Slides from Sean Carroll, From Eternity to Here
Miss Kitty is a quantum object defined by its wave function. All that is 'real' to Miss Kitty is what is in the wave function, nothing else.
In this first slide, we see that Miss Kitty's wave function has a 50% probability of being "under table" and a 50% probability of being "on the sofa". While one is tempted to think that Miss Kitty is either under the table or on the sofa, that would be incorrect. It is also wrong to think that Miss Kitty is 1/2 under the table and 1/2 on the sofa, i.e., that Miss Kitty is in both places. The correct interpretation of quantum reality is that Miss Kitty has no "where" until observed. The wave function is all that is Miss Kitty.
And the wave function for Miss Kitty, before observation, is a superposition of these two "worlds", under the table and on the sofa. Once a observation is made, Miss Kitty becomes a classical object and has position. And note that the wave function evolves in a deterministic manner, only our expectations are probabilistic.
Now in the above slide, Miss Kitty interacts with either the scratching post or the food dish before ending her journey either under the table or on the sofa (think of the post and dish as being the two silts of the double slit experiment). If we observe Miss Kitty at the dish or the post, then the probability of ending under the table or on the sofa are still 50/50.
However, if we do not watch the dish and post, than the resulting final probabilities of under the table or on the sofa have radically changed. This is interference where there is no pattern on the screen if we watch the slits (50/50) but there is a pattern (0/100) if we do not watch the slits.
The wave function itself is not probability, but can be used to calculate probability. And waves can be positive and negative (like an ocean wave) or all positive (like a bell curve). As the probability is the square of the wave function, this will always be positive.
So Miss Kitty approaches the scratch post and scratches, gaining energy so the wave function is always positive. Or Miss Kitty approaches the food dish and eats (gaining energy) or does not (losing energy) and the wave function is both positive and negative. The probabilities are the same when we observe Miss Kitty at the post or dish.
But if we do not observe the post and dish, then the table probabilities cancel out (destructive interference) and the sofa probabilities sum up (constructive interference) to produce a new reality. Many-worlds interprets this scenario in that we do not have a 'split' of the Universe, both worlds are already in the wave function and we observe one or the other.