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Let's say I have a photon collector in orbit around the sun. It manages to collect photons perfectly efficiently, that is, without radiating off any energy.

Then, using Einstein's equation:

$$E = m c^2$$

since the collector is absorbing energy, its mass should increase.

Is this correct?

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You may find some insight by reading physics.stackexchange.com/questions/11449/… or physics.stackexchange.com/questions/16351/… . –  dmckee May 15 '12 at 19:54
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2 Answers 2

up vote 4 down vote accepted

Yes.

I feel like there should be more of an explanation, but it's pretty straightforward. A blackbody absorbing energy will increase in mass. The absolute amount of increase is pretty miniscule, but it is not zero.

Since you ask about an object that does not also radiate energy, a blackhole might be a decent analogy. So, does a blackhole increase in mass when photons fall into it? Sure. If it helps, you can imagine that a photon of sufficiently high energy can produce pairs of electrons (or other particles) that could subsequently fall into the blackhole... well, except the antiparticle that would be annihilated shortly after creation. Either way, it seems easier to imagine the scenario with particles that have a rest mass because it more closely corresponds to our quotidian experience.

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Is this an increase in rest mass? I'm actually not sure which mass the equation I gave is referring to. –  Matt Fenwick May 16 '12 at 12:52
    
Or is this an increase in gravitational mass? –  Matt Fenwick May 16 '12 at 13:46
    
I think you are confusing a couple of different mass concepts. There is a difference between rest mass and mass as measured in a non-inertial frame but all kinds of mass are gravitational. There is theortically the potential that gravitational mass and inertial mass are different, but this has been tested to very high degrees and found not to be the case. –  AdamRedwine May 17 '12 at 12:05
    
As to whether this mass is "rest mass," that kind of depends on what happens to the photon. You claim that the photon was "absorbed." Okay, how? Say you have a scintillating gamma detector; in that case, the photon looses its energy via the photoelectric effect. There might be some change in rest mass, depending on the binding energies of the affected atom before and after interaction, but most of the energy will eventually become heat. This still represents an increase in mass, and it is still gravitational though. –  AdamRedwine May 17 '12 at 12:13
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While it is true that the mass will increase your requirement of perfect absorption without radiation cannot be satisfied so easily. Total absorption would require a black surface at 0 K. Every surface would, according to the Planck's law and the Stefan Boltzmann law radiate thermal energy with $\propto T^4$. This limits the temperature rise to the surface temperature of the sun.

With the thermal energy of $k_B/2\cdot T$ per degree of freedom you can try to estimate the increase in mass between the minimum starting temperature and 6000 K for a given set of properties of the collector.

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Is this an increase in rest mass? –  Matt Fenwick May 16 '12 at 12:54
    
Thanks for the extra information, but I'm not asking about the impossibilities of total absorption. Just trying to focus on the spirit of the OP, which is whether light emission/absorption can change mass. –  Matt Fenwick May 16 '12 at 12:56
    
@MattFenwick: It is hard to answer, whether this is just an increase in rest mass. Absorbing photons includes momentum transfer, so the net momentum of the collector also changes. –  Alexander May 21 '12 at 10:57
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