The One Ring and invisibility

[Galendor]

Why the shadow, then? And why can someone wearing the Ring still see the real world, although dimly? It's simple: the Ring transports its wearer into the wraith world, but not all the way.

Good thinking, good find on the quote from Gandalf, and it makes sense. I guess to be all the way in the wraith dimension, one would have to be, um, dead. So the Ring shifts the wearer part way into that dimension. I suppose we can only speculate why this effect would be useful to Sauron.

When light interacts with matter, it is either reflected, refracted, or absorbed. Refracted light changes direction, and we can't really see that effect. Absorbed light we can see - objects absorbing light will appear darker, or a different color if they only absorb certain wavelengths (colors) of the visible spectrum. I suspect that the wearer of the Ring casts a faint shadow because he/she still absorbs some tiny amount of light. Under bright light, this would cast a faint shadow, and possibly also be seen by an observer as a slighly darkened form if the Ring wearer were standing between an observer and a light source. If the person wearing the Ring were not betwen the observer and the light source, they might appear as a faint "darkness" in front of whatever they were standing in front of.

As far as reflected light is concerned, I wonder if the wearer of the Ring were wearing something very reflective (such as a mithril coat), if light might be reflected from that and be visible to an observer, in a similar fashion as the visible light emitted from a magical glowing sword or vial.

On another note, it seems like the fact that Bilbo wore the Ring continuously for weeks or months while in the Hall of the Mirkwood Elves doesn't quite fit with later interpretations of the Ring's "wraithifying" effect on mortals.