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This may or may not be an incredibly stupid thought experiment, but a short time ago I read that most of the "mass" in the proton was actually energy from the quarks and gluons, as opposed to the actual mass which was coupled to the Higgs field. This made me start thinking about objects on macroscopic scales and the effects of energy and mass in a closed macroscopic system.

I have only a superficial highschool level understanding of relativistic mass, and I have read extremely vigorous debates and arguments about the significance of the mass-energy equivalence, and what it means in terms of the "weight" of an object.

So my question is that if said atomic bomb were to explode inside of a completely impenetrable container of some sort, would the measured weight of the container change, assuming no radiation was able to escape the container itself?

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Nice container. Can I get one? Anyway, the short answer is no. The weight measured would be the same. The energy content of the container remains the same, hence the coupling to gravity (the weight) remains the same as well. I'm not sure where the debates are coming from. The physics is unambiguous: it is the energy content of the box (+ the gravitational field of the Earth) that determines the weight. All energy gravitates. It matters not one jot whether you think the energy inside counts as the rest mass of some particle(s). –  Michael Brown Jul 2 '13 at 8:27
    
The box would indeed be impressive! No matter how small your bomb is, the box will need to shield neutrinos, which even for the best materials you can find makes it at least a few light-years thick. Those minor complications aside, the answer is pretty straightforward. –  Martin J.H. Jul 2 '13 at 9:37
    
The explosion will most probably shake the container; therefor if you put your container on a scale its number will show a pick during the explosion. For instance, put a box on a scale(a rather big one), then go inside the box and trap its door and jump. Although the energy content of the box will not change, a judge will indeed agree that the scale's number will vary. –  Ali Jul 2 '13 at 11:11
    
See also physics.stackexchange.com/a/69717/520. –  dmckee Jul 2 '13 at 13:32
    
The company you bought the container from cheated you. And so did the company you brought the atomic bomb from. –  Dimensio1n0 Jul 3 '13 at 5:57
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1 Answer

No, it wouldn't change due to the energy conservation law or mass conservation law – these are the same laws in relativity where $E=mc^2$. The nuclear energy extracted from the nuclei by fission would be converted to other forms of energy inside the box – ultimately the thermal energy.

High temperature means that particles are moving at higher speeds and they also have a higher mass, due to the relativistic dependence of mass on the speed. This increase of the mass due to the higher velocity/temperature of the particles would exactly compensate the total decrease of the rest mass.

Inside the box, the gravitational field would be different because in general relativity, it is not only the mass/energy density but also the pressure – all the components of the stress-energy tensor – that influence the local gravitational field. However, assuming that the box would be perfectly incompressible etc., the gravitational field outside the box would be fully dictated by the total mass of the box, and not the details about the pressure inside the cavity, so it wouldn't change. Because of the equivalence principle, the mass measured by a scale and/or the resistance towards acceleration would remain unchanged, too.

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Does this mean that the radiation inside the box, despite its "form" being either mass or energy, contributes to the gravitational field which then influences the scale? So all the radiation that is left in the box, and all the radiation that goes into processes like heating the interior walls of the box etc. will all contribute the same amount of "gravity", as before the explosion? –  Kalle Koskinen Jul 2 '13 at 8:46
    
Yes, as I hopefully wrote, radiation in the box does contribute the same to the gravity. Radiation has nonzero stress-energy tensor (momentum and energy density and flux) and the nonzero stress-energy tensor is what causes gravity in GR. –  Luboš Motl Jul 7 '13 at 5:50
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