Electro-gravitation - is it real? I came across an article claiming that if you charge two plates, one positive and one negative, and fasten them together (assuming they are insulated from each other), they will float in the air. I kind of got the idea that it depends directly on the voltage and it seems to require at least a hundred thousand volts. Is this actually possible, and if not, why not. I realize that this is asking for technical answers, and I definitely encourage that. If you give a big technical explanation, however, please summarize it in layman's terms as well.
T.T. Brown published a paper describing an experiment relating to it: How I control gravity. There are a few other papers published later (which I can't find links for right now) by T.T. Brown, as well as a Nasa proposal (Google nasa seop pdf).
 A: This is bunk, you can't do anything to the gravity felt by an enclosed system, it is always as the energy in the enclosed system.
What you can do with a similar setup make electrically charged thing float in air using the electric field on the surface of the Earth, caused by electrical separation in rainclouds in the atmosphere, and transmitted by lightning strikes to the ground. So it isn't inconcievable that there is some floating obect demonstration using either a big charge, or a very light dipole in an environment with enough conductors around to deform the Earth's field so that it is getting stronger with height.
A: I would bet that these "devices" are just variations on the ionocraft. Look at this document for a detailed experiment setup. These devices create a soft current of ionized air between the electrodes that thrusts the device. 
As Ron explained, it doesn't have anything to do with gravity (unless you want to think in normal aircraft or helicopters as "gravity-altering" devices as well)
A: The described action is not bunk.
But.  The effect, as NASA proved, is due to ionized air flowing from one charge to the second.
There is not enough air in Space for this effect to work.  It does nothing in a vacuum.
And propellers and foils are a much more efficient means of travel through the air.
You can watch this demonstrated on an episode of "Myth Busters".
A: The standard physcial model taught in most universities today does not allow for electrogravitics, although there are several alternative theories which can provide explanations and even predictions for the phenomenon. Without weighing my opinion on one side or the other, here are a couple of books oft-recommended for one interested in the subject:
One with more narrative, written in a  documentary-style,
and another which dives into many of the technical and theoretical details.
A: Two charged plates that are insulated from each other describes in electronic parts what is called a capacitor.  Most electrical devices have them in one form or another.
All of electricity is based upon the electron shells of the atoms.  Quantum levels of energy are transferred from one atom to the next to create a balanced system of energy potentials.
If you were to charge each plate up to 500,000 volts and separate them just far enough that a spark would not fly off one plate to transfer charge to the other plate.  The charge is based upon excess (negative) or deficient (positive) ionized atoms.
The relative gravity only changes by the amount of gravity associated with the mass of the electrons and it is equivalent to moving some marbles in to equal size containers from one container to the other.  Gravity is mostly omni-directional.  So what you see in transferring marbles from one container to the other, is pretty much what happens to gravity when charge transfers from one plate to the other.
For the most part, gravitational influences are unchanged when considering the system of the two plates.
However, in really small amounts, the movement of the electrons can interact gravitationally with the surrounding materials.  Very tiny gravitational influences too small to detect will influence the plates and shift the gravitational center of the two plates.  But there is no practical use for something you can not detect, unless it is used in conjunction with other systems like an interferrometer to create some form of extremely sensitive sensor.  But the electrostatic forces are far stronger than the gravitational forces, so isolating the electrostatic forces from interferring with the detection of gravitational forces would be difficult.
