Wire A
-----R-----
/ \
------I--->-[P]-- ---------I-->
\ /
-----R-----
Wire B
Wire A and B both have a resistance of $R$ and a current of $\frac{I}{2}$ flows through each of the wires. How come electrons know which wire path to choose in this configuration?
What I am thinking is if we consider electrons at point P are in a state $\frac{|A\rangle + |B\rangle}{\sqrt{2}}$ and at the junction some kind of measurement occurs which leaves half of the electrons in the state $|A\rangle$ and the other half in the state $|B\rangle$.
Could you please explain how exactly does this work? Please point out why the argument given above is right or wrong (or at all relevant) in this situation.
EDIT: How can one derive basic laws for series and parallel circuits from more basic principles?