like charge is fundamental property of matter which exist in both negative and positive aspect and help us to understand the electro-magnetism ,in the same ways would mass be negative ? in that scenario gravity could be repulsive too?
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Negative (inertial) mass would mean that objects accelerate towards you when you push them away.... – Marius Ladegård Meyer Nov 06 '23 at 14:56
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2@MariusLadegårdMeyer Throw in enough minus signs and that approach becomes useful. – rob Nov 06 '23 at 15:37
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We don't have any physical evidence for negative masses. In general relativity there are some interesting mathematical solutions, such as "wormholes," that become stable if you have access to material with "negative energy density," which is sort of the same thing. But such materials are generally considered to be unphysical.
In the submillimeter gravitation experiments at the University of Washington, a number of experiments measured the gravitational interaction between parallel metal plates with holes around the edges, sort of like the dial of an old rotary telephone. The mathematical analysis treats these a solid positive-mass discs with negative-mass cylinders representing the holes. The trick works because gravity is (in the weak-field approximation) a linear theory, where gravitational forces from different mass distributions add like simple vectors.
Here's a rendering and photo of a recent version of the Washington apparatus, from Lee et al. (2020):
On the top right is one of the test masses, with 18 rectangular "outer negative masses" and 120 wedge-shaped "inner negative masses." On the left is the torsion pendulum. The vertical gap between the two discs is varied between $3000\text{–}50\rm\,\mu m$. Gravity makes the hanging disc twist so that the positive-mass chunks between the holes line up with each other. This is exactly the same, mathematically, as having the negative-mass holes attract each other, and/or having the positive and negative masses repel.
rob
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