Continuous-spontaneous-reduction model involving gravity

A continuous-reduction model implying the dynamical suppression of linear superpositions of macroscopically distinguishable states, presented recently by Di\`osi [Phys. Rev. A 40, 1165 (1989)], is investigated. The model exhibits appealing features; in particular, it relates reduction to gravity and contains no constants besides Newton's gravitational constant G. It turns out, however, that the model is not fully consistent. A slight modification of this model is proposed, which overcomes the difficulties and retains partially its appealing features. The resulting model deals with systems containing distinguishable or identical constituents, allows the derivation from microdynamics of wave-packet reduction, and accounts for the emergence of definite macroscopic properties for macro-objects. Reduction is related to gravity in the same way as in Di\`osi's model, but a fundamental length must be introduced to avoid inconsistencies.