Sunday, March 24, 2019

Superfluid Dark Matter [Video]

I am at home with a cold, and so I finally got around to finish this video on superfluid dark matter which has been sitting on my hard disk for a few months.

This is a sequel to my earlier two videos about Dark Matter and Modified Gravity.

For captions, click CC in the tool bar. Will add German captions in the next days. Now I need a few ibuprofen.


  1. Another excellent exposition. The bit with the Alaskan Bernoulli correspondent was funny and effective.

  2. You say that dark matter works better for the cosmological and galaxy cluster scales, but isn't it because these are easier to fit?

    For example, if there are only a few types of clusters and one type of universe to fit, it's easier than finding a fit for gaz-rich/gaz poor, elliptical/spiral, big/small, satellite/not satellite galaxies.

    Since Modified Gravity works for galaxies (that come in many variations) but not for clusters and the universe, by your argument we should try to find environmental explanations to apply it also to clusters and the universe. But you have described the opposite approach.

    Great video by the way. With others, they provide excellent summaries of these issues.

    1. dlb,

      I believe this is a misunderstanding. I did not mean that dark matter works better for cosmological and clusters scales than dark matter works for galaxies. Though this is true, this may well be, as you say, because galaxies are just more complicated. I mean that on cosmological and cluster scales, dark matter works better than modified gravity, whereas on galaxy scales, modified gravity works better than dark matter, where by "better" I concretely mean that it's parametrically simpler.

    2. Yes. Even MOND enthusiasts note that dark matter works well in cosmology and that MOND doesn't.

    3. "For example, if there are only a few types of clusters and one type of universe to fit, it's easier than finding a fit for gaz-rich/gaz poor, elliptical/spiral, big/small, satellite/not satellite galaxies."

      Actually, if you think of all the data in the CMB, it is not easy to fit in the sense that one could fit anything to it. Quite the opposite. On the other hand, the interesting thing about MOND is that (on the scales where it works), it really is one size fits all, i.e. there is one additional parameter, and one gets the same value for it everywhere.

    4. MOND phenomenology is definitely real. However, the fact that MOND hasn't been made to work in cosmology might indicate that MOND isn't a glimpse of new physics, but rather that something more conventional explains MOND phenomenology, especially if it can also work in cosmology. Superfluid dark matter might be that something.

  3. Hi Sabine
    Well done! The Video, I mean. This is a short and excellent explanation of superfluid dark matter. Is it possible to get the spoken content of the video as a text file, so I can read it thoroughly with its details?
    Greetings from Switzerland

    1. rhkail,

      I don't have the transcript as a text-file, sorry. But on the youtube page, you can read the transcript. Click on the dots "..." below the video, chose "Open Transcript" and this should open a box next to the video which shows the text. Make sure to chose "English" (rather than automatic English). You can probably copy & past this if you want (haven't tried).

  4. I have seen this idea in a couple of other contexts. First one I remember is from Dirac, early 1950s. He posited a fixed relation between the An potential of electrodynamics and a vacuum super-current, thus giving the potential a fixed gauge. I'm sure something similar is going on here (gauge fixing). I read the Dirac work carefully and eventually found it a dead end. One needs gauge invariance for a consistent description of conservation laws. This of course was in the days before general gauge theories had been investigated. I still think you should look at Cooperstock's work on rotation curves. Also it would be interesting to relate the work you mention to the serious problem of energy conservation in GR. I think I will have a look.

  5. Hi Sabine,

    I'm wondering what would be expected in the galaxies if the density of matter was about 100 times what we had expected. Would this change affect the velocity curves of galaxies significantly?

  6. Great video, and I love the Bernoulli story!

    Extra parameters explain everything if one is sufficiently lazy. As von Neumann once said, "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

  7. I would like to submit the polariton for consideration as a process that can support the superfluid that you are now considering as dark matter. The polariton in dark mode has been found to produce negative mass.

    The polariton is ubiquitous in nature and is not solely confined to exist in cavities. Polaritons will form on the surface of any type of structure from dust to metalized ultra dense matter inside a wide variety of celestial bodies.

    Also being coherent, it could support a mechanism that gives photons positive mass.

  8. I think you are a gifted communicator.

  9. There are some cross currents of physics here. The Lagrangian for gravitation may be thought of as L_g = G(\bar ψ)ψ(\bar ψ)ψ. There is also the theory of superconductivity as Bogoliubov terms for a quartic theory of fermions. Finally there is the Thirring fermion theory, where a quartic theory with a scalar φ ~ exp[(\bar ψ)ψ] produces the sine-Gordon equation in the scalar field φ. The graviton in a gauge-like theory is an entanglement of vector spin 1 fields or gauge bosons, and we can also build the graviton from four spinor fields or fermions.

    The superfluid state from a quartic term in the fermions is transformed with Bogoliubov terms into one that has a quadratic term. This gives a total potential that is Higgs-like. With superconductivity there are optical phonons, and this Higgsian physics breaks the U(1) symmetry of QED. which are QED-like, assume a mass and this breaks the symmetry of the QED optical phonon field. The route to superfluidity is similar. See Ziman's book for this.

