Depends on what you mean by "physical contact." Some folks see quantum interference as an interaction between these different universes.
Also, about the branching. Another conceptualization of the multiverse, analogous to certain conceptions of spacetime, is a fully elaborated "static" multiverse. For any event that occurs in N universes and can have two outcomes with probabilities p and 1-p, pN of them have one outcome and (1-p)N have the other.
Depends on what you mean by "physical contact." Some folks see quantum interference as an interaction between these different universes.
I had in mind interactions via one or more of the four fundamentals, but, you're right, one mustn't forget about the quantum jitters.
Also, about the branching. Another conceptualization of the multiverse, analogous to certain conceptions of spacetime, is a fully elaborated "static" multiverse. For any event that occurs in N universes and can have two outcomes with probabilities p and 1-p, pN of them have one outcome and (1-p)N have the other.
The "it's in there!" view of reality.