Ghirardi--Rimini--Weber theory

The Ghirardi--Rimini--Weber theory modifies unitary time evolution by random Gaussian position localizations. Each constituent collapses at a small fixed rate, while the rate for an entangled macroscopic body grows with its number of constituents.

For localization length $r_C$, the GRW localization operator acting on particle $i$ isA collapse centred at $\mathbf{X}$ sends $|\psi ⟩$ to the normalized state $L_i(\mathbf{X})|\psi ⟩$ with probability density $\Vert L_i(\mathbf{X})|\psi ⟩{\Vert }^2$.

For $N$ entangled constituents, independent localization rates add to approximately $N\lambda$. One constituent's collapse localizes the correlated macroscopic configuration, rapidly suppressing macroscopically separated branches.

GRW position localization increases the ensemble mean momentum variance. In three dimensions one collapse adds $3{\hslash }^2/(2r_C^2)$ to $⟨{\mathbf{p}}^2⟩$, producing mean kinetic-energy increase $3{\hslash }^2/(4m{r}_C^2)$.