Is it (theoretically) physically possible to project an image into thin air? Is there some law of physics that strictly prohibits the projection of 2D or 3D images into thin air (such as holograms in movies) or is a solution to achieve this still up for grabs by an eventual discoverer?
 A: Depends what you mean by project (and image!)
You can create a real image anywhere in space it's just that you can only see it if there is a screen or something to reflect it into your eyes - the image is obviously still there if you remove the screen.
You can also create a virtual image where the path of rays into your eye is the same as if the light was coming from an image at a particular position - even though there is nothing at that position. This is essentially what you are doing when you use a magnifying glass
So if you wanted to create the illusion of an image floating in space - you could do this by projecting the correct image directly into your eyes. If you want to do this and be able to move your head around then it gets trickier!
A: This imaging seems about state of the art right now
http://www.gizmag.com/burton-true-3d-laser-plasma-display/20499/
Basically, a laser is focused at a certain point in air, and ionizes the air at that point, causing it to glow (and crackle.. not too safe)
Other approaches, use a similar principle, but with water or steam to require less power - not needing to ionize the air at the focal point.
An interesting paper that I have come across (can't find the reference just now) is not to use thin air but to use a clear aerogel, with quantum dots embedded in it.
A: Yes. http://www.youtube.com/watch?v=lFqlQiTTHRs
A: In principle you could do it using two carefully tuned laser beams that scan a volume of air with invisible to the human eye light but feeding a two photon transition to a state that falls back to the ground state with a visible light transition.
There would, however, be the practical problem of having two fairly intense laser beams being shot out into the general environment...probably not eye safe without googles (and maybe protective clothing) to adsorb the (invisible) laser beams.
A: The most common way used to "project images on thin air" is by optically creating a virtual image. That's what 3D TVs and holograms do. (Note that 3D TV create a only a "static" virtual image : the point of view of the scene does not change if you move around ; unlike holograms). But one can tell none of those technologies can be used to reproduce what you see in (for example) StarWars : there is a need for a screen or a glass behind (every single pixel of) the 3D image for it to appear : the light rays have to come from somewhere, and we cannot yet curve them.. so.. in StarWars they are using a totally different technology : it litterally projects the image on thin air either by changing the state of the matter at the point of the projection or.. by curving light rays.. or.. by using some software like 3D Studio Max or Adobe's AfterEffect :P
