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Is there law/rule in physics that precludes the existence of a negative mass, wherein similar negative masses attract but positive and negative masses repel?

To keep this on-topic in Astronomy SE: Has this ever come up in the context of Astronomy? Do cosmologists consider the possibility? Has anyone looked for signs of negative mass, perhaps on galactic scales?

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    $\begingroup$ This is a nice question, but it probably should belong on Physics SE. $\endgroup$
    – WarpPrime
    Dec 22, 2021 at 14:15
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    $\begingroup$ Not a direct answer, but related. In general, one can imagine all sorts of possible physics (magnetic monopoles, a new type of force, strings, etc.) but whether that physics is true is determined by observations. Observations don't support the existence of negative mass. $\endgroup$
    – zephyr
    Dec 22, 2021 at 15:47
  • $\begingroup$ zephyr: I think we should be thinking in two directions... sometimes observations look for a theory, and sometimes a theory says possible, but we require more observations to confirm it. I believe the positron did go this second path in the past. regards. $\endgroup$
    – Riad
    Dec 22, 2021 at 17:59
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    $\begingroup$ Of course, it already has an answer on physics physics.stackexchange.com/questions/44934/… (tl;dr this doesn't exist) $\endgroup$
    – James K
    Dec 22, 2021 at 18:37
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    $\begingroup$ voting to leave open here because I think it's a net positive to have one good question and answer(s) about negative mass here in Astronomy SE. Rather than close and block anyone from adding an answer, let's leave this one open! I've modified the question accordingly, and notified the current answer author asking them if it looks okay. Otherwise we can just roll back. $\endgroup$
    – uhoh
    Dec 23, 2021 at 3:25

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It would be rather difficult to make negative mass consistent with the rest of physics and not have a bunch of weird stuff happen. According to general relativity, mass causes a curvature in spacetime, and objects follow that curvature. So whatever effect negative mass has on spacetime, and thus on positive mass objects, would also be the effect it has on the movement of negative mass objects. If negative masses repel positive masses, then they also repel negative masses.

Now, you may think that in the gravitational force formula, the force is the product of the two masses, so two negative masses would give a positive force (where "positive" means "directed towards the other mass"). However, there's also the fact that acceleration is force divided by mass, so a positive force divided by a negative mass would give a negative acceleration. As the answer given in James K's comment notes, this means that given a negative and positive mass, both of them would experience a negative force, which for the positive mass would mean repulsion, but for the negative mass would mean attraction.

If we try to make an atom out of particles that are identical to protons and electrons, except that they have negative mass, then the electrical force would still be a positive force as it is with normal atoms, but this would result in the particles being repelled. The strong force, which normally keeps nucleuses together, would instead push them apart. So coming up with a way of making matter, rather than just isolated particles, would be rather nontrivial. You could have a negative-proton and a negative-position (that is, a particle that's like an electron except its charge is positive and its mass is negative) or a negative-anti-neutron and a negative electron making an analog of a neutron atom, but a helium atom has four particles in its nucleus, so this tactic wouldn't work for them. Even single baryons would be problematic, since the force that holds quarks together would be repulsive. Moreover, since like charges would be attracted and opposite would be repelled, particles would segregate into clumps of all-positive charges and other clumps of all-negative.

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  • $\begingroup$ +1 I think it's a great question and this is a great answer, and I think it's good to keep the question open and not block further answers and possibly loose visibility by closing. So I've added to the question to tie it in to Astronomy better. I realize we should generally avoid modifying questions after an answer is posted, but I'm wondering if the change is okay with you? If not, we can roll it back. Thanks! $\endgroup$
    – uhoh
    Dec 23, 2021 at 3:27
  • $\begingroup$ Related in Physics SE: What is the Current Status of Measurement of the Gravitational Mass of Antimatter? $\endgroup$
    – uhoh
    Dec 23, 2021 at 3:30
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In simple Newtonian gravity, uniform mass density does not give rise to any gravitational field (avoiding arguments as to whether the universe is finite or infinite or expanding or stationary). So, within a universe of constant mass density, any mass concentrations give rise to negative (converging) fields and likewise mass voids give rise to positive (diverging fields). This can be examined by observing the motion of a small test mass which will be attracted to a mass concentration but repelled from a mass void. In this scenario, mass voids behave as negative masses.
The net result is that two mass concentrations or two mass voids will tend to be attracted to each other, whereas a mass concentration and a mass void will tend to be mutually repelled.

See also: https://physics.stackexchange.com/questions/591103/is-the-force-due-to-gravity-between-two-objects-immersed-in-a-fluid-correctly-gi

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