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If we assume that I consist of 100 elementary particles in a box, then there is a continuum of their configurations. Furthermore, these configurations are entangled with other subsystems in the box. Speaking about a "branch" is not very intuitive in such a setup.

David Bohm's model assigns a marker to each elementary particle in the box. These markers then sail on the wave function in a very complex way, not affecting anything in the wave function. They are just markers.

In Bohm's model, I, as a subject, am in a "branch" determined by the markers. It is a very clear model but hard to generalize to relativistic quantum mechanics.

Bohm's model is a Many Worlds model. The physical thing is the wave function and the markers just point out one individual configuration.

However, the fuzziness of the continuum does creep into the Bohm model, too. The branch which it picks interacts very strongly with nearby branches. We may ask again if I, as a subject, am some collection of nearby branches. If so, what branches we should include in the collection?