Does the Many Worlds interpretation of quantum mechanics necessarily imply every world exist? I know the Many Worlds interpretation is controversial among physicists, but it's been a pop culture hit nonetheless. I frequently see people making statements like, "Well in another universe I'm a rock star", where you can substitute rock star for any given fantasy.
But one thing that's always bothered me about that kind of statement: does Many Worlds really imply Every World? You can have an infinite set of numbers that doesn't include every number. 
So even assuming MWI is true, is it necessarily true that one of those universes contain a rockstar version of myself?
 A: Basically yes, there are infinite worlds with different "outcomes" in each one. However, the Many Worlds interpretation says that some are less probable than others. So your rock star you might be less probable than, say, your normal you. (Just an example, obviously.)
The other important thing to note here is basically that every option of every decision or thing in the world has been carried out. So the Declaration of Independence might have been signed five minutes later than it was in our world. These changes then might lead to further changes and so on. 
So, if you are feeling especially philosophical one day, go to the fridge and drink some chocolate milk or lemonade, whichever you want. The decision you make will (according to the MWI) create multiple new alternate universes (depending on whether you choose to ignore me, mix them, choose one or the other, or choose something entirely different).
Hope this helps!
Edit: NathanFig brought up a good point in the comments that needed clarifying; these universes would, for instance, have to follow the laws of physics. There would only be a universe for every outcome for which a "decision" has been made in our universe. So the answer would be yes, every outcome possible from the decisons made in our universe (if that makes sense).
The other thing worth mentioning here is that the data is the same whether there is an alternate universe where something else happens or there isn't. It is merely an interpretation. 
A: The MWI interpretation of quantum mechanics does not introduce any substantially new answer to this question than already exists in any other interpretation of quantum mechanics or indeed classical statistical mechanics. 
In the MWI interpretation of quantum mechanics (as originally conceived by Everett), viewed at the microscopic level there is only one universe evolving according unitary deterministic dynamics. 
The MWI interpretation provides an explanation for the measurement problem by saying that whenever an entangled quantum system undergoes decoherence and approximately forms a mixture then each member of that mixture forms its own evolving branch effectively independent of the evolution of the other members.
Within this emergent branching structure we can ask questions like "what is the probability of ending up in a branch with all the atoms in a box ending up in the left half" but such a question is not greatly different from the similar question in classical statistical physics - given enough time it will happen. 
A: No, it doesn't. For example, since charge is conserved, every "world" in the wavefunction must have the same charge. This goes for any other conserved quantity, too.
(This doesn't rule out you being a rockstar, though.)
A: 
But one thing that's always bothered me about that kind of statement:
  does Many Worlds really imply Every World? You can have an infinite
  set of numbers that doesn't include every number.

Quantum mechanics places restrictions on the set of possible worlds.
Worlds are structures in the quantum multiverse where information is copied, see
https://arxiv.org/abs/quant-ph/0104033.
The version of me that is typing this is in the same universe as you because it is possible for information to be copied between this version of me and your eyes, brain etc. That has implications for the set of possible universes, e.g. - they are a discrete set that can be labelled by numbers 1,2,3... not a continuous set:
https://arxiv.org/abs/1212.3245.
More generally, there are no universes in the multiverse in which the laws of physics are broken. For example, there are no universes in which energy is not conserved.

So even assuming MWI is true, is it necessarily true that one of those
  universes contain a rockstar version of myself?

It is not necessarily true that there is a universe in which you are a rock star. I can't see any particular reason why that would be physically impossible so I would guess there is such a universe.
A: Many Worlds is really a misnomer, despite being the most commonly used name for Everett's interpretation. Everett initially called it the Relative State Interpretation. The "many worlds" and "universe splitting" terminology was introduced later by DeWitt. 
There are no multiple universes or splitting in the formal statement of Everett's interpretation any more than in any other interpretation. The dimensionality of the state space remains constant throughout the evolution of any system and the state consists of a single state vector. Any apparent "splitting" is just the representation of the state-vector in physically meaningful bases becoming less sparse due to entanglement. In Everett's interpretation measurement is just a form of entanglement if you include the experimental apparatus in the system description. The odd thing that is brought out by the Everett interpretation, but I believe is intrinsic to QM in general, is that there appears to be a preferred basis for macroscopic objects. For example we do not seem to be able to observe cats in the $|alive+dead \rangle$, $|alive-dead \rangle$ basis, though there is nothing in the quantum formalism that would make this any harder than the usual $|alive \rangle$, $|dead \rangle$ basis.
Everett's interpretation is really just the Copenhagen interpretation without observers, measurement &  state collapse.
The Stanford Encyclopedia of Philosophy has accessible explanations of these issues:


