Is it true that quantum mechanics technically allows anything to happen? Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time.
The ultimate question is: Is everything (in our Universe) possible ?
I've read some books (Penrose, Hawking, Greene, etc.) where it was clearly stated several times that quantum mechanics allows any situation to happen (e.g. everything is possible) - even with absurdly tiny probabilities?
Does this mean only physically possible - or "ultimate" possible ?
For example (I know this example seems really absurd, but I'm saying this so you get the idea) what my friends clame it is possible:


*

*If I ask my friend(s): "Is it possible there is a Sun-sized star in my pocket right now?" They will respond: "Yes, there is very very tiny possibility this can be true!"

*Etc.

 A: With quantum mechanics, you have to ask your questions very, very carefully.
Is it possible to have a Sun-sized star in your pocket?  It depends on what you mean by "in".  Do all of the atoms of the star need to be entirely in your pocket, or is it sufficient that some part of each atom's wave function be inside your pocket?  It is possible to have any number of atoms counted as being in your pocket and they could just appear there.  A nonzero probability of that could be calculated, but perhaps not contemplated.  There is a small chance that a dropped coin will come to rest on its edge - a rare event that can be calculated and contemplated.  There is a small chance that one atom will disappear from one side of the room and reappear and the other side. That can be calculated.  The odds of a Sun's worth of atoms disappearing from nearby stars into your pocket in a second is nonzero and calculable, but probably not contemplatable.
That said, if you said "Is it possible there is a Sun-sized star in my pocket right now?" and a Sun's worth of particles just found themselves located in your pocket as you uttered "now", your friends could not respond: "Yes, there is very very tiny possibility this can be true!" because they would be sucked into the black hole that just came into existence before they could speak those words.
The way you ask the question will lead to different answers.
A: No, there is zero probability (and thus no possiblity) of that event.  Quantum mechanics does not allow for anything to happen.  In fact, QM often specifies exactly what must happen in a given situation... that's why we use it!  For example, QM tells you that immediate re-measure of an observable property will always yield the initial result.
See also my response to this question.
A: No, quantum mechanics does not allow anything at all to happen with some probability. For example, the beta decay process $n\rightarrow p+e^-+\bar{\nu}$ is possible, but the process $n\rightarrow p+e^++\bar{\nu}$ is not, because it violates conservation of charge. The second process isn't just unlikely, it's impossible given the known laws of physics.
A: In QM you have things called "selection rules" that explicitly forbid a process to happen (its probability is EXACTLY 0). Usually, these rules arise from some symmetry or conservation law (like, for instance, conservation of charge, conservation of parity in strong interactions etc).
I think your question is really vague, and you should define the physical system you want clarifications about more precisely than "a sun sized star in your pocket".
A: This question is not of physics but is of maths. Actually, the probability cannot be taken on one sided scale.... Probability of happening exists along with probability of not happening. In case of sun in your pocket question probability of it not happening is too large, nearly 1 which is the maximum probability.........
Also probability of everything possible also make probability of everything not possible "POSSIBLE" i.e. it makes the situation where nothing is possible..... possible...... it a paradox..... 
So it either gives you zero or infinity as an answer...... which neither we or the scientists could accept,....... and causes these types of conflicts.
So, as NEIL BOHR would have said.... it could be only possible if u do not observe them both...... the pocket and sun at any point of time..... same different past future etc....  
