I visualise the many worlds theory in the following way...

Imagine if you will, the universe starting in the big bang, much like a bottle of perfume being un-stoppered in a room, and the molecules of scent diffusing throughout the space. Okay, now imagine that each molecule represents one precise arrangement of matter and energy of the entire universe (or its quantum wavefunction, if you prefer). The position in this room is equivalent to a coordinate in phase space (follow dat link) that the universe occupies. Coordinates that are close together in phase space might represent universes that are nearly the same..

As the universe evolves over time, it moves from position to position in phase space, and the likelihood of it going from any one position to another can be determined by quantum mechanics. In the many world picture of things, all possiblities open to the universe, at anyone time exist; or all the molecules of perfume really are there. With the Copenhagen interpretation they may or may not exist, but one definitely does when an observation is made, and all the others do not!

In the many worlds universe, what we experience is in fact a path being drawn from coordinate to coordinate through the total phase space of the universe, back through time until the start of the universe, position zero. I imagine it as a chain of perfume molecules linked together, leading back into the perfume bottle. This theory is said to be untestable, as the different universes aren't supposed to be able to effect each other. Some people say that aspects of paranormal experiences can be explained if the theory is true however; perhaps ghosts etc. are events in a universe near to ours in phase space quantum tunneling through to our own.

It might be that if any of this 'universe to universe' interaction goes on, it has a low probability of happening, and any particle physics experiments set up to test it may have an infinitesimal chance of working. However, on a universal scale the effects will most likely be cumulative, perhaps affecting cosmology. Incidently recent measurements of supernova have shown the universe may well be expanding at an ever increasing rate, for reasons that are as yet, unprovable!