  10. any chance you can review conformal gravity and MOND?

    1. @ neo

      You are hitting on a nice topic! Conformal gravitation occurs with the Weyl tensor, usually denoted by C_{abcd}. The full Riemannian tensor is

      Rie = C + ½ (Ric - ¼ Rg)#g + R/24g#g

      where Rie is the Riemann tensor, C the Weyl tensor, Ric the Ricci tensor, R the Ricci scalar and g the metric tensor. The # is the Kulkarni-Nomizu product. Consider a spacetime where there are no sources of mass-energy.. The Einstein field equation R_{ab} - ½ Rg_{ab} = 0 so the spacetime in an Einstein space or the Ricci curvature is entirely due to the Ricci curvature. It is then not hard to see the Riemann tensor consists then of the Weyl tensor plus metric terms times the Ricci curvature. The action then consists of the standard S = ∫d^4x√g R and the action

      S = ∫d^4x√g C_{abcd}C^{abcd}.

      An interesting equation to emerge from this is the Bach equation

      ∇_a∇_dC^{abcd} + ½R_{ad}C^{abcd} = 0,

      where the Ricci tensor is an eigenvalue of the second order covariant differential of the Weyl curvature.

      The complexified form of the Weyl tensor splits this into two parts. Then for any shearing that exists in spacetime the C and C^* have opposite shearing. This means the phase space volume is preserved and conformal spacetimes obey a general form of the Huygens principle.

      Now write C_{abcd} = C^0_{abcd} + δC_{abcd}, where δC_{abcd} is a quantum correction. The Lagrangian C_{abcd}C^{abcd} will then have

      C_{abcd}C^{abcd} = C^0_{abcd}C^0^{abcd} + 2C^0_{abcd}δC^{abcd} + δC_{abcd}δC^{abcd}.

      The first term is the classical background. The next is the classical background with a graviton and the last is for two gravitons in an interaction or entanglement. This term has connections to the Hirzebruch characteristic and is a topological quantum number. At high energy the last term may dominate and the classical background is less important. There are stability issues though. Now if the graviton is in turn an entanglement of two spin 1 field, such as with gravity QCD correlation ideas of Bern et al, then this is a sort of quartic field term. It then will have for lower energy as the gravitational sector approaches classicality some Higgsian-like physics. This may even by a form of some symmetry broken gravi-field.

      Sorry to get technical, but there is no other way I can see to discuss this. This occurs I think for the transition to classical gravity. Maybe this has something to do with Bee's superfluidity and MOND-like gravity. This is connected to a whole lot more! It gets into Bott periodicity of symmetries, the simplex geometry of quantum mechanics and spacetime and so forth.

  11. In the video, at about 3:19, you mention that the correlations between the dark matter particles can span a whole galaxy. Would these correlations be instantaneous or propagate at light-speed?

    1. Correlations do not propagate. The statement does not make sense. You may ask at what speed perturbations propagate. They propagate at whatever is the speed of sound in the medium. It is always below the speed of light.

  12. Sabine, months ago I read the superfluid dark matter model that you and your grad student devised, but it basically went in one ear and out the other, with only the most superficial comprehension. Heading for the launch point of my afternoon bike ride, and having quickly scanned the paper's abstract beforehand, I came up with what I thought was a layman-friendly interpretation of yours and possibly other similar models. In condensed matter systems quantized phonons (sound vibrations) are exchanged between constituents of the superfluid (hopefully a correct description). Now, the putative dark matter particles couple to baryonic matter only via gravity, and presumably to each other also via gravity (I think that's assumed). So, my guess is that in superfluid DM models there is a net repulsive force between DM particles in the superfluid phase that mostly, or entirely, cancels out the gravitational attraction between the DM particles. The net result is the Newtonian potential of the DM in the condensed region is largely, or entirely, cancelled out and standard gravitational physics is restored. This phonon-mediated repulsive force presumably would be the "Scalar field" in yours, and maybe other similar models.

    I'm going to watch a Youtube video by Justin Khoury on superfluid DM that hopefully will clarify how this approach works, and enable me to truly understand your model, when I read it afterwards.

    1. David,

      The superfluid particles need to have a self-interaction otherwise they will not condense. They also couple to baryons in a non-gravitational way, this is what causes the appearance of an excessive gravitational force. The phonons are perturbations in the phase of the scalar field. (Or in one of the components of the vector field. If you have sufficiently many symmetries, the distinction doesn't matter all that much.)


    What about this sabine?

    "“Ironically, the lack of dark matter in these UDGs strengthens the dark matter theory. It proves that dark matter is a substance that is not coupled to normal matter, as both can be found separately.”

    “The discovery of these galaxies is difficult to explain in theories that change the laws of gravity on large scales as an alternative to the dark matter hypothesis.”


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