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If you take two atoms that each weigh X, and bind them together so that Y energy is absorbed by the breaking of the bond, the resulting molecule will have (2X-Y/c^2) mass.
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The moclecule has mass.
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If you take a proton and a neutron that weigh P and N, and you bind them together such that Z energy is absorbed by breaking their bond, the resulting atom will have (P+N-Z/c^2) mass.
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The atom has mass.
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You heat something up, the same amount of matter will now have an extremely small increase in the amount it bends space and how hard it is to change it's velocity. Otherwise known as it's mass.
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That something, has mass.
See the pattern here? The property, _Mass_, is a characteristic of the material you are talking about. The property, _Energy_, is also a characteristic of the material you are talking about. The property, _Mass_, is not a characteristic of the property, _Energy_. Again, Atom, Molecules, Photons, My beer gut, all have mass. They also all have energy.
Energy doesn't have mass. Energy is not a thing. Energy cannot have mass, because Energy itself is a characteristic of some material. It cannot, it does not, exist independantly of matter.
My beer belly can have Energy. The more Energy my beer belly gets, the more inertial Mass it obtains. It's not the Energy that "has mass", it's my beer belly. It's not the energy that has mass, it's the molecule. It's not the energy of a nulcear bond, it's the atom that has mass.
Only things can have mass. Energy isn't a thing, it's not a particle, it's not some object, it's a property of matter. It doesn't make any sense to say "Blue has Shiny", so it doesn't make any sense to say "Energy has Mass".
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As an aside, fckm, you forgot 'in a closed system' requirements in your 2nd law.
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Ah yes. Thanks for pointing that out. Oops.
The reason I'm being so pedantic here, is because of the thread in Philosophy, titled E=MC^2, discussing beings made of energy. I just want to make it clear that energy isn't a thing, it's a property.
Edit: more clarity?
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The statement E=MC^2 is an equivilance statement. X amount of energy is equal to Y amount of mass. It doesn't mean that energy has mass, or mass has energy (it's like saying Red has Shiny. It makes no sense). Mass and energy are both properties of matter. It simply means that these two properties are equivilant under certain contexts.
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I'm quoting myself for emphasis here.