# Does shadow have mass? [closed]

I know it sounds like a foolish question but I have a reason for asking and I'm hoping someone here, can give a convincing response.

Here is why I pose the question...it seems to me that all this discussion of photons, and other sub-atomic particles possessing mass or negative mass is really a discussion about the mass of shadows.

Although we can't really weigh shadow we can see it, we can measure its area, observe its outline. a photon- which is massless - may seem heavier than shadow. It is really driving me crazy when I think about it.

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## closed as unclear what you're asking by user1504, Waffle's Crazy Peanut, twistor59, Alan Rominger, Manishearth♦Jun 29 '13 at 10:28

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You first have to define what is the shadow. For example, if the shadow is a surface, then we don't actually define a mass for surface in physics. – fffred Jun 14 '13 at 19:24
Maybe, a shadow in the wall makes it weigh less actually. Wondering the usage of the QM tag, I think the negligible value (though it's GR) can be taken into account :) – Waffle's Crazy Peanut Jun 14 '13 at 19:37
Bad ghosts have negative norm. – Trimok Jun 14 '13 at 20:02
I guess this is what you are looking for m.youtube.com/… – Mark Jun 15 '13 at 7:50

The shadow of a body is the region where the light of the source doesn't arrive so since their isn't any photon (assuming that the body is 100% opaque) in the shadow, we shouldn't be able to see it. The only reason we see the shadow is by the contrast effect with the surrounding which reflects or scatters light. This is analogue to the way we see black holes in astrophotographs.

Another problem is what do you exactly mean by shadow? The definition I gave above is mathematical and we can't talk about mass until you define "shadow" physically. Note also that if a body is opaque for visible light, it isn't opaque for the rest of the electromagnetic spectrum and so there's a lot of invisible photons hitting the shadow area and if you meant by the mass of the shadow the mass of the photons present in this region, yes the shadow have a mass but I don't think you want this definition.

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I'll give only a funny answer:

I will prove by contradiction that mass of the shadow cannot be proportional to its area.

Take light source, ball and paper in empty space, this system as whole is closed and hence its total mass is constant. The ball makes a circular shadow on the paper. Now move the paper further from ball so make the shadow bigger. Now the shadow has higher area thus it has higher mass :O. Total mass of the system got higher but that is contradiction.

Edit: Ok I add the conclusion :D. Shadow of zero area should have zero mass right? But shadow's mass cannot depend on its area(as proved above) therefore shadow of any area should have zero mass.

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This only proves that the mass of the shadow is not proportional to its area. Where is the answer? – Mhmd Jun 15 '13 at 7:43
It does show that to first order a shadow does not affect mass by its size, as it should by any definition of mass. – anna v Jun 15 '13 at 8:34
One would expect that shadow's mass would be proportional to its area like paper's mass is proportional to its area. So I show that this cannot be happening. Paper don't get bigger and smaller when you move it around but shadow does! – Tom Jun 15 '13 at 8:58