Shadows

[Jordan14]

This must have been discussed before but i want to see the opinions on the dimensions of a shadow.

I would understand a shadow to be an absence of photons however a shadow does exist in 3 dimension and it couldn't exist in too dimensions so i would have actually thought that a shadow is dimensionless.

What do you think?

[Paul]

I would understand a shadow to be an absence of photons however a shadow does exist in 3 dimension and it couldn't exist in too dimensions

Perhaps this requires some understanding of some specialized definitions...? Could you explain more precisely what you mean by this?

[pat]

Sure, shadows can exist in two dimensions, if you've got 2-d photons/light-sources and 2-d objects.

[Jordan14]

I presumed that a shadow couldn't exist in the 2nd dimension because the shadow has nothing to lie on (if you understand) I probally have the wrong idea here. I would presume that in the 2nd dimension they have a equivalant of a shadow that lies on the 1st dimension but not a shadow that exists in 3 dimensions.

[PWrong]

I'd say an object in 2D would cast a 1D shadow. But that would depend on the kind of 2D universe you want. In Flatland, I don't think they had ordinary light, at least not from a sun.

In general, an object in N dimensions will cast a shadow of N-1 dimensions.

[Jordan14]

Would a 0th dimension shape then have it's shadow on top of itself or can a 0th dimensional shape not have a shadow. Because thinking about it the light source, the object, and the shadow would all be in the same place.

[houserichichi]

In zero dimensional space a zero dimensional object would have no shaddow because it is the entire space. If, however, that zero dimensional shape were, say, in a three dimensional world, it would have a zero dimensional shaddow. (Say a point was sitting above the floor. If we shone the light in any direction, there would be a zero-dimensional "space" of light missing, which would be the shaddow).

[pat]

I would think that a point in three-space would cast a one-dimensional shadow, no?

[houserichichi]

Would it? Perhaps we're thinking in different terms? Oops. I had in mind the "common real life" scenario, whereby a point in three-space is suspended above a two-dimensional surface (ie the floor or a wall) and its shaddow projected in that direction. I suppose, however, that it would trace a one dimensional shaddow THROUGH 3-space, but would it not project zero-dimensionally onto 2-space?

[pat]

Sure.... it was your statement that there would be a "zero-dimensional 'space' of light missing" that made me think you were talking about the full shadow... not just where it struck a surface.

[houserichichi]

Oops!!!!!!! Point well taken. Curse my pathetic grasp of English :wink:

However, as a thought experiment, the shadow space of a point in two dimensions would then be...zero dimensional?

[pat]

I don't think so... assuming the light was in the same plane.... it will still have a shadow sweeping out a ray.

[houserichichi]

I keep thinking in terms of a lightsource in the third dimension. You're right - I'm done talking now!! :wink:

[Polycell]

This must have been discussed before but i want to see the opinions on the dimensions of a shadow.

I would understand a shadow to be an absence of photons however a shadow does exist in 3 dimension and it couldn't exist in too dimensions so i would have actually thought that a shadow is dimensionless.

What do you think?

Well, a shadow has length and width, certainly, so it has <i>at least</i> two dimensions. It's not "dimensionless." On the other hand, how would you measure the height of a shadow (how far it extends above the surface it is cast on)? Until you can do this, it's fair to say that a shadow has just two dimensions. In three-space, that is.

[Rkyeun]

Shadows are 3D shapes, usually extruded conically away from the light source in cross section of the object casting the shadow. To see a shadow you need but move into it, or move to an angle where you can see it intersect another object. When the moon has its new phase, you are looking at the earth's shadow, just as when the earth has night you are looking at the earth's shadow.

[Jordan14]

But isn't the light the actual shape the 3D form, I know this runs into alot of problems. And isn't a shadow a lack of shape so thinking about it a shadow is maybe an anti-shape . It's like went you have a sphere but inside the sphere is hollow it's the material that is the shape, not the existanct of nothing

[Rkyeun]

Shadows are a lack of substance, not a lack of shape. A shape is a set of points. A spherical object projects a (roughly) conical shadow. Cones and spheres are both shapes, it doesn't matter that one defines an area that is filled with matter and the other defines an area which is darker than its surroundings.