Quantum mechanics (QM) is the physics of the small stuff of the universe - the smaller the better. (General relativity applies to the big stuff - the bigger the better.)
There are three conceptual formulations of QM. They are formulations, not separate theories, because they are exactly equivalent mathematically. One, due to Schrödinger, is based upon space-time, wave patterns, and makes the universe look continuous. (Like, really continuous. Schrödinger functions have no boundary - each one fills all of possible space.) A second, Heisenberg, is based upon energy movement, quantum jumps, and makes the universe look like particles. (In this view, all particles but one are made of other particles. The universe is the ultimate particle.) The third, Everett, is based upon information, and makes the universe look sensible - like we think we are.
In the world of physics, if you want to be right, use Schrödinger and Heisenberg. But, if you want to get things right, try Everett.
When physicists are between ideas, they argue about the meaning of QM. It's like democracy being your right to say what you think, without thinking. However, some of the nonthoughts out there about the Everett formulation are really, well, out of this world. It's usually referred to by denigrating physicists and would-be mystics alike as the 'many worlds theory'. As I've mentioned, it isn't a theory. It's exactly the same thing as the Schrödinger and Heisenberg formulations. Any criticism of one is a criticism of them all. But, the Everett formulation is indeed about many worlds, as long as you clarify what a QM world is.
I submit that the world of a quantum particle is everything that has happened to that particle that can affect its future interactions with other particles. "Many histories" is a better way of describing the concept. But, only things that can affect future interactions are part of QM history. Most of what has 'happened to a particle' can no longer affect its future, because each particle only has a small number of memory locations (quantum degrees of freedom) with which to 'remember' things. (The far past is not an observable, or, past states are decorrelated.) So, "many memories" is the way I prefer to think of a QM world.
The easiest idea in the many worlds formulation to jump on at first glance is that each time a particle interacts with another particle, 'new worlds' are created, each containing a different possible result of that interaction. So, the number of worlds seems to increase without limit and that is nonsense.
It would be nonsense. But, it isn't what happens, in this world anyway. Here is a human analogy of a quantum jump and of multiple worlds.
Suppose that your significant other is visiting the next town and, on the radio, you hear that half that town has been blown up by a gas leak. By the time you hear the news, your other is only in one state. One way or another, the explosion is complete. But, you sure aren't in one state! Half of you is worried that your bed won't be warm tonight, the other half is worried that the breakfast argument will be continued at dinner. You phone your nurturing parent for some solace, and promptly create a pair of worlds at the other end of the telephone line...
Finally, you get that phone call, from your s.o. or from the police. One way or another, you make your quantum jump and one of your states (worlds) dissolves from reality. Gradually, your family and friends follow suit as they talk to you. Of course, years later, you can still run into someone who asks "Did your ? ?" But, once everyone who interacted with any of you when you were in two pieces (in superposed states) has heard the news, or has passed on to that other world, your world is back to being one again with regard to that particular matter.
That's what happens in quantum particles. Quantum worlds fade from existence as fast as new ones are created. Schrödinger's cat is in one state - it's the observers outside the cat's closed box that are in two states. But, you'd never guess that from Schrödinger's formulation of QM - even he didn't.
An 'observer' can be as small as a single radioactive nucleus - things our size and complexity are not required. In fact, any two even partially-correlated quanta can 'observe' another single quantum. Ultimately, quantum mechanics is a continuous function.
There is another aspect of QM that Everett's formulation makes too obvious to avoid - there is no one reality. Every quantum world differs from every other. Existence is relative. How can this be? Is our universe not consistent?
Again, a human analogy is useful.
When you go to a party, you usually meet people you've never met before, whose worlds you have never known. Some of those worlds can be quite something, too! In physics language, there is little correlation between your states. By the end of the evening (interaction), you have some shared party experiences - your states are more correlated than they were before. If you never meet again, the shared memories fade, and your worlds slowly return to almost their previous separateness (they decorrelate). You'll never be the same again, but you're still the same you.
That's what happens in the quantum world too. However, QM takes the concept to its limit - every quantum world seems correlated with every other world precisely to the degree necessary to keep the universe consistent, and no more. QM is not the uncertainty principle, it is built upon Planck's constant. The many worlds of QM are very precise entities in their own way - the most precise of any physical theory we know.
Another aspect of the universe that Everett's formulation can help to understand is time direction. Time has two distinct attributes. Cyclic time is like a pendulum. It's reversible, related to Planck's constant, and is obvious from Schrödinger's equations. But, time also has a direction to it, and that's not obvious from Schrödinger or Heisenberg at all. In fact, many physicists whose student days predate Everett still consider the arrow of time to be a flaw of our understanding. It is, however, self-evident in the Everett formulation - quantum worlds abruptly appear, then gradually fade from existence, a clearly time direction dependent phenomenon analogous to the appearance and spread of ripples on a pond after a point disturbance. Things do happen to individual quanta in QM.
For some, it is an article of faith that there must be things that can never be understood. Having listened as a student at Cambridge to Paul Dirac, and having ended up as a Maxwell's daemon with respect to a single electron of a single atom, I no longer agree. I believe that QM (and cosmology) will ultimately prove to be as simple and as understandable as is possible for a theory that permits the self-organization of such complex creatures as us. In few areas is this view more useful than when considering what happens when one quantum splits into two.
It's often said that to understand politics, follow the money. Well, to understand QM, I follow the information. And, Occam's razor. Barely half a century ago, the greatest minds we then had mostly considered that everything I did in my last years at NRC was impossible. Impossible even in principle! And yet, what I observed was as simple as possible: one quantum, via a Poisson series that was perfectly random excepting only one degree of freedom - the time scale. A quantum exists between observations - I've followed one for 12 hours, others have for almost a year.
When one quantum splits into two, look for the simplest view that is consistent with that. One such view is, that we have already observed them both - at the moment of separation. Both quanta remain local to this first observation. Then we observe each of them a second time. If it were not for the first observation, we would know nothing about their relationship and there wouldn't be one. With this view, EPR is a local experiment - we just don't understand what the math is telling us yet. Just as we didn't understand for half a century what the math was telling us about single quanta.
Planck length is roughly 10-35m. We believe this to be the minimum characteristic length that space can have. The size of our universe is roughly 1026m (depending on how you measure it).
In between these, there seem to be two islands of minimal complexity: the size of a proton plus an electron (atoms): 10-8m, which is determined by QM, and the size of typical stars: 109m, which is determined by general relativity. Our size, 2 m, is the geometric mean of these last two.
If QM is complex to only a few parts in 108, we can exist between these two islands. In fact, QM seems more complex than that: consider the asymmetrical shape of a water molecule H2O with only 3 elements. Mach's principle may be sufficient to break the apparent discontinuity between Planck length and universe, but not between atom and star.
In any case, somehow, the universe is all of us together. There must be many quantum worlds, but there can be only one quantum universe for us.
The QM arrow of time is related to information - see What is Time? for more details. And, if you wonder what my interest in all this is, you can check out a few of my last papers before I retired: