How do I decide that a particle is isolated?

[frogeraie]

Every particle in the universe has been, at a given point of its history, interacting with other particles. So, how is it possible to decide whether a given particle can be treated as an isolated quantum system the states of which are vectors of a single Hilbert space? Altenatively, what conditions will force us to consider electron pairs emitted by radioactive decay or photon pairs resulting of radiative cascade, as a single system describe by a tensor product of two Hilbert spaces?
What is the criteria to decide whether a system is bipartite?

 

[mfb]

For the evolution of a particle or a system of particles, you can ignore the rest of the world if there is no decoherence happening within the timescale of your experiment.