the generalization, but some crucial conceptual points which have come into focus in this attempt.

Anirudh Gundhi, Lajos Diósi, Matteo Carlesso

Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem. While experiments are providing increasingly stronger bounds on their parameters, a full-fledged relativistic extension is still missing. Previous attempts have encountered different obstacles, such as violation of microcausality, infinite energy rate, and particle production from vacuum. Here, we propose a generalization of the collapse master equation that is characterized by a local field collapse operator and a non-Markovian noise with a Lorentz invariant correlation. Our construction is able to overcome previously encountered problems and has the desirable properties in the nonrelativistic limit. A specific choice of the noise correlation function is also introduced and discussed.

L. E Ec

Daniel Bedingham

Energy diffusion due to spontaneous localization (SL) for a relativistically fast moving particle is examined. Spontaneous localization is an alternative to standard quantum theory in which quantum state reduction is treated as a random physical process which is incorporated into the Schr\"odinger equation in an observer-independent way. These models make predictions in conflict with standard quantum theory one of which is nonconservation of energy. On the basis of proposed relativistic extensions of SL it is argued that for a single localized particle, nonrelativistic SL should remain valid in the rest frame of the particle. The implication is that relativistic calculations can be performed by transforming nonrelativistic results from the particle rest frame to the frame of an inertial observer. This is demonstrated by considering a relativistic stream of noninteracting particles of cosmological origin and showing how their energy distribution evolves as a result of SL as they traverse the Universe. A solution is presented and the potential for astrophysical observations is discussed.

Rafael de la Madrid