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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.
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""quantum mechanics allows any situation to happen "" You should read those books more carefully. – Georg Oct 3 '11 at 11:11
But examples in the books were also quite unbelievable - like this: "There is a tiny probability you can put a finger through a concrete-wall, etc." – sabiland Oct 3 '11 at 11:47
Again, that example is not logically incoherent. What it would take to put your finger through a concrete wall is for the atoms making up the space into which your finger would go to be located somewhere else; since each atom's wave function allows it to be far removed from where it would be expected to be, there is a possibility that all of them would be simultaneously far removed from their original location. This is different than a particle either existing or not which, due to the law of conservation of mass/energy, is much more tenuous. – AdamRedwine Oct 3 '11 at 12:24
You know, to me this is actually an interesting question, which it will take some precision and subtlety to discuss properly. As an aside, what is the level of education of the questioner, and his/her friends? I have known a least one biology Nobel Laureate who disagreed with me about this. A way of restating the question might be, "Are all quantum mechanical propositions necessarily probabilistic?" Lederberg said yes. I very much appreciate the comment below, that events with 0 measure could also actually happen. – sigoldberg1 Oct 3 '11 at 21:34
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I'm late to the party, but it occurs to be that this might be the end result of a whisper-chain-like distortion of the totalitarian principle: "Anything that is not forbidden is mandatory", which does not mean that everything is possible because somethings are forbidden. – dmckee♦ Oct 7 '11 at 17:58
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5 Answers

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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.

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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.

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and what about those Feynman diagram which says there are infinite possibilities of interaction possible from which the most probable occurs?? – Vineet Menon Oct 3 '11 at 11:40
@AdamRedwine, you wrote: "It is true that the mathematics allows for such things, but the probability associated with them is unimaginably small." But that's the point. Even unimaginably small probability is still != 0 probability. – sabiland Oct 3 '11 at 11:50
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@sabiland: Yes, but it is important to keep in mind which "things" I was saying were possible. The possibility that an object (of arbitrary size or complexity) would materialize are unimaginably small, but the possibility of an event that is logically incoherent (like an object fitting inside a container smaller than it) is zero. – AdamRedwine Oct 3 '11 at 12:11
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@Vineet: It is true that there are an infinite number of interactions possible, but we learned from Georg Cantor that there are different kinds of infinities. Just because there are an infinite number of possible reactions does not mean that all reactions are possible. As an analogy, there are an infinite number of numbers between 1 and 2, but 3.5 is not one of them. – AdamRedwine Oct 3 '11 at 12:13
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Mathematically speaking, zero probability does not always indicate that the event will not happen, this is a common misconception. If we're talking about continuous variables, probability is defined as a measure and the measure of a finite set is zero. – recipriversexclusion Oct 3 '11 at 14:42
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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".

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up vote 0 down vote

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.

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up vote -4 down vote

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....

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