The Philosopher's stone and 'Defying Gravity'

I have just remembered a conversation had with a Physicist some years ago. I was staying a friend's mother's manor house near the south coast, and we were all sat around talking post supper. One of the guests was a scientist, and the conversation lead to the idea of defeating the earth's gravitational field. He told me of how two bodies acting upon each other could effectively produce gravity, and if a way to manipulate such forces was found then escaping earth's gravitational field would be achieved without recourse to what he considered primitive rocket propulsion. I thought about this, and some years later thought that maybe two (or more) aligned particle accellerators may be the answer. If two such devices could be syncronised to produce a 'lift' greater than the gravitational force of the earth, one would have achieved antigravity. Theoretically simple, but one would need a PhD in physics to make it work. The premise tho' is based on the idea that as an atom/particle approaches the speed of light, its mass increases. Thus something as small as an accellerated subatomic particle could have what would appear to have, from our position in the continuum, 'a mass approaching infinite'. Certainly enough to produce 'lift'.