The definition of Antigravity

Before going any further we need to clarify what is generally the perceived meaning of the term 'antigravity'. In a sense a helicopter is an antigravity device but few of us would regard this a 'antigravity'. Also a helium balloon defies gravity but here again not really an antigravity device.
If, on the other hand you placed the helium balloon in a vacuum and it still went up instead of down then that would be antigravity.

Antigravity refers to the action of defying gravity without an associated reactive force

or, perhaps a better definition is the creation of a space isolated from the normal effects of gravity.

Action with reaction is pretty fundamental as a physical concept. However, sometimes the reaction part is not initially obvious. For example, the moon circles round the earth. The fact that it is moving in a circle means that a force is being applied to it. With every force there is an opposite reaction. The opposite reaction is there somewhere but the dynamics are not as obvious as, say, rocket propulsion.


Is 'antigravity' possible?

A useful analogy to get an understanding of the magnitude of the problem is that it's like you are given the task of creating a machine made only of ice that can move against the flow of a waterfall without touching the rock face. In this analogy, ice equates to matter and the waterfall equates to gravity or the stuff that causes it.

There is one sure fact that if gravity can effect matter then matter can effect gravity.
It is the same logic as saying that if a bat can have an effect on a ball then the ball can have an effect on the bat.

If we ignore the engineering problem then antigravity is not so hard to achieve. This example is not to be taken seriously but it illustrates a point and may even offer a clue. All you have to do is get another planet with the mass of Earth and keep it suspended about 20 metres above your head by getting the two planets to orbit each other extremely fast.
The interesting thing is, apart from being practically weightless, you would not feel any centrifugal/centripetal effects. The only thing you would notice is the stars spinning round. In your vicinity, spacetime has been altered. To achieve antigravity, the clue here is to alter the vector of space without resorting to the use of mass.

I'm going to substitute the word 'gravity' for 'motional field'. Matter can influence motional field but, unfortunately, very poorly, except at speeds approaching that of light. Matter is like a sieve, almost transparent to this mass-less substance.
A fast spinning disc will very slightly distort gravity. An exotic sounding term for this is 'frame-dragging'. It's really just making the energy field flow in a slightly different manner. This changes the local gravitational vector compared to when the disk is stationary.
A magnetised disc, provided it is magnetised in a sympathetic plane, will enhance this frame-dragging effect. This is due to the trajectory alignment of subatomic elements contributing to the frame-dragging mechanism - see Dr Eugene Podkletnov

so far so good ...

We know for sure we can influence the surrounding energy field. Pulse a current through a coil of wire and you produce an electromagnetic wave. Will it produce motion - no because it is pulsed in both directions. Bounce one side off a mirror and you have all the waves going in the same direction but you won't have much reactive force. Cranking the power up will help. Construct a loudspeaker type series of coils to try and accelerate the energy and you may get a bit more reactive force. But still not enough to get you anywhere.
You can't beat getting a chunk of matter and accelerating it in the opposite direction to where you want to go, and hence my opening statement, we need to know at the fundamental level why this should be. We need a theory of Inertia.



Addendum

In the not too distant future, the human race will understand all things regarding the physical world in which we find ourselves. We will understand how matter is created, the cycles of the universe, all things both micro and macro.

However, there is one thing that is probably going to stump us and that is understanding the concept of Infinity. It is inconceivable that infinity can actually exist either spatially or in time. We know this to be true otherwise the universe would be crawling with mega advanced aliens spawned from aeons in the past. They are not here, thankfully.