Continuous-spontaneous-localization scalar-field relativistic collapse model

The continuous-spontaneous-localization dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field ϕ[over ̂](x,t) (mass m) is discussed. A complete solution for the density matrix is given, for an initial state |ψ,0〉=1/sqrt[2][|L〉+|R〉] when the Hamiltonian H[over ̂] is set equal to 0, and when H[over ̂] is the free field Hamiltonian. Here |L〉,|R〉 are coherent states which represent clumps of particles, with mean particle number density Nχ_{i}^{2}(x), where χ_{1}(x),χ_{2}(x) are Gaussians of width σ≫m^{−1} with mean positions separated by distance ≫σ. It is shown that, with high probability, the solution for H[over ̂]=0 (identical to the short time solution for H[over ̂]≠0) favors collapse toward eigenstates of the scalar field whose eigenvalues are close to ∼χ_{i}(x). Thus, this collapse dynamics results in essentially one clump of particles. However, eventually particle production dominates the density matrix since, as is well known, the collapse generates energy/sec-volume of every particle momentum in equal amounts. Because of the particle production, this is not an experimentally viable physical theory but, as is emphasized by the discussion, it is a sound relativistic collapse model, with sensible collapse behavior.