Relativistic Spontaneous Localization: A Proposal

A. Rimini

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.

L. E Ec

Philip Pearle

Abstract Before examining experimental consequences of CSL, this chapter discusses the spontaneous localization (SL) theory of Ghirardi, Rimini and Weber (GRW). As for CSL, the chapter presents the structure of the theory, and then specializes it to a non-relativistic theory. SL does not add a term to Schrodinger’s equation. Instead, the state vector is suddenly altered by a “hit” (GRW’s ‘spontaneous localization’), that is, multiplication by an operator, followed by renormalization. The hits occur at random times. The chapter shows the specific choice of operator made by GRW for their non-relativistic theory. Emphasized are two aspects of SL that helped the journey to CSL. One is that the collapse is always acting (one need not “turn it on.” The other is the “smeared” character of the GRW operator. The chapter then shows how the density matrix is calculated. Finally, it discusses the numerical values, chosen by GRW, of the two parameters of SL theory, λ and a, that are provisionally adopted for CSL.

Rafael de la Madrid