No, negative masses have not revolutionized cosmology

By Sabine Hossenfelder

Figure from arXiv:1712.07962
A lot of people have asked me to comment on a paper by Jamie Farnes, titled
Farnes is a postdoc fellow at the Oxford e-Research center and has previously worked on observational astrophysics. A few days ago, Oxford University published a press-release celebrating the publication of Farnes’ paper. This press-release was then picked up by phys.org and spread from there to a few other outlets. I have since gotten various inquiries by readers and journalists asking for comments. In his paper, Farnes has a go at cosmology with negative gravitational masses. He wants these masses further to also have negative inertial masses, so that the equivalence principle is maintained. It’s a nice idea. I, as I am sure many other people in the field, have toyed with it. Problem is, it works really badly. General Relativity is a wonderful theory. It tells you how masses move under the pull of gravity. You do not get to choose how they move; it follows from Einstein’s equations. These equations tell you that like masses attract and unlike masses repel. We don’t normally talk about this because for all we know there are no negative gravitational masses, but you can see what happens in the Newtonian limit. It’s the same as for the electromagnetic force, just with electric charges exchanged for masses, and – importantly – with a flipped sign. The deeper reason for this is that the gravitational interaction is exchanged by a spin-2 field, whereas the electromagnetic force is exchanged by a spin-1 field. Note that for this to be the case, you do not need to speak about the messenger particle that is associated with the force if you quantize it (gravitons or photons). It’s simply a statement about the type of interaction, not about the quantization. Again, you don’t get to choose this behavior. Once you work with General Relativity, you are stuck with the spin-2 field and you conclude: like charges attract and unlike charges repel. Farnes in his paper instead wants negative gravitational masses to mutually repel each other. But general relativity won’t let you do this. He notices that in section 2.3.3. where he goes on about the “counterintuitive” finding that the negative masses don’t actually seem to mutually repel. He doesn’t say in his paper how he did the N-body simulation in which the negative mass particles mutually repel (you can tell they do just by looking at the images). Some inquiry by email revealed that he does not actually derive the Newtonian limit from the field equations, he just encodes the repulsive interaction the way he thinks it should be. Farnes also introduces a creation term for the negative masses so he gets something akin dark energy. A creation term is basically a magic fix by which you can explain everything and anything. Once you have that, you can either go and postulate an equation of motion that is consistent with the constant creation (or whatever else you want), or you don’t, in which case you just violate energy conservation. Either way, it doesn’t explain anything. And if you are okay with introducing fancy fluids with uncommon equations of motion you may as well stick with dark energy and dark matter. There’s a more general point to be made here. The primary reason that we use dark matter and dark energy to explain cosmological observations is that they are simple. Occam’s razor vetoes any explanation you can come up with that is more complicated than that, and Farnes’ approach certainly is not a simple explanation. Furthermore, while it is okay to introduce negative gravitational masses, it’s highly problematic to introduce negative inertial masses because this means the vacuum becomes unstable. If you do this, you can produce particle pairs from a net energy of zero in infinitely large amounts. This fits badly with our observations. Now, look. It may be that what I am saying is wrong. Maybe the Newtonian limit is more complicated that it seems. Maybe gravity is not a spin-2 interaction. Maybe you can have mutually repulsive negative masses in general relativity after all. I would totally be in favor of that, as I have written a paper about repulsive gravity myself (it’s quoted in Farnes’ paper). I believe that negative gravitational masses are the only known solution to the (real) cosmological constant problem. But any approach that attempts to work with negative masses needs to explain how it overcomes the above mentioned problems. Farnes’ paper falls short of this.

In summary, the solution proposed by Farnes creates more problems than it solves.