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Let's assume that we have a mechanism for producing EM radiation suspended in the air, and that that mechanism itself is invisible to the naked eye (e.g. a microscopic light bulb on a microscopic wire or a suspended molecular reaction giving off energy.) When off, the light source would not be visible. When turned on however, any light cast from the source to the environment around it would also reach the viewer's eye, and identify the source of light.

Is it theoretically possible to cause the lit light source to cast shadows on the environment that are visible, but for the source itself to remain invisible? As an example, most 3D graphics programs can create invisible light sources which are only identifiable by the scene they illuminate.

I imagine this may be possible with certain environments, such as an environment covered in phosphorescent paint and a black light source, where the light source is not seen but the environment which it illuminates is identifiable.

But what about in the general case, when we limit the variables to the source of the light itself, stipulating it must work in a general environment?

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Think about this. A shadow is noticed when the difference in reflected intensity between the places where the source light doses and does not shine is detectible to the eye, and the in ordinary materials albedo is confined to be between 0 and 1. Now ask, is the difference in intensity between look at the source and not looking at the source detectible? Why or why not? – dmckee Mar 9 '13 at 16:52
    
@Dan Rasmussen Am I Missing something really crucial here? What about a bottle of a gass emitting X-rays and falling on a metallic object, like a key, casting a shadow on a film or paper? Wouldn't that suffice? – JKL Mar 10 '13 at 2:24

There are multiple ways in which you can in principle disguise the source of light, but photons still must be emitted in order to illuminate something. So a shadow can only really be generated if there is a source of light, although the specific location of the source can be easily masked.

The simplest example is the case of knife-edge diffraction, which is used to send signals over obstructions, particularly in radio wave propagation. Essentially, the transmitter is behind a relatively sharp edge object (like a mountain in the case of radio waves), and the light will actually "bend" around the object to a receiver on the other side.

More advanced cases look at "bending light" from a laser around an object. Experimentalists now claim to be able to "bend light" an arbitrary number of degrees.

Much of the research into metamaterials is focused on different applications involving refracting light using materials with negative refractive indexes. These materials play key roles in the concepts of modern "cloaking devices" where the idea there is to mask an object in a cocoon of meta material well into the visible spectrum.

If you get into the metamaterial realm, the idea might be that one could not only bend the light around the object, but amplify the light in some way so that in some arbitrary direction light passing through the metamaterial exits with greater intensity than the background ambient light such that an object in the path of the amplified light would cast a shadow. I would imagine that the impression of the observer would be that some region they are looking at somehow appear brighter, although the exact location of the light source might not be identified exactly.

So in general it is possible to mask the specific location of a source, but you simply shouldn't be able to generate a shadow without there being some change in intensity between the front and back of the object casting the shadow.

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Think of shadow as absence of light. So if you can a source of light and an object that is obstructing the path of the light,then a shadow is created. The length and shape of the shadow depends on the angle from which light was sourced.

The source of light could be an infrared light.IR light is invisible to human eye. Yes, it casts a shadow which is only visible using a device which detects infrared light, like your phones camera.

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It happens every time a hill or build blocks a radio broadcast – jean Jan 7 at 19:05

Your eyes cannot see invisible light, but, invisible light (e.g. infrared light) does cast a shadow (i.e. an area with less light intensity than its surrounding area, due to being blocked by some obstruction)--however, only some animals would be able to see it.

Now then, how could we use an invisible light source (let's stick with IR) and create a shadow that is visible to the human eye. Here are a couple of possibilities:

  1. We use/discover a material that will absorb IR wavelengths & produce what appears to be an absorption of normal light. The surface of the obstruction & the area around the shadow would have to produce a brighter reaction to the invisible light source than the shadow area. You might also have to coat the back of the obstruction with a reflective coating of some kind to increase the reflected light level that would fall in the shadow region to make it look more realistic--otherwise, the shadow might appear too dark for the setup. This possibility is of course not a real shadow--it's more of a pseudo shadow, if you will.

  2. Shine invisible light onto a specially coated object which produces a bright enough reaction that it serves as a light source for the environment, obstruction, & real visible shadow. This of course would create a visible light source from invisible radiant energy--which may not meet your criteria, however it would be sourced initially from an invisible light source.

  3. Bombard the obstruction & surrounding area with invisible high-energy photons. If the obstruction & surround area are designed to react ideally when absorbing the energy, then they could possibly appear like normal regions in our visible spectrum & the region behind the obstruction would be significantly less bright. This is similar to 1, but using higher energy invisible wavelengths.

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