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Dramatic title, I know. But it's shorter than Measuring a person's effective mass through radiation and comparing it to their weighed mass and I figured this would get people's attention.

I just thought of this a while back. If we were to collect the EM radiation a person emits, we could find a measure for their rest energy and therefore we should be able to use $E = Mc^2$ to calculate a corresponding mass $M$. Now I reasoned that this would not yield the same result as an actual measurement of their 'weighed mass' $m$ with a weighing scale due to the fact that humans are living creatures and there's loads of biochemical processes going on inside of us to try and keep our temperature at a certain stable level, among other things.

Then I started thinking about the meaning of the mass we could calculate from the radiation and more specifically about the exact meaning of the difference $M-m$. If all of my above reasoning is correct, I should think this gives us some measure for the amount of energy (maybe power might be a more appropriate quantity) we need to keep us alive. Obviously, in this context it might make more sense to talk about energies (so to transform $m$ to an energy $e$ instead of transforming $E$ to a mass $M$) but hey, they're equivalent and I'm quirky.

Anyway, to get to my question: is there any truth in my reasoning or have I made a mistake? If there is truth to it, I'm guessing other people have explored this already and I'd be interested in any results.

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up vote 2 down vote accepted

No, that is not correct. A person will emit thermal radiation that corresponds to his/her surface temperature, and is fuelled by the energy reserves being burned to actively maintain that temperature. As such, measuring the radiated power would, in equilibrium, give you a good idea of how much food someone is burning up. (Beware, though! A sizable fraction of the energy one consumes and stores as ATP goes into building stuff - making proteins and such molecules with a higher internal energy than their constituents - and this will be an additional energy outlet in that budget.)

However, this has nothing to do with the person's total mass. (Consider, for example, someone swallowing a very dense block of lined lead, that does not participate in biological processes. This adds to the total mass but cannot influence the radiated IR.) Schade!

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That makes sense, I suspected I was oversimplifying matters. And of course I should have realized the radiation would correspond to the surface temperature. I guess I got carried away in my enthusiasm too easily. Oh well, thanks for your answer. :) –  Wouter Feb 13 '13 at 22:23
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