Background to Anti-Gravity
In 1992, Russian physicist Evgeny Podkletnov claimed to have tested a device that shields an object from gravity. The experiment involved levitating a superconducting disc above a magnet. No one -- including NASA researchers -- has been able to replicate this experiment.
NASA researched antigravity under Breakthrough Propulsion Physics Project (1996-2002) publishing a booklet titled "Responding to Mechanical Antigravity" to help amateur and professional researchers, most of whom submitted ideas (as many as 100 per year) involving machines that falsely appeared to create an antigravity effect.
In Newton's law of universal gravitation, gravity was an external force transmitted by unknown means. In the 20th century, Newton's model was replaced by general relativity where gravity is not a force but the result of the geometry of spacetime. Under general relativity, anti-gravity is impossible except under contrived circumstances. Quantum physicists have postulated the existence of gravitons, a set of massless elementary particles that transmit the force, and the possibility of creating or destroying these is unclear.
"Anti-gravity" is often used colloquially to refer to devices that look as if they reverse gravity even though they operate through other means, such as lifters, which fly in the air by using electromagnetic fields.
Will it ever be 'invented' in your lifetime or indeed will experiments at Cern on antimatter bear fruit - who knows but for now the only person who has perfected it is Marshall Miller and for details on that you will have to read The Heaviness!
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