Among the many, seemingly impossible, characteristics reported in UFO/abduction cases, there are two elements that stand out as the most unfeasible in the view of conventional wisdom. The first is "invisible" or "transparent" UFOs. In "Sight Unseen" by Budd Hopkins and Carol Rainey (Atria Books, NY. 2003), several documented cases are cited where only the person or persons being abducted are able to see the craft in the sky above them, while others around them are totally oblivious to its presence.
In the May 2004 incident in Mexico's southern Campeche state, Mexican Air Force pilots filmed 11 unidentified flying objects employing a FLIR or infrared camera. Although the infrared camera, as well as ground and air radar, confirmed the objects presence, they were totally invisible to the unaided eye.
There are many bizarre incidents where the outline of the craft is observed but the witness is able to see the background through the center of the object as it passes overhead. It is often described as appearing "mirage-like."
One theory is that the craft is capable of bending light around itself. In this way, the observer is not actually seeing through the craft but around it. Another is that the energies emitted from craft are in the infrared spectrum that is just outside the range of human perception but are visible to devices such as the FLIR camera.
At the 2005 conference of the UFO Congress in Laughlin, Nevada, Jaime Maussan gave an excellent presentation where these invisibility technologies were addressed. He showed the actual footage of the 2004 Mexican incident as well as video evidence taken by an average citizen of an unidentified object; first with a normal camcorder and then with an infrared lens. The object was visible only with the aid of infrared and unmistakably well within Earth's atmosphere, as thick clouds could be seen behind the object.
Maussan then went on to show evidence of the beginnings of invisibility technologies as demonstrated by Japanese scientists. Admittedly, it is an optical illusion and does not actually render an individual invisible. However, the technology is in its infancy and is just as effective - so much so that the American military has taken a great interest in its development.
An explanation of this technology may be found at http://www.wired.com/wired/archive/11.08/pwr_invisible_pr.html. It reads, in part: "A camera behind the wearer feeds background images through a computer to a projector, which paints them on a jacket as though it were a movie screen. The wearer appears mysteriously translucent - as long as observers are facing the projection head-on and the background isn't too bright."
The second element that confounds mainstream science, and is therefore dismissed as fantasy, are the reports by alleged alien abductees of being in a brightly illuminated room, the source of which cannot be determined. The lighting seems to be coming from nowhere but is so evenly emitted that it rarely produces a shadow of the objects and entities within the enclosure.
A recent NBC News article brought my attention to an amazing new discovery in quantum physics that they feel will, one day, replace the light bulb. It is called "quantum bits". The technical explanation is far beyond the scope of this article, however the basic description is that a substance comprising quantum-sized bits of silicon, only two or three hundred atoms in size, is applied to any surface.
An electromagnetic grid is placed behind the surface and, when engaged, the entire surface produces its own illumination. In theory, if the visitors are employing this technology, the grid could be connected to the ships main power source and controlled in each area of the craft by independent control panels. The quantum silicon bits in the wall's coating would illuminate accordingly. The luminescence could be tuned to any wavelength within the visible spectrum. The result would be an even, virtually shadow-less illumination of the area. If one were unfamiliar with the process, they would certainly be baffled as to the source of the lighting.
It is tempting to jump to the conclusion that the aforementioned technologies have been back engineered from crashed disks. It may be more likely that Earth science is catching up with that of more advanced civilizations simply by the natural evolutionary process. Whichever be the case, science is beginning to come to the realization that many elements of the UFO/abduction experience are not outside of the laws of physics - only outside of our previous understanding of those laws.