Maybe it was modeled as a curvature of space? So positive masses curve space so that everything moves toward them - including light, massless particles, and negative mass. And negative mass repels everything, including other negative mass, by shaping space differently.

[Edit: jbay808 has a better explanation below, and negative mass attracts negative mass.]

That behavior is described here https://en.wikipedia.org/wiki/Negative_mass#Runaway_motion but it's not what I was expecting either.

Yeah this helped me create a mental picture that kind of makes sense. It would clarify why negative mass is also concentrated in areas of high mass, and could also provide the mechanism for constant universe expansion, as the space between masses is constantly being pushed away by the diffuse negative mass. Heh, armchair physics is fun :)

Huh, very interesting. Definitely not intuitive by comparison to electric charge.

Negative mass inverts signs in ways that are not intuitive. Best explanation is a diagram from the author's twitter page [0][1].

When a positive and negative mass particle interact gravitationally the positive mass is repelled and the negative mass is attracted.

[0] https://twitter.com/Astro_Jamie/status/1070303556266283008

[1] https://i.redd.it/qt2tf2tbni221.jpg

I think what they're saying is that positive mass galaxies attract the negative mass, even as the negative mass repels the positive mass (and all other negative mass). In a stationary system, eventually the two will reach an equilibrium.

However, the effects of this in a system in which the positive mass galaxy is spinning is that the negative mass counteracts the forces of inertia, allowing the galaxy to spin at higher speeds without shattering like a cd spun too quickly. Now, whether the math of all that makes sense, I'm am not in a position to comment on.

Wouldn't that allow for a "perpetual motion" setup where a blob of normal mass is in front of a blob of negative mass? The negative mass would push the positive mass forward, and then be attracted to it and follow. What am I misunderstanding?

You can't ignore the gravitational force of the normal mass. The two would rapidly reach a zero-value equilibrium at some point where the repulsive force of the negative mass is perfectly cancelled out by the attractive gravity of the positive mass, so you have a net force of 0 at some distance.

For an easier to visualize example imagine placing one magnet positive pole up inside of a tube, and then you place another magnet positive pole down in the same tube. It would create a similar effect. There is a repulsive force being perfectly balanced out by an attractive force and the two reach an equilibrium where the magnet on top is 'floating' with the net of all forces in this closed system being 0.

Screwily to our intuitions negative mass goes in the opposite direction of its acceleration.

It still goes away but the acceleration is in the same direction. It is weird and easy to be confused.

I think you meant to say that the mass accelerates opposite to forces acting upon it.

An idealized -M + M = 0 pair of particles (one normal, one negative mass) could experience runaway acceleration. Author touches on this in the paper as a potential source for the incredibly high-energy extra-galactic cosmic rays.

Granted, the paper describes a model in which something that acts like a particle with negative mass exerts this force upon things, but has no claims as to what a physical manifestation of this would look like.

Damn, you're right, there goes the hoverboard.

It would be perpetual motion, but momentum and energy would remain the same. Both depend on mass (so negative mass accelerating creates negative momentum and energy).

That's an interesting point. Thank you!

The galaxy is in the center, and with a large positive mass it attracts negatively-massed matter towards it. But the negatively-massed matter repulses rather than attracting, so it has the effect of "squeezing" the galaxy in on its self.

Negative mass is like playing opposite day. Negative mass is attracted to other negative mass, but because of the inverse acceleration to force relationship of negative mass the end result is that it is pushed away from other negative mass. Negative mass would also repel positive mass, which is straightforward for the positive mass but for the negative mass (again, inverse acceleration) it would end up with an "attractive" motion toward the positive mass.

I was just about to quote that same sentence.

How can positive matter attract negative matter which at the same time is repelling positive matter?

The author is described as an Astrophysicist at Oxford (a reputable place) so I assume I'm either just not getting it or this is poorly worded.

To approximate with Newtonian laws:

F=ma

Meaning that positive and negative masses will accelerate in opposite directions in response to the same applied force. The effect is different, but it's a bit like how when you are in a car and hit the gas pedal, and your kid is in the back seat holding a helium balloon, the kid feels pushed backward into the seat but the balloon flies forward toward the windshield.

F = GMm/r^2

Meaning that gravitational forces between opposite signed masses is the opposite direction from the force between masses of the same sign.

Thus, the gravity force repels the normal mass away, but this repulsive force actually drags the negative mass along with it, because the negative mass accelerates the wrong way when "repelled".

We have an intuitive ~~example~~ approximation of this in real-life: balloons in a car[1].

[1]: https://www.youtube.com/watch?v=uAJlg8MDAlU

I'm intrigued. Isn't the reason a balloon moves forward more of buoyancy? If you do the same experiment with the window open, doesn't it do as expected by most people?

I didn't read that positive matter is attracting negative matter. What I gathered is that the presence of a cloud of negative matter in the right place would be held in place by mutual repulsion of the outer arms of the galaxy and the inner galaxy. And that the neg matter supplies enough repulsion to the diffuse outer galaxy that it can spin a bit slower than it would have to otherwise.

Positive matter creates a gravity well. This much most people are familiar with.

Seems to me what they're saying is that this well will pull in negative matter until a balance is reached, this will, in turn exert force on the internal structure of the galaxy.

Think of it as one pushes while the other one pulls.