UPDATED: August 2014
Acronym for Extradimensional Hypothesis. In ufology , the EDH postulates that UFOs are of extradimensional origin. However those who are skeptical of the EDH point out that there are less exotic explanations for the factors that gave rise to the EDH. Furthermore, logical analysis reveals that the EDH is implausible to begin with, and seems at times to be confused with the concept of alternate universes.
Factors in UFO reports that gave rise to the EDH include:

Alternative Explanations

Instant disappearances or appearances could be as simple as an illusion caused by a sudden maneuver that exceeds the observers visual capacity to follow the UFO as it approaches or departs. Such maneuvers are consistent with the level of performance found in UFO reports, so we shouldn't be the least bit surprised to find reports in which the witnesses say that the UFO they were watching seemed to vanish.

Another possibility is active camouflage, which is a type of camouflage that adapts its appearance to match the visual surroundings in a manner that conceals the object it belongs to. Although known Earth based systems have yet to be perfected, it's reasonable to suggest that the superiority of alien technology isn't limited to their propulsion systems alone. Ultra high-tech active camouflage could be capable of causing a craft to vanish, appear as another type of craft, or take on any one of a vast number of objects in the system's database.

When considering the movement of solid objects through walls as reported by alien abductees, it should be noted that alien abduction cases typically involve hypnotic memory recall and are not considered to be as reliable as other types of reports. However even if we are to assume that some of those stories are true, the interposition of matter doesn't require that we invoke any other dimensions. It is merely a hypothetical situation in which the atoms that make up two pieces of material within our present spacetime are able to slide past each other without interacting.

Such a situation sounds unlikely, but at the atomic level, the distances between particles are enormous compared to the size of the particles themselves, so we can easily imagine them passing between each other, and stories involving the interposition of matter aren't limited to UFOs either. When I was much younger, an older electrician friend of the family told me about a freak accident at a shipyard in Australia that happened back in the 1960s. Apparently several witnesses observed a ship welder's hand slip from his work and momentarily interpose with the charged steel plate he was working on. Workers on both sides of the plate saw it happen.

The interposition of matter described above is also reminiscent of the legendary Philadelphia Experiment. Similarly, I've heard numerous stories in which automobile collisions seem to have been avoided by the ghost-like interposition of the vehicles involved. Given these alternatives to the EDH, it's fairly easy to see that there's no shortage of less exotic explanations than alternate dimensions for the phenomena reported, however Ockham's razor isn't the only principle that can be applied to the EDH. Pure deductive reasoning also reveals that the sci-fi like transport of objects in and out of so-called higher dimensions is a logical impossibility.
Logically Impossibility

Strictly speaking, the EDH is logically impossible, however the word "dimensions" has been tossed around so haphazardly by everyone from New Age gurus to pop-science personalities, that EDH advocates appear to have become confused about what it really means. Or perhaps they aren't confused and are exploiting the confusion to promote their pet theory. Either way, it is probably wise to demystify the concept of dimensions before we proceed.

In the real world, dimensionality isn't something mystical, or even all that hard to grasp. It consists of the spatial dimensions of length, width, and height. Most of us are familiar with these dimensions and learned the basics about them in grade school. They are used to calculate distance, area, and volume. All physical objects, including UFOs must possess these three dimensions in order to physically exist.

Time is considered by scientists to be a fourth dimension and is used in calculations involving movement, however it's role as a spatial dimension is purely abstract, as are any additional dimensions such as those found in complex mathematical models ( e.g. Hilbert Space or M-Theory ). However proponents of the EDH set aside the purely abstract nature of such dimensions and suggest that UFOs originate in some unspecified higher dimension, and that they can travel from there into our dimension at will.

The main error in assuming that UFOs can pop in and out of our dimension is that the initial premise is faulty. It's setup in such a way that it assumes that physical objects can travel from one dimension ( singular ) into another, as if they exist independent from the dimensional environment in which they're found. However physical objects cannot exist within single dimensions alone. They must exist in at least three spatial dimensions simultaneously.

To elaborate, no physical object exists in the third dimension ( height ) alone. Without length and width in place, the dimension of height collapses into a single linear dimension. This logic is inescapable and reveals a fundamental truth about the nature of dimensions. No higher spatial dimension can exist without the full set of dimensions that precede it in place. Therefore no physical object can exist exclusively in a fifth dimension any more than a three dimensional object ( e.g. a cube ) can exist exclusively within the third dimension ( height ).

By extension, any five dimensional object would by necessity consist of all our familiar spatial dimensions as part of its intrinsic makeup. For example, a five dimensional skyscraper would still have its foundation firmly rooted in the ground, and it would still extend upward into the sky where its first three dimensions could clearly be seen. At no time would it be possible for any extra dimensions to cause these first three dimensions to simply become irrelevant, allowing the skyscraper to vanish or dematerialize.

With only a little more reflection it's not hard to see that riding an elevator up into the fifth dimension within our hypothetical five dimensional skyscraper isn't any more possible than it is for us to ride one down into the second dimension, and this gives rise to another fundamental truth. The nature of dimensionality is such that within a universe constructed of x number of dimensions, all dimensions exist simultaneously everywhere. Nowhere in our universe will we find any purely two dimensional moons orbiting some two dimensional planet.

Given the above, popping in and out of one dimension or another as though they are mutually exclusive is simply not an option. The mathematical models that describe a higher number of dimensions are purely abstract representations. They may seem convincing on paper, but so is Escher's impossible staircase. It's entertaining to imagine ( see video below ), and all the coordinates can be mathematically mapped, but it cannot possibly exist as a physical object in the real world.

Although the EDH is fundamentally flawed, it does not mean that other exotic explanations may not work. For example, the Alternate Universe Hypothesis better explains some of the phenomena that proponents of the EDH use to support their position. Also, it's only fair to mention that the concepts of universes and dimensions are sometimes used interchangeably as though they are synonymous. Although such usage is incorrect, the proponents of the EDH who mean separate universes are starting with a plausible foundation.

Trapped In Escher's Impossible Staircase