Lower and upper bounds on CSL parameters from latent image formation and IGM heating

Abstract

We study lower and upper bounds on the parameters for stochastic state vector reduction, focusing on the mass-proportional continuous spontaneous localization (CSL) model. We show that the assumption that the state vector is reduced whan a latent image is formed, in photography or etched track detection, requires a CSL rate parameter $\lambda$ that is larger than conventionally assumed by a factor of roughly $2 \times 10^{9\pm 2}$, for a correlation length $r_C$ of $10^{-5}{\rm cm}$. We reanalyze existing upper bounds on the reduction rate and conclude that all are compatible with such an increase in $\lambda$. The best bounds that we have obtained come from a consideration of heating of the intergalactic medium (IGM), which shows that $\lambda$ can be at most $\sim 10^{8\pm 1}$ times as large as the standard CSL value, again for $r_C=10^{-5} {\rm cm}$. (For both the lower and upper bounds, quoted errors are not purely statistical errors, but rather are estimates reflecting modeling uncertainties.) We discuss modifications in our analysis corresponding to a larger value of $r_C$. With a substantially enlarged rate parameter, CSL effects may be within range of experimental detection (or refutation) with current technologies. ADDED NOTE: A careful calculation of radiation from atomic systems in the CSL model (Adler and Ramazanoglu, arXiv:0707.3134) has reinstated the bound obtained by Fu as the best upper bound on lambda, with significant implications for CSL model phenomenology.