In a 1957 paper, the cosmologist Hermann Bondi considered the possibility that an object with a negative mass would create a repulsive force of gravity. When placed next to a positive mass, it would repel it, but the positive mass would attract the negative mass. If the two masses are equal but of opposite signs, the pair will accelerate in the same direction indefinitely. The total kinetic energy would be zero, consistent with the conservation of energy.
If the positive mass is an Earth-like planet, this engine can accelerate at 1 g, the comfortable acceleration we feel on the surface of Earth. Including passengers made from the material of this planet, like humans, comes at no cost. Accelerating at 1 g for a full year would bring the planet to the speed of light. Steady acceleration for several decades would allow the planet to traverse the entire Universe during the lifetime of the passengers, thanks to the time dilation experienced very close to the speed of light.
The only missing component of the engine that would allow us to engage in this journey is the negative mass. Robert Forward wrote a paper about the opportunity offered by this propulsion concept in 1990. I am currently co-authoring a paper that shows how to engineer a negative mass object from a scalar field, consistent with Albert Einstein’s General Theory of Relativity.
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