 D. Bedingham (2011) following strictly the original proposal by Pearle (1990) of a quantum field theory inducing reductions based on a Tomonaga- Schwinger equation, has worked out an analogous model which, however, overcomes the difficulties of the original model. In fact, Bedingham has circumvented the crucial problems arising from point interactions by (paying the price of) introducing, besides the fields characterizing the Quantum Field Theories he is interested in, an auxiliary relativistic field that amounts to a smearing of the interactions whilst preserving Lorentz invariance and frame independence. Adopting this point of view and taking advantage also of the proposal by Ghirardi (2000) concerning the appropriate way to define objective properties at any space-time point \(x\), he has been able to work out a fully satisfactory and consistent relativistic scheme for quantum field theories in which reduction processes may occur.