Abstract
We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: d/dt ρ_ij =-i/ℏ[H,ρ]_ij-ρ_ij/τ_ij. Different from other collapse models, the collapsing scale τ_ij here does not contain a universal parameter, but is specified by the two states | i and | j: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then τ_ij is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\em without} any actual monitoring. Otherwise, τ_ij=∞, which means no collapse and everlasting superposition. This happens if one state is not repeatedly readable, or if the two states cannot possibly be discriminated in a particular circumstance (for example in the Rabi oscillation). Detailed analysis shows that for a "trapped Schr{\"o}dinger's cat", the superposition of | here and | there is forbidden if E D ≫ 4π ℏ c, and allowed if E D ≤ 4π ℏ c, where D is the trap separation and E is the energy gap, which can be estimated with M v². The model also constrains a "free Schr{\"o}dinger's cat" to display double-slit interference if pθ D≥ 8ℏ, where p= Mv, θ is the angle spanned by the two trajectories, and D is the slit separation. In contrast, this model sets no limit on the coherent length of massless photon, thus the arm of a Michelson interferometer can be arbitrarily long. The spontaneous collapse which we propose can occur for an isolated system, and parallels the decoherence induced by interaction with environment.