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?