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When it comes to things like gravity and the electromagnetic force, masses aren't reduced-but with nuclei the mass difference is noticeable. What about nuclear forces makes them capable of putting mass into binding energy?

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The only difference is that the strong force is stronger; meaning that binding energy can be a notable fraction of the total energy. You write

When it comes to things like gravity and the electromagnetic force, masses aren't reduced

which is not quite true, but then let on that you know by continuing

but with nuclei the mass difference is noticeable

which is the whole answer. Masses are reduced by electromagnetic or gravitational binding, but not by enough to be noticed.

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How is energy radiated from atomic bombs then? Won't the binding energy simply return to mass? –  Anthony Aug 4 '13 at 0:30
    
After fission the ex-fissile material is stable in it's new form. Likewise with fusion products. How would it get back together again going up the potential slope? The interesting question is "How did you get the fissile material in the first place?" and the answer is wrapped up in the unusual and rapidly changing conditions of a supernova. Lots of loose neutrons and beta decay. –  dmckee Aug 4 '13 at 0:37
    
I see. But in the case of fission, the first atom has some mass/energy stored in the atomic forces. Upon breaking apart, the two resulting atoms also have this force... It's confusing to me as to why all of the binding energy doesn't just turn into more binding energy. Mass goes into the potential, what determines whether or not mass returns to mass, or changes to kinetic energy? –  Anthony Aug 4 '13 at 0:44
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I think you are imagining "mass" as a special thing, different from other energy. But asking "is this energy mass or something else" only makes sense if you have specified the scale on which you probe the system. On the sub-nuclear scale there are distinct nucleons and they are bound to one another by the residual strong force. On a large scale there is just the nucleus and it has some mass. Both pictures are valid ways of understanding the system. To understand the fission, however, you have to use the sub-nuclear scale. Afterwards you can use the large scale again and find the lost mass. –  dmckee Aug 4 '13 at 0:58

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