Beyond Dark Matter

Could Mordehai Milgrom help us detect dark matter?

In deep underground laboratories, buried below rock and shielded from cosmic radiation, physicists have build extremely sensitive detectors aimed at solving one of the Universe’s greatest mysteries. They are awaiting signals of a new kind of particle, promised to them by cosmologists and astrophysicists: Dark Matter. The highly elusive particle is thought to dominate the mass budget of our galaxy and of the Universe as such. There should be about six times more Dark Matter than ordinary, “baryonic” matter (which includes everything from interstellar gas clouds, stars, and planets, to the screen you are reading this on, and you yourself). Dark Matter has not yet been directly detected, despite numerous experiments, their painstaking efforts to reduce background signals, and thus ever increasing sensitivity. Many researchers nevertheless remain confident that a detection is within reach. Yet some worry: what if we are chasing a phantom? What if Dark Matter does not exist?

There are several lines of argument for the existence of Dark Matter. On the scale of galaxies, the need for Dark Matter is mostly inferred from their dynamics. Disk galaxies rotate. Counting up the distribution of mass visible in a galaxy – in the form of stars and gas – we can use Newton’s law of gravity to calculate how fast the galaxy should rotate at different distances from its center (the “rotation curve”). The rotation should be faster in the center and slower with increasing distance. Yet measurements reveal that galaxies rotate faster than expected and that the rotation velocity does not drop at increasing radii. Taken at face value, this would imply that galaxies are not gravitationally bound; the gravity of their stars and gas is insufficient to keep them from flying apart. To be stable, galaxies would have to contain large amounts of unseen mass. This mass has been termed “Dark” Matter because it only interacts through gravity, but not with electromagnetic radiation.

This argument for Dark Matter implies one crucial assumption: Newton’s law of gravity applies on galactic scales. This is a long stretch. Newton’s law was uncovered on Earth, where the gravitational acceleration is 1011 times stronger than typical for galaxies, and in the Solar system, where even the most distant planet Neptune experiences a 10,000 times stronger acceleration than stars in galaxies. It is therefore far from confirmed whether Newton’s law can be extrapolated to the very low acceleration regime that galaxies live in.

This was also noticed by Israeli physicist Mordehai Milgrom. In 1983, he suggested a radically different approach to explain the high rotation speeds of galaxies. Instead of introducing Dark Matter, Milgrom proposed that the laws of gravity are different on the scale of galaxies – that Newtonian Dynamics becomes “Modified Newtonian Dynamics” (MOND). In MOND, or Milgromian Dynamics, the gravitational acceleration of a given mass is stronger than in the Newtonian case, and does not scale as 1/r2 with distance r but rather as 1/r. This explains why galaxies rotate fast without tearing themselves apart, and why the rotation curve does not drop at larger radii. Since MOND must preserve the successes of Newtonian gravity, which is very well tested in the solar system, there has to be an acceleration at which a transition occurs. This acceleration scale is called a0.



"Laboratory searches for Dark Matter are important...However, detectability is not falsifiability. What if we do not succeed in detecting Dark Matter?"

The parameter a0 is not fixed by the theory. It has to be measured. Such measurements provide a first test. Does every galaxy require the same a0, or does the parameter have to be fixed for each system independently? The former is consistent with a fundamental theory, whereas the latter would be much less convincing. It turns out that the former is indeed the case: every galaxy results in the same a0. In fact, the parameter can be measured in several independent ways, not only for different galaxies. They all point to the same value.

One hallmark of a scientific hypothesis is that it makes testable predictions. Dark Matter cosmology makes predictions for the large-scale evolution of the universe and for statistical samples of galaxies. However, it has almost no predictive power for an individual galaxy. While the rotation curve of a galaxy can be fitted by adding a distribution of Dark Matter to it, this does not work the other way around. Given just the distribution of stars and gas in a galaxy, Dark Matter models do not predict the detailed rotation curve. The visible galaxy could, in principle, be embedded in a variety of different Dark Matter distributions, all resulting in different rotation curves.

MOND, in contrast, makes precise and accurate predictions for individual galaxies. If the distribution of stars and gas in a galaxy is known, Milgrom’s law allows us to calculate what its rotation curve should look like, down to bumps and wiggles. These predictions are routinely confirmed observationally.

While a modified gravity law offers a conceptual explanation for why such predictions work, the underlying, extremely tight correlation is purely empirical and independent of MOND. It has been termed the Radial Acceleration Relation (RAR). One can not stress enough how fascinating it is that the distribution of baryons (stars, gas) in a galaxy uniquely predicts the galaxy’s dynamics. This observational fact must be understood in any model of the Universe, especially in Dark Matter models in which such predictability is not necessarily expected.

Nevertheless, MOND does have problems if applied beyond the regime of galaxies for which it was developed. An example is galaxy clusters, large agglomerations of galaxies that even in MOND appear to require the addition of Dark Matter to be bound structures (albeit of only a factor of about two compared to the ordinary matter). A related issue is colliding galaxy clusters such as the Bullet Cluster, in which the mass distribution inferred from gravitational lensing also appears more consistent with the presence of Dark Matter than with a modified gravity interpretation. However, what is often neglected in discussing this issue is that the clusters’ collision speed is surprisingly high for Dark Matter cosmology, but more reasonable in MOND. The Bullet Cluster thus neither uniquely supports nor uniquely falsifies either of the two competing concepts.

