Particle mixing and the emergence of classicality: A spontaneous-collapse-model view

Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamiltonian and a dissipator of the Lindblad form in an enlarged Hilbert space, we show that spontaneous collapse can induce the decay dynamics in both quantum state and master equations. Moreover, we show that the decay property of a flavor-oscillating system is intimately connected to the time (a)symmetry of the noise field underlying the collapse mechanism. This (a)symmetry, in turn, is related to the definition of the stochastic integral and can provide a physical intuition behind the Itō-Stratonovich dilemma in stochastic calculus.

Figure 1

Lower bounds for the estimated value of the collapse rate ${\lambda }_{\mathrm{CSL}}$ via Eq. (51) as a function of the reference mass $m_0$. The blue, orange, green, and red areas correspond to the values of ${\lambda }_{\mathrm{CSL}}^{\mathrm{estimated}}$ given by $K, D, B$, and $B_s$ mesons, respectively. The colored points refer to the rest masses of the corresponding mesons, the purple line is given for the nucleon mass, and the cyan line corresponds to the rest mass of the Higgs boson. Plotted are the theoretical values of the collapse rate ${\lambda }_{\mathrm{CSL}}={10}^{-16}{\mathrm{s}}^{-1}$ proposed by Ghirardi, Rimini, and Weber [8] and ${\lambda }_{\mathrm{CSL}}={10}^{-8\pm 2}{\mathrm{s}}^{-1}$ proposed by Adler [73] for $r_C={10}^{-7}\mathrm{m}$. The inverted mass ratio ${\tilde{m}}_i=\frac{m_0}{m_i}$ is assumed in accordance with Ref. [55].