The Schrödinger equation rotates the state vector in Hilbert space continuously (i.e. without jumps). This makes sense for individual systems, but I'm finding this hard to reconcile with coupling or entanglement. For example, consider how Schrödinger's cat paradox is typically presented (in Dirac notation). We have a cat initially in the state |Alive> and we have a vile of poisonous gas in the state |contained> and we have some radioactive material in the superposition a|decay> + b|~decay>. The overall system is set up so that if the material decays (i.e. is in state |decay>) then the vile of gas enters the state |released> and the cat evolves to |Dead>. The linearity of the Schrödinger equation then entails the entire system should evolve to: |Alive>(a|decay>|released> + b|~decay>|contained>) And then to: a|decay>|released>|Dead> + b|~decay>|contained>|Alive> Here's what I don't understand: If the Schrödinger equation always rotates the state vector continuously (without sudden jumps) then how could the state vector in the composite state space go from this: |Alive>(a|decay>|released> + b|~decay>|contained>) to this: a|decay>|released>|Dead> + b|~decay>|contained>|Alive> These two vectors (in the composite vector space) are surely not an infinitesimal rotation apart. But then how could amplitudes a and b just pass immediately from the radioactive material, to the vile, to the cat? I'm clearly missing something here. Any help would be appreciated.