In a sense, Dark Matter and MOND have distinct regimes of applicability. The former is more successful on larger scales, while the latter is most successful on smaller scales, being able to predict galaxy dynamics and also offering an explanation for several observed scaling relations between galaxy properties. Once we attempt to expand the models beyond their respective regimes of primary applicability, problems appear. Dark Matter models suffer from a number of “small-scale problems” on the scale of galaxies and their satellite galaxy populations. MOND cannot be successfully applied to large systems of galaxies or the universe as a whole.

This apparent complementarity could offer a way out of the current conceptual stalemate. Some physicists are developing models that join the two seemingly incompatible approaches. One example is Superfluid Dark Matter, developed by Justin Khoury at UPenn. In this model, Dark Matter around galaxies phase-transitions into a superfluid, which gives rise to a MOND-like behavior for ordinary matter, but only in this region. Interestingly, this results in some predictions that are distinct from those of both “pure” Dark Matter and MOND, making this a testable alternative born out of two competing concepts.

Laboratory searches for Dark Matter are important. They hold the potential for a groundbreaking detection confirming the hypothesis. However, detectability is not falsifiability. What if we do not succeed in detecting Dark Matter? The reason could be that Dark Matter really does not interact with ordinary matter except gravitationally, or because it does not exist. One can imagine falling for a sunk-cost fallacy in such a case, by sticking with the Dark Matter hypothesis because of the amount of resources already invested in it. To prevent such a risk, we should already be considering and developing alternative approaches. Maybe the best argument for this is the predictive power of MOND. Since this is an empirical success linking the observed distribution of stars and gas directly to their velocities, it will have to be understood in any successful model of cosmology, including those based on Dark Matter. Therefore research into models based on the modified gravity concept are a worthwhile addition to the Dark Matter approach. A diversity of ideas (as well as people) should be cherished and supported. Ultimately, building on the successes of both the Dark Matter and the modified gravity approach might offer the crucial insights necessary to unravel the composition of the universe and the nature of gravity.

Latest Releases
Join the conversation

Joe Bakhos 11 April 2018

I would like to ask that you consider the following alternative gravity theory as regards dark matter. At the bottom of the page given in the link, there is also a discussion of gravitational lensing and how this theory deals with it.

I think that at a certain galactic distance, gravity reverses and the galaxies begin pushing against each other. This would do away with cosmological expansion, dark matter, and dark energy. This is a claim that can be easily tested:
A revised gravity equation looks like this (I have made an adjustment compared to my last version):

F = (1.047 X 10^-17) m1m2 [-cos(Θ)] / r^2 where tan Θ = r / (1.419 X 10^22)

By playing with the constants, this equation can be fitted and tested against the data of galactic motion. It means that at a certain distance, gravity will reverse and the galaxies will be pushing against each other. This pressure against each other does away with the need for dark matter or dark energy in cosmology.

So the equation can be tested against current data to see if it fits. This equation also predicts that galaxies near the edge of the universe will be deformed -- concave with the concavity pointing towards the center of the universe.

This equation also predicts the existence of isolated galaxies that are far away from other galaxies, that would behave normally without the need to posit dark matter. An example of this type of galaxy is NGC1052–DF2 . Talked about in this article:

So what I am asking is very precise, very narrow, very testable: Someone please test this equation to see if slight adjustment of the constants will account for galactic motion or not. If it does, then proceed to the rest of the theory.

If it cannot, then the theory can be dismissed. Either way, I would like to know -- but I would not be convinced with a simple "absurd!" or dismissal unless it has been tested out.

If it is true that the motion of galaxies can be modeled in this way, I would ask that you take a look at the explanation in this theory:

David Brown 24 March 2018

"What if Dark Matter does not exist?" I have suggested to Professor Milgrom that relativistic MOND is simply the alleged Fernández-Rañada-Milgrom effect, i.e., replace the -1/2 in the standard form of Einstein's field equations by -1/2 + dark-matter-compensation-constant, where this constant is approximately sqrt((60±10)/4) * 10^-5 — however, Professor Milgrom seems to believe the Gravity Probe B science team. I suggest that the Gravity Probe B science team misinterpreted their own experiment. Have pro-MOND researchers carefully studied this issue?
Everitt, C. W. F., M. Adams, W. Bencze, S. Buchman, B. Clarke, J. W. Conklin, D. B. DeBra et al. "Gravity Probe B data analysis." Space Science Reviews 148, no. 1-4 (2009): 53-69.
I suggest that the problem with "patch potentials" is merely an imagined explanation for an actual detection of the alleged Fernández-Rañada-Milgrom effect. I have suggested to the Gravity Probe B science team that they should investigate the "patch potentials" problem in the manufacturing process for the 4 ultra-precise gyroscopes.