Negative Mass is Everywhere in Physics. It Also Explains Dark Matter

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Depiction of what filaments of Dark Matter would look like if we could see them with our naked eyes. The yellow spots represent galaxies.

In early December 2018 the physicists’ blogosphere went berserk because of a 2017 paper (in fact still a preprint to this date: arXiv:1712.07962) in which the author James Farnes, University of Oxford, tries to explain Dark Matter and Dark Energy with a seemingly preposterous hypothesis: the presence of a negative-mass fluid that permeates the Universe. The idea itself is not new, and the author acknowledges past works by Albert Einstein, Hermann Bondi and others. In a nutshell, negative-mass matter behaves in the following way:

  • Positive-positive interaction: the two particles attract each other;
  • Negative-negative interaction: the two particles repel each other;
  • Positive-negative interaction: both particle accelerate in the same direction, pointing from the negative mass to the positive mass.

As a particle physicist, I’m not particularly convinced by the argument, but I concede that there may be a loophole, if we allow mass to be an effective parameter as in solid state physics, thus violating (at least apparently) the cherished equivalence principle. This means that the mass that enters the equation that govern the gravitation behaviour of this fluid is not strictly equivalent to the inertial mass (the one that appears in the glorious Newton’s law of motions such as F = ma). My understanding is that aggregates of regular matter may present such behaviour under unusual circumstances, often associated with very low temperature. For example, even electrons can exhibit effective mass in the superconductivity regime (H. Frölich, Nature volume 168, pages 280–281). There are indications that negative effective mass which arises from periodic potential in lattices might explain a number of odd properties of high-temperature superconductors (cond-mat/0210455).

Farnes’ paper go much well beyond basic speculations. The author claims to be able to explain the flattening of galaxy rotation curves, formation of galactic Dark Matter halos, large formations such as filaments of dark matter connecting galaxies, and even the ultimate fate of the Universe (spoiler: it would expand and contract cyclically). I’m not an astrophysicist and I prefer to leave to the experts give any meaningful comment to these claims. Some spoke up saying that the model is so contrived that in the end one can invoke Occam’s razor and keep going with the ΛCMD model of cosmology. Personally, some of the arguments in the paper sounded to me quite hand-waving, for example the explanation of the flatness of space and the position of the first peak of the CMB power spectrum (see Sec 4.4). On the other hand, I have found very stimulating the arguments supporting a revision of the interpretation of some critical measurements, such as the expansion of the Universe with Supernovae explosions. While the measurements themselves are taking for granted, what may be incorrect is the set of assumptions that lead to the final interpretations. Most notably, the positiveness of the mass-energy density that is almost always enforced even though in some cases the experiments themselves seem to prefer otherwise (see sec 4.1 for further details). From a Bayesian perspective, I can only warn you that most of our mistakes are caused by incorrect assumptions: it’s always the prior!

In any event, I have found the model simple enough to be implemented in a computer code that can be run on a laptop. In the paper you can find a reference to a more proper implementation, while mine looks more like an animation rather than a realistic simulation. The code is based on a previous simulation of Dark Matter that I created a few years ago. You can read more about this model in this post. The new, adapted code can be found here. To execute it, you need to install Processing and the Traer physics library. In my implementation, differently from what I think James Farnes did, I create all matter with positive mass, but assign a negative coupling (-G) to interactions between negative-negative objects.

I scatter randomly with a uniform distribution the negative-mass particles. Instead, regular matter is placed in two “clumps” that represent roughly two galaxies. What do you think will happen? The N-body simulation proceeds without any explicit long-term goal. At least intuitively, what happens is that regular matter tries to coalesce even further, while negative matter tends to expand. However, interesting dynamics happen in proximity of large clumps of regular matter: negative particles are attracted by the “galaxies”, but do not get too concentrated due to self-repulsion. The net effect, according to Farnes’ paper, is the creation of a “halo” around galaxies, and “filaments” connecting them. Can you spot these things in the video? Or is it just wishful thinking?

Simulation of negative-mass dark matter showing galaxy formation. The code is based on Processing and is publicly available from here.

To wrap up, new life was given to the old and quite un-fashionable idea of negative-mass matter to explain some of the biggest mysteries of the Universe: Dark Matter, Dark Energy and the overall dynamics of formations on a cosmological scale. If extraordinary claims require extraordinary evidence, I don’t think such an evidence has been presented beyond any reasonable doubt. However, it may not be the first nor the last time a toy-model evolves into something more complicated.

Originally published at on December 9, 2018.

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