One Law to rule them all, One Law to guide them,
One Law to form them all and in the dark halo bind them.


Galaxies appear to obey a single universal effective force law.


Early indications of this have been around for some time. It has become particularly clear in our work using near-infrared surface photometry to trace the stellar mass distribution of late type galaxies (SPARC). It takes a while to wrap our heads around the implications.


The observed phenomenology constitutes a new law of nature. One Law to rule all galaxies.


The Astrophysical Journal just published our long and thorough investigation of this issue eponymously titled One Law to Rule Them All: The Radial Acceleration Relation of GalaxiesIt includes this movie showing the build-up of the radial acceleration relation in the data.

So far, the ubiquitous effective force law had only been clearly demonstrated in rotating galaxies. Federico Lelli and Marcel Pawlowski went to great lengths to also include pressure supported galaxies, from giant ellipticals to dwarf spheroidals. They appear to follow the same effective force law as rotating galaxies.

The Radial Acceleration Relation defined by rotating late type galaxies (blue points) is also obeyed by early type galaxies, regardless of whether they be fast rotators (orange points) or pressure supported slow rotators (red point) or dark matter dominated dwarf spheroidal satellite galaxies (grey and green points).

This is not a fluke of a few special galaxies. It involves galaxies of all known morphological types spanning an enormous range in mass, size, and surface brightness. I have spent the last twenty years adding new data for all varieties of galaxy types to this relation in the expectation that it would break. Instead it has become stronger and clearer.

Understanding the observed relation is one of the pre-eminent challenges in modern physics. Once we exclude metaphysical nonsense like multiverses, it is arguably the most important unsolved problem. Why does this happen?

The usual ad hoc interpretation of rotation curves in terms of dark matter does nothing to anticipate the observed phenomenology, which is in fact quite troubling from this perspective as it requires excessive fine-tuning. This has been known (if widely ignored) for a while, but doesn’t preclude the more rabid advocates of dark matter from asserting that it all comes about naturally. Lets not mince words here: claims that the radial acceleration relation occurs naturally with dark matter are pure, unadulterated bullshit fueled by confirmation bias and cognitive dissonance. Perhaps dark matter is the root cause, but there is nothing natural about it.

The natural explanation of a single effective force law is that it is caused by a truly universal force law.

So far, the theory that comes closest to explaining these data is MOND. Milgrom, understandably enough, argues that these data require MOND. He has a valid point. It is a good argument, but does it suffice to overcome the other problems MOND faces? These are not as great as widely portrayed, but they aren’t exactly negligible, either. I tried to look at the problem from both perspectives in this review for the Canadian Journal of Physics. [Being able to see things from both sides is an essential skill if one is to be objective, an important value in science that seems disturbingly absent in its modern practice.]

MOND anticipates an asymptotic slope of 1/2 at low acceleration (gobs ~ gbar1/2). In the figure above, the data for the faintest (“ultrafaint”) dwarf spheroidals show a flattening in the empirical law at low accelerations that is not predicted by MOND. Perhaps the underlying force law is subtly different from pure MOND? On the other hand, weak lensing observations show that the MOND slope extrapolates well to much lower accelerations.

It is possible that the data for ultrafaint dwarfs are in some cases misleading. Are these objects in dynamical equilibrium (a prerequisite for analysis)? Are they even dwarf galaxies? Some of the ultrafaints are not clearly distinct objects in the sense of dSph satellites like Crater 2: it is not clear that all of them deserve the status of “dwarf galaxy.” Some are little more than a handful of stars that occupy a similar cell in phase space – perhaps they are fragmentary structures in the Galactic stellar halo? Or the rump end of dissolving satellites? This is anticipated to occur in both ΛCDM and MOND. If so, their velocity dispersions probably tell us more about their disruption history than their gravitational potential, in which case their location in the plot is misleading.

Detailed questions like these are the subject of much current research. For now, lets take a step back and appreciate the data for what they say, irrespective of the underlying theoretical reason for it. We’re looking at a new law of nature! How cool is that?

Ash nazg durbatulûk, ash nazg gimbatul, ash nazg thrakatulûk, agh burzum-ishi krimpatul.

7 thoughts on “One Law to Rule Them All

  1. “MOND anticipates an asymptotic slope of 1/2 at low acceleration (gobs ~ gbar1/2). In the figure above, the data for the faintest (“ultrafaint”) dwarf spheroidals show a flattening in the empirical law at low accelerations that is not predicted by MOND. ” This problem arises from the proposition that gobs =vobs^2/r. This proposition accepts Keplerian dynamics and is valid in the Dark Matter Paradigm. Accepting it also removes the BTFR from Mond.


    1. Just to expand further, once you derive vobs^2=sqrt (GMa) you have eliminated r from the equation and cannot re-introduce it ad hoc. You have to derive the acceleration dynamics by other means such as differential calculus. The act of re-introducing r is accepting the proposition that Keplerian dynamics is valid in the system.


  2. Stacy, you mentioned elsewhere TeVeS as a covariant version of MOND. This is just to ensure that you’re aware of John Moffat’s MOD, another variant that’s been under development since 2005. Sabine summarized it here: . John mentions you in a recent paper comparing his MOG to your Law: arXiv:1610.06909.
    Check out his pub list: . He also addresses Train Wreck, Bullet, Abel 1689…
    Really appreciate your blog!


  3. Thanks. I think we are in a period where we need to try all these things out, even if it amounts to a grand version of the parable of the blind men and the elephant.


  4. I have given this matter some attention from the point of view of the underlying symmetry groups, and how one law of gravity can also be reconciled with quantum mechanics. It has taken me years to cut through all the crap and find the essential content, but I believe I have now done it, and you can read about it on my blog if you wish. The mathematical foundations are now completely clear and consistent across the board from the internal structure of the proton up to the scale of the whole universe. The derivation of all the empirical theories with all their differential equations is lacking, and will take some time. But it is already clear that back-of-an-envelope calculations solve all the big problems, including quantum gravity, dark matter, the origin of mass, the fine-tuning problem, the measurement problem and the interpretation of quantum mechanics. This is an outrageous claim, of course, and you must not believe me until you have read the evidence.


    1. I’m not competent to assess your theoretical paper, but I would just point out that if you really want to get people’s attention, explaining the anomalous magnetic moment of the muon is one great way to do it. I couldn’t find anything about muon g-2 in your paper on fundamental constants.


      1. I am sure you are right, but unfortunately I am not competent to do that. I try to stick to my area of expertise, which is a deep mathematical analysis of symmetry. The symmetry groups cannot be put together in the way that is done in the standard model – it is mathematically incoherent, and physically nonsensical. I can then follow this into physics just as far as my undergraduate education in quantum mechanics and special relativity goes, but not much further. I somewhat naively thought that if I could explain the electron/proton/neutron mass ratios to 1/60 of a percent, and predict the mass of the tau lepton to 8 significant figures, that would be enough to grab people’s attention. Apparently not – it just defines me as a nutter, for some reason I can’t really understand.


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