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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.
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Is a Photon Matter? Or, are you asserting a Photon cannot exist without Matter? That's getting pretty obtuse. Gravaton?
Because, Photon's aren't very "Matter"-like, and they contain Energy (and hence have Mass).
(ok ok, Non-Baryonic matter. Meh, not very Matter-esque!)
How about Negative Energy Fields? I think it is believed they have negative mass. (you can apparenly build them by placing two metal plates very close together in a vacuum -- between the plates, you end up with something that is more empty than a vacuum.)
Are Negative Energy Fields matter? (I suppose you can renormalize the universe, so hard vacuum isn't at zero, and thus make 'Negative Energy Fields' just 'a place with less stuff than a hard vacuum')
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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.
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Being further pedantic, I think I can build a non-bounded universe model in which heat-death never occurs. So, your conclusion you rolled into the 3rd law isn't derivable from the 0th, 1st 2nd and 3rd laws of thermodynamics. In order to do this, I think I need negative enthropy systems (which isn't ruled out by the 0th, 1st, 2nd or 3rd law).
Build a universe model where the total enthropy is unboundedly negative, but for all compact subsets of the universe it is bounded. You end up with a universe that looks like ours does locally, but possibly never reaches heat death (there is always some point that is hotter than others by as any margin you want).
I don't know what "negative enthropy" systems would look like.
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(well, I suppose you could use E=MC^2 to calculate the mass equivilance of all energy and say that mass is constant, instead of energy, but that would be silly and none in physics would do that.)
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Measuring energy as mass has some nice properties. It does away with two extra units: distance and time are no longer "dimensions" to your energy unit.
The photon has 2*10^-16 kg of Energy.
We provided 2*10^-20 kg of heat to the water.
The bomb blast was 2.5 * 10^-1 kg of Energy! (5 megatonnes, if I did my math right)
It is sort of like measuring distance as time, or time as distance. Once you have a nice conversion factor (c), keeping track of both units seems silly.
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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 think this is a philosophical position, or a convention, not a scientific statement.
If you interprited Energy as the thing (maybe the only thing!) that has Mass, and note that all Matter has Rest Energy, you should be able to do the exact same physics. Just with slightly different translations into English.
Hell, you could say that Energy is the only thing, and that it "must" have Matter (instead of Matter "must" have Energy).
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What I failed to convey was that the laws of conservation of mass/energy only work in classical physics. fckm has done a much better job.
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Slavakion, from what I can tell, Fckm was mostly disagreeing with terminology.
I don't believe Fckm disagrees with the statement "the gravitational and inertial mass of a closed system is constant". Which means melting an icecube results in water that weighs more than the ice cube did, by an increadibly small amount.