In the MW interpretation of quantum mechanics, the double slit experiment can be explained this way:
- a single particle's wave function approaches the pair of slit apertures.
- The wave function is spread out laterally so that it impinges on both slits.
- The wave function goes through both slits and is diffracted, forming an interference pattern on the detector.
- The detector can only detect the particle at one point, and the probability that it is detected at any given point is proportional to the squared amplitude of the particle's wave function at that point.
A reasonable person might ask, "What happens to the rest of the wave function - the portion that is not at the detected point?"
The MW interpretation answers that question by saying that #4 doesn't tell the whole story: that in fact the detection event at the detector must, itself, be described by a wave function. That is, the detection event exists as a superposition of possible outcomes, just as the particle's trajectory exists as a superposition of possible paths. Extend the reasoning farther, considering an observer to be put into a superposition of states, each "observer state" observing the detector indicate that the particle has been detected at a different point.
At first glance, it might seem that the observer would see all those states at once, but he/she doesn't because of the fact that the wave function is linear -- which means in effect that the different possible paths do not "see" or interact with each other. Each state represented in the superposition that describes the observer is invisible to all the other states, as if they don't exist.
The "branching" in the MW interpretation is just the recognition that at each event in the evolution of a wave function that describes a system, a set of new - mutually invisible and non-interacting - states may be added to the wave function describing the whole system. (E.g., the "event" might be diffraction at the slits, detection of where the particle hits a screen, or the observer's perception of where the detector says the particle hit the screen).
When the whole system (source, slits, detector, and observer) is included in the original wave function describing the double-slit experiment, there is much less reason to be confused by the MW interpretation of the experiment.