I can’t understand why entanglement has to involve action at a distance.

When I try to interpret entanglement and the nature of superposition, no action at a distance is involved. To take an example of a pair of electrons, each a superposition of up and down spins, when the spins are measured there are four possible results representing four potential worlds (up up, up down, down up and down down). When a pair of electrons are entangled so that their spins, although not determined, will be opposite when measured, these four possibilities are reduced to two potential worlds (up down, down up). So when the pair are then separated and the spin of one is measured, the world splits at that location and the observer also splits and will be in one of these two worlds. If a measurement is taken of the other electron, the world splits at that location and the observer will be in one of the same two worlds. When news of the outcome travels from one location to the other it travels to the world where the electron spin is in the opposite direction. The influence travels from one location to the other at a speed no faster than the news of the outcome (or light) can travel.

I guess there is a connection between the entangled electrons - it is the "line" along which the world will split.