One would probably have to do quite a lot of reading to really understand what is going on. Keep in mind that what you will find in the article is mostly analogies to try and understand the underlying phenomena. Sometimes this is useful, sometimes it causes confusion. I find that with quantum mechanics, that most people get very confused over the 'particle/wave' duality. The problem is they are pushed as analogies but everyone forgets from time to time that they are analogies not facts.
Mass also has the complication that it is involved in both momentum and gravity. We also tend to think of it as an inherent property of particles, when in reality it isn't. Mass is intricately tied to the amount of energy in a system ( E=mc^2 ) and chemical reactions involve changes in mass.
I wonder if the 'negative mass' particles have negative energy. I believe negative momentum is perfectly acceptable in quantum mechanics.

Originally posted by twhitehead One would probably have to do quite a lot of reading to really understand what is going on. Keep in mind that what you will find in the article is mostly analogies to try and understand the underlying phenomena. Sometimes this is useful, sometimes it causes confusion. I find that with quantum mechanics, that most people get very confused over the 'particl ...[text shortened]... have negative energy. I believe negative momentum is perfectly acceptable in quantum mechanics.

I often have the impression about subatomic physics that it is a universe of discourse consisting almost entirely of equations, not facts, certainly not facts in the everyday sense of the word, and that physicists themselves are at a loss to come up with any better explanations than metaphors.

Originally posted by moonbus I often have the impression about subatomic physics that it is a universe of discourse consisting almost entirely of equations, not facts, certainly not facts in the everyday sense of the word, and that physicists themselves are at a loss to come up with any better explanations than metaphors.

The equations are the facts.
They are somewhat non-intuitive equations so we make up analogies but the analogies are not exact and we forget that they are analogies and end up all confused. We just cant get the image of a marble like particle moving through space, or a wave like object moving through space out of our minds, however hard we try.

Unfortunately one needs to subscribe to Physical Review Letters to see the full text. But the abstract states that they engineered a negative effective mass. So as a result of the dynamics of the whole system some of the excitations behave as if they have negative mass. What they have not done is produce a fundamental particle with negative mass, unless anti-matter has this property which I doubt strongly, that will not happen.

Originally posted by moonbus Negative mass as such defies imagination, .....

I think that depends on what context you are thinking of mass.
On earth, we usually think of weight, where things are held down by gravity. But we are not completely flummoxed by helium balloons which at first sight appear to have negative weight. We are fascinated (at least I am) by floating magnets (especially when super conductors are involved, but that is not necessary). We all know about electromagnetic repulsion and attraction. So negative gravity is really not all that far fetched.
However, the OP is about inertia ie the resistance to a force and a resulting acceleration from a force. Instead of accelerating away, it accelerates towards the force. This is confusing mostly because we imagine forces as physical objects pushing, but if we instead think of magnetism as the force in question then attraction seems more than feasible, and the question is whether the mass is negative or the force is negative and whether one can distinguish between the two.

Yes, if we are talking about effects, it is not counter-intuitive; attraction and repulsion are essentially the same thing. There is nothing perplexing about mass being attracted by one force and repulsed by another. So, is negative mass a mass which is attracted by a repelling force?

Originally posted by moonbus So, is negative mass a mass which is attracted by a repelling force?

That is what the article says. My question of course is how do you decide whether a force is 'repelling' or not? Electromagnetic charge is repelling or attractive depending on its charge, and the charge of the particle it is acting on. The article doesn't say what forces are involved and the summary of the original paper is just as confusing:

Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features—shock waves, soliton trains, self-trapping, etc.—originate from a modified dispersion.

Originally posted by twhitehead That is what the article says. My question of course is how do you decide whether a force is 'repelling' or not? Electromagnetic charge is repelling or attractive depending on its charge, and the charge of the particle it is acting on. The article doesn't say what forces are involved and the summary of the original paper is just as confusing:

He ...[text shortened]... s—shock waves, soliton trains, self-trapping, etc.—originate from a modified dispersion.

Suppose there were two particles with the same charge but opposite mass. They exert an equal but opposite repelling force on each other. The positive mass one is accelerated away from its counterpart. However, because of its negative mass, the negative mass particle is accelerated towards the positive mass one. This means the pair accelerates along the line joining them for ever more. The net momentum is zero, and in classical physics the energy is 1/2 mv^2 per particle so the net energy is zero. Taking relativity into account we run into a problem. For the pair the mass is zero, so the point equally distant from each of them (the centre of mass is undefined) should move at the speed of light, however each particle has non-zero mass and so must be traveling slower than light, which gives us a contradiction.

The dispersion relation they talk about is a relationship between frequency and wavelength. For a non-relativistic free particle, and remembering de Broglie's relations E = hf and p = h/l ( l for wavelength) this is just E = p^2/2m. So they are saying that for some values of momentum their effective mass (which is just the value in that formula) is negative.

Originally posted by twhitehead Which leaves me wondering how one defines a 'repelling' force.

Well, except in the fairly exotic circumstances described in the article referenced in the OP, we don't see negative mass particles so the problem doesn't arise. Since negative effective mass particles are exotic the term "repulsive force" can be read as short for "force that would normally be repulsive.".

In the meantime I have watched a few videos on the Internet about this phenomenon. The circumstances certainly are exotic. The experimental conditions consist of a superfluid (which already never occurs in nature), being forced through an aperature a few microns in diameter, and the observed (apparent) negative reaction is very short-lived. I expect that if someone forced five turkeys through a hatch only one turkey wide, strange things would happen there, too.