How much does a shadow weigh?

Work with me here.  It's way too late at night, I can't sleep and this is the kind of thing I think about at this hour.

Here's the problem: "Does a shadow have mass, and how much does it weigh if it does?"

Remember how in Peter Pan, when Pete loses his shadow and has to sew it back on when he finally catches it?  That's how this started (though why I was thinking of Peter Pan so randomly is beyond me).  So if Pan loses his shadow, and it gets away from him and he has to catch it and attach it back to himself, then...

Logically, the shadow must have mass.  Because Pan couldn't take hold of it if it didn't have mass.  Except it's impossible for a shadow to have mass, right?  Right?!

Okay, let's look at this from the angle of physics.  What is a shadow, exactly?  It's the absence or diminishing of light upon a surface because an object is between the surface and a source of light.  There is no "there" there for a shadow.  It just is.  It's the effect of an object with mass absorbing light energy.

But for more than a century now, we've known that per Einstein's equation E = mc² that energy and mass have an equivalence.  Matter is energy and energy is matter.  And among other things the addition of energy to a system increases the mass of that system.  So in our situation the light hitting Peter Pan is increasing his mass (although almost insignificantly so).

The system being discussed here is Peter Pan, his shadow, and the light cast upon the local environment.  The surface of Peter has increased mass and so does the wall (or whatever) that the light is hitting.  The shadow however is not absorbing energy.

With the local environment as a baseline, and the ultimate source of the mass being the sun or lamplight or some other source of light, the shadow has less mass than it would without being impeded by Peter's mass.  And not only that but the shadow both exists and has a mass of less than 0.  All without absorbing energy on its own.  It has existence and mass because of the mass/energy equivalence of its surroundings.

Therefore, a shadow does possess mass.  And despite the absence of light it does have corresponding weight.

So then, we can conclude that a shadow has weight.  And said weight is dependent upon the surface it is cast upon, the area of the shadow, the size of the object casting the shadow, and the size and strength of the source of light.

Which means that in theory, Peter Pan could have lost his shadow and had to sew or staple it back on.

Well, that settles that question then.  Me go back to sleep now.

Categories: albert einstein, particle physics, personal reflection, physics, quantum physics, science