Is the concept of people having a doppelganger, an apparition of themselves, a real phenomenon, and if so, what is the mechanism for this?

There are many layers of confusion here because there are many phenomena people have witnessed. The idea is often ill-defined and does not sink in and then becomes confused and confounded with other observations made and that, too, enters consciousness and the interplay of information flowing about and can create further confusion and alteration of thought in consequence. So the prosaic physical level is that many people have physical lookalikes to one degree or another. This is simply DNA doing what it does, rendering form as well as function, and that has relatively little meaning except in the case of identical twins sharing the same parentage and part of a family unit or separated at birth and then reuniting later, and so forth. But there is a kinship through that shared heritage that is on display visibly. In the case of people who are lookalikes, there is little to link them together other than some overlapping of DNA components creating the morphologic features that you see on the outer surface of the body and the architecture within reflected in the overall shape and density and mass and size configuration. Those things are very unimportant compared to karmic involvement with one another, that is by far the greatest link between people, it is shared karmic history rather than physical resemblance. The true origin of the doppelganger phenomenon was a realization there is a spirit form of humans that can be sensed by others. In some cases, this is the perception of the non-local consciousness of a person extending out from their physical persona but meeting up with a person at a distance and then being recognized as that individual energetically. This may be read, in a sense, as a visual image of the person intuitively and perceived as an actual presence like an apparition. Apparitions are largely seen intuitively, although some can condense energetically into a physical manifestation of light and shadow and be perceptible to the eye. That is also a phenomenon of consciousness on display. In most cases, it is the viewer more so than the source projecting their sensory apparatus and witnessing the energy that is present. This can also be experienced by witnessing the presence of a person during astral travel when they have exited the body, and again it may be perceived intuitively as their physical appearance rather than a mass of energy as in an orb of light. This depends on the observer and their way of perceiving things intuitively. Some will only have a kinesthetic awareness, others a kind of inner knowing there is something present, and a few will have a visual perception of the actual energy and may well see this displayed as a quite real image of their makeup and appearance. So this is largely a spirit phenomenon in the sense of consciousness representing a spirit essence of the person.