*

*https://plato.stanford.edu/entries/qm-manyworlds/

*https://plato.stanford.edu/entries/qm-everett/
A: The crucial word is "interpretation".
In physics it means that the results of calculations, hard numbers to be checked with data  for interactions and processes that we can measure in the lab, are the same in all interpretations of  a theory. 
There is no difference in the hard data.
One can see the integrals as "many worlds splitting off", but it is just mathematics; going further than that it is metaphysics, not physics.
I will give an example:
Take an apple. One can fit it with a fourier series  in three dimensions. The series has an infinity of terms with sines and cosines and the sum of the terms gives the apple's shape. Is the apple full of sines and cosines? One could make an interpretation that each term is real and exists in some space, coming together to make the apple.
A: Any alternate present must be the result of a whole possible alternate history. Assuming our decision making is not sensitive to quantum effects in our rather noisy brains (and you did not make your career choice as a random outcome of a quantum experiment, with rockstar already being on the table), significant alterations might be necessary to make rockstar-you happen. The alternate-reality person might be rather different from present you. There also might be careers that are unavailable in any history, though I have no idea how one would go about proving such a thing.
A: I think this question comes down to determinism. Our universe might or might not be deterministic, so I think the answer to this question is "nobody knows for sure".
If the universe is deterministic, then two universes that are identical at any given point in time will continue to be identical for the remainder of all time. So, if another universe exists that is exactly the same as this one at the moment of your birth, then it is impossible that you became a rockstar in that other universe, because you did not become one in this universe. 
So, the next question is, is there a universe similar enough to ours that a person with your exact DNA was born at the exact moment and place that you were born, but with sufficient differences that you became a rockstar? Maybe or maybe not. If the universe is deterministic, then only one timeline is possible given a set of inputs, so a different universe would require a different set of inputs. A universe with different inputs might necessarily be quite different from our own. This is debatable. 
If the universe is not deterministic, then it is probabilistic. In which case I'd have to say anything is possible within the laws of physics. 
A: No.  Keep in mind that all universes where you are you, everything up to your conception was identical (or very, very close).  Otherwise due to chaos theory/butterfly effect, it's likely a different sperm won the race, or the... event happened at a different time, and you lost your chance entirely.  So even if they are named Nathan Fig, the genetics might be slightly different (or maybe they are named Natalie.  Who knows).
So out of that relatively small subset of the Many Worlds where your specific genetics exist, most will be substantially the same.  As an easy counter example to your question, if you were born after 1945, there is almost certainly no universe with you in it where the Axis powers won WW2.  So right off the bat, that eliminates a large number of potential jobs that are no longer available to you in any universe.
A: In case of eternal inflation theories, one can show that the MWI ensemble is realized physically such that the relative frequencies are given by the Born rule. There is then no doubt about the reality of the alternate MWI Wolds even if the MWI is false. One can then argue like is done in this article that all physically possible histories of the universe are realized:

Some readers will be pleased to know that there are infinitely many O-regions where Al Gore is President and - yes - Elvis is still alive.

A: In MWI, universes branch off all the time, with every possible quantum "observation". So let's say a version of "you" to exist or at least existed in any universe which branched off after your conception.
So, question becomes: Is there a series of quantum "choices" which leads to you becoming a rock star?
I think that is certain. Even if that was impossible under "normal" circumstances, consider radioactive decay causing brain tumor, which in turn causes behavioral changes. It could happen to a version of you, but also to an artist agent or your music teacher or parents, leading you to become a rock star. This is just an example to demonstrate that there almost certainly exists MWI universes where quantum "choises" and events unfolding from them lead to you becoming a rock star.
Not only that, but by same logic, in countless MWI universes branching off after this moment, you will become a rock star, and then later wonder how that relates to you having asked this question here.
A: The answer to your question is basically depending on if you decide to:


*

*allow all other worlds to have totally different physical laws then ours, different combination of them, maybe no laws at all

*all other worlds must obey the same exact physical laws 


In the case of 1. the answer to your question is yes, all of them exist. In this case all kinds of combinations would be existing, since there is no limit for example on the amount of energy, speed of expansion etc. The size of these parallel worlds would not be limited either. 
In the case of 2. the answer would not be so simple. In this case the number of parallel worlds would still be infinite. But all these infinite worlds would just be versions of our current one. All of the infinite ones would start with a big bang like ours, just they would end up differently, depending on little changes in the starting setups, like the allocation of energy, particles differently allocated, (though the amount of energy would be the same as our world's), but maybe the size of the starting point would be different (where everything is bunched into before starting the big bang), and so the energy of explosion would be different. maybe the era of inflation would be different too, longer/shorter then ours. So this way all those worlds would exist, but maybe the arrangement of the particles/energy would be different in them.
A little background on this to understand the question:
(Imagine a 6D world, where our 3D space would be then extended infinitely in a 4th dim., can call it time. Then we have a infinitely long (both directions) line, with every point of the line having one of our current 3D spaces. So then we have the 4D timeline, and infinitely replicate it on the 5th dim. That looks more like a flat surface filled with our 3D spaces in 2 dimensions now, the 4th and 5th. And then you just replicate this 5D world infinitely into a 6th dim. So then basically you have Our 3D world infinitely expanded in 3 more dimensions. Each coordinate of this 4th,5th, 6th dim system has one 3D world on it. Those are our parallel worlds. Now imagine that the timeline as we imagine it now is not linear, but moving in 3 dimensions, the 4,5,6th. So basically our world is currently in this 3D sytem somewher and as we pass through time, we move on this 3D grid. our timeline describes the possible line through this system based on our starting settings and out laws. Nobody can change it, since that wouldre  quire too much energy. But those other worlds on the other spots of this 6D grid are all existing parallelly) 
