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My roommate who studies physics once showed me the leftovers of an interesting experiment:

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They filled up those metal balls with water and then froze it. The water expanded and with all of its power blasted away the metal shells. Amazing stuff.

But I came up with a question he couldn't answer with confidence when I saw that.

All of these "balls" are imperfect. They have different materials all over the place. Let's say they're mostly some metal $m$, but at no point is there exclusively any $m$, there are always other things (oxygen, hydrogenparts out of the air, ...), therefore those spheres can sustain different pressure levels at different parts and in one part or another, they will crack first and release all the energy. At least I imagine it that way and I cannot think of any other way.

But now imagine you had a perfect ball of metal like those. Every nm² and smaller is exactly as durable as any other one. And then you did the same experiment: at which point would the metal first start to crack? Would it crack at all without any differences in structure?

Wouldn't a perfect children's balloon then be able to stand any pressure from the inside without breaking? That seems paradoxical to me, but logical if my assumption is true that the balls only break at a certain point because that point cannot handle as much pressure as the other points

Does anybody know the answer? It would really interest me.

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  • $\begingroup$ a perfect sphere is something that, in reality, is nearly impossible to achieve. Even so, one could still invoke quantum fluctuations to argue that eventually the sphere will break as a consequence of a spontaneously broken symmetry. $\endgroup$
    – Phoenix87
    Commented Jan 3, 2015 at 17:34
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    $\begingroup$ There is no such thing as a perfect sphere. Things that don't exist can't break. They can't do anything, really. $\endgroup$
    – CuriousOne
    Commented Jan 3, 2015 at 17:35
  • $\begingroup$ There will always be a defect somewhere in the molecular structure. $\endgroup$
    – Kyle Kanos
    Commented Jan 3, 2015 at 17:37
  • $\begingroup$ creating a perfect ball isnt practical , There would be some form of void/dislocations or defects always. So there would be always some crack initiation point due to imbalance in local strain fields. If indeed a perfect sphere is created then it should break at all points(each atom to atom). You should read about single crystals $\endgroup$
    – Gowtham
    Commented Jan 3, 2015 at 17:38

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Well I think the problem won't be in the sphere no matter how perfect it is. It will probably brake relatively random. That would be caused the way the water freezes, because it can't freeze "perfectly". some areas will freeze faster than others be that to gravity, temperature layering of the freezing liquid, or the movement of molecules in it.

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According to classical non-statistical mechanics, if such a perfectly symmetric sphere existed (I think such symmetry might not be possible even in theory because every material consists of particles), the sphere would not break. In practice, however, the sphere would at some point become unstable to deformations. Micro-scale deviations of symmetry, caused by effects such as non-zero temperature or even quantum effects (as pointed out by Phoenix87), would amplify almost instantaneously to macro-scale breaking of the sphere.

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