Matter Rephasing (MR) technology is frequently used in science fiction stories (particularly those which use pseudoscience to explain why things happen) as an excuse why something can pass through normal, solid matter (like walls, doors and the occasional rock).
The basic idea behind matter rephasing technology is that it shifts the particles which make up one object so that they can pass through the gaps between the particles making up some other object. For example, in the following diagram, the '+' represents a particle (atom, molecule, whatever). The first diagram shows two objects constructed from normal matter - not under the influence of any MR technology:
Object One Object Two
+ + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + +
As you can see, the second object cannot pass 'through' the first, because the particles which make up the second object are in the same
lateral position as the particles which make up the first.
In the second diagram, however, the second object has been rephased using MR technology, while the first is still free from any MR
influence:
Object One Object Two
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
+ + + + + + + + +
Now that the second object has had its particles rephased, they are in a different lateral position to those in the first object. This means that they can now freely pass between the particles in the first object, creating the
illusion that the second object is passing straight through
solid matter.
The diagrams above are somewhat crude, and only in two dimensions, but the same principle applies to three-dimensional objects as well.
Obviously, such technology is extremely advanced, requiring not only a device capable of detecting the precise position and momentum of every particle within an object, but also some way of manipulating individual particles precisely, and a computer powerful enough to calculate the correct position for each of the trillions of particles composing an everyday macro-sized object. With regards to the computer, we're talking something of a HAL 9000-esque level or more, so it's clear that this technology is far outside what anyone is capable of today, and probably won't be possible for quite some time (ie: a fair few years - probably somewhere in the hundreds).
One thing that I feel I must point out in this node, however, is the frequent misuse of MR technology in science fiction. Normally when the author needs a person (let's call him "Dave") to be able to pass through another object, he/she describes how Dave rephases his particles, and then goes ahead and walks through that inconveniently placed wall over there. You may not immediately see a problem with this, however a very fundamental point seems to slip peoples' minds when dealing with MR technology - that most of the time it is used, it is used in an environment with gravity. If you think about it, if someone is out of phase with the matter of the wall, they're also going to be out of phase with the matter of the floor and are going to go through it like a hot knife through runny butter. Not good for poor old Dave. Looks like he's going to take an express trip to the nearest strong gravitational force - probably the core of a planet.
Thusfar, I have only come up with one way in which matter rephasing technology could be used effectively in a gravity environment (obviously, an environment with no gravity would mean that most1 objects are simply going to go ahead and pass through whatever they're moving towards) - rephase the matter making up the object you want to walk through, rather than rephasing yourself. Effectively the same as the original idea, but looked at from a different perspective.
To illustrate this, allow me to introduce Dave's co-worker, Frank. Frank has our new MR device, and decides to take a walk through the wall poor old Dave was heading towards. This time, when Frank turns on his MR device, he remains unaffected. Instead the wall over there is rephased, and Frank can pass through it as though it were as substantial as air. Luckily for Frank, since he does nothing to either his own particles, nor those that make up the floor which holds him up, he is saved from plummeting towards the nearest large gravitational source. Good for Frank. Now he can go get a coffee or something.
It's been brought to my attention by rootbeer277 that the above method would result in the wall falling through the floor. This might make Frank's landlord somewhat unhappy. After some careful consideration, I believe I have a solution: "graduated phasing". If you have a system capable of performing matter rephasing, it should presumably also be delicate enough to only partially offset each particle from its position. By having an area fully phased for Frank to pass through, and then surrounding that with an area that gradually fades from 'fully-phased' on the inside edge to zero phase difference on the outer edge, there should be no problems with walls falling through floors, higher stories falling down onto lower ones (other than by outside occurances such as shoddy construction or termites) and other architectural nightmares. A slightly more complex solution, but undoubtedly a necessary one.
1 - I say most objects, because some could be magnetic, and hence attracted towards the nearest large magnetic source. Or a few other options, such as equally phased bungee ropes or somesuch.