An Indication From the Magnitude of CP Violations that Gravitation is a Possible Cause of Wave-Function Collapse

Abstract

We consider experimental evidence for the hypothesis that the Planck energy, $E_p \approx 10^{19}GeV$, sets the scale $\epsilon$ at which wave function collapse causes deviations from linear Schr\"{o}dinger evolution. With a few plausible assumptions about the collapse process, we first show that the observed CP violation in $K_L$ decay implies a lower bound on $\epsilon$ remarkably close to $E_p$. If the bound is saturated, the entire CP violation is due to collapse and a prediction made that the branching ratio for CP violation in the B meson decay will be $\gamma \approx 10^{-5}$. We then show that the assumptions are consequences of a simple non-linear, stochastic modification of the Schr\"{o}dinger equation with $\epsilon$ setting the scale of the non-linearity.