Shadows
I had a lot of driving to do this last week. 1 For work I drove about 11 hours total on two separate days combined. Then, on Friday, I drove another 4 hours or so to visit some friends. Thankfully, driving back Saturday was only 3 hours.
Driving back at around dusk on Saturday meant lots of glare, lots of long shadows. And then it struck me… There must come a point when the Earth rotates relative to the Sun such that an object on the surface of the earth could cast an infinitely long shadow. And, really, this should happen twice a day.
Now I think I have a new mission. I need to find someplace on our planet to stand such that either at sunset or sunrise I would cast an infinitely long shadow.
In order to cast an infinitely long shadow on a surface, you would need to be standing on an infinitely long, perfectly flat plane with the light source closer to the plane than the top of your head. You would also need to be in a vacuum to avoid atmospheric scattering, gravity-free (making it hard to stand) to avoid curvature of the light rays, and the light would have to be of infinite intensity (which would instantly fry you) for the shadow to be distinguishable an infinite distance away. Kind of a spherical-chickens-in-a-vacuum situation.
You could theoretically, however, make your body momentarily obscure the sun’s light from an infinite volume of space by standing in the path of photons that would not only miss the Earth and continue back into space, but not hit any other celestial body on their path through space. Interestingly, this region of space would not be linear, and it probably wouldn’t even remain a coherent area long enough to leave the atmosphere due to the atmospheric scattering those photons would have undergone had you not stopped them.
@Whosa: Those are… very good points. It makes me, in turn, wonder does a shadow require a surface upon which it is cast to really be a shadow? Can a shadow’s length be measured without such a surface? If larger object A is in front of smaller object B, and object A’s shadow completely envelopes object B’s shadow, is the shadow behind object B considered to be part of object A’s shadow? Does object B have a shadow at all?
I hadn’t really thought of it that way. Though I wouldn’t want to try to justify it, my instinct would be that a shadow belongs to whatever defines its shape. That is, if a small object casts a small shadow on a larger object that in turn casts a larger shadow on a still larger object, the shadow on the third object is the second object’s shadow. If the first (smallest) object is instead entirely in the shadow of the second object both shadows belong to the second object. If, however, one of the first two objects casts part of its shadow on the other and part of it (directly) onto the third (largest) object, the single shadow visible on the third object is that of both of the other objects, and it is not proper (or useful) to try to divide the shadow into separate shadows of the two objects unless they move apart so that neither casts any shadow on the other.
This complicates the original question to the extent that I no longer want to try to answer it, and that’s without considering other light sources, reflected light, or the various types of scattering. I suppose, though that it means that it would be acceptable to say that, if you are standing where part of your shadow never touches the ground and continues into space, the shadow that would be cast would be the shadow of the Earth and you.
@Whosa: :/ Sorry… It’s just that there were some interesting metaphysical implications once we start talking about what it means for an object to have a shadow or two objects to have a mingled shadow. :)