In 1957, the astrophysicist Herman Bondi wrotea paper in which he considered the possible existence of a negative mass in Albert Einstein’s theory of gravity. A negative mass would repel a positive mass away from it. Given that, a pair of positive and negative masses could accelerate together up to the speed of light. The negative mass would push away the positive mass which in turn would pull the negative mass for the ride. The runaway pair would accelerate indefinitely, without any need for fuel or a propulsion system. Energy conservation would not be violated because the sum of the two masses is zero.
However, in a recent discussion I had with my brilliant collaborator, Mark Hertzberg, we agreed that the existence of a negative mass in nature would allow for a time machine in which one can visit the past. The reason is simple. A positive mass delays the arrival of light that passes near it, as recognized in a seminal paper by my distinguished colleague, Irwin Shapiro.
The “Shapiro time delay” near a positive mass reverses sign and turns into a “Shapiro time advance” near a negative mass. If the sender is moving sufficiently close to the speed of light, the Shapiro time advance would mean that a light signal can be reflected off a mirror and arrive back to the sender when the sender’s clock shows a time earlier than the original transmission time of the same signal.
Effectively, the Shapiro time advance is equivalent to communicating with a faster-than-light particle which violates causality. Within Einstein’s gravity, the technical term for a time machine of this type is a “closed timelike curve.”
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