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Question about MOND and gravity

  1. May 2, 2012 #1
    I'm trying to figure out the formula adjustment to Newtonian mechanics using MOND but I'm getting stuck. Wikipedia states:

    "Assuming that, at this large distance r, a is smaller than a0 so: μ × (a/a0) = a/a0"

    Why does 'a' being smaller than 'a0' get rid of μ?
  2. jcsd
  3. May 2, 2012 #2

    Jonathan Scott

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    It doesn't actually say what you've quoted; you've inserted the multiplication sign.

    In MOND, μ(x) is actually defined to be a function of x such that μ(x) = 1 when x is much larger than 1 and μ(x) = x when x is around 1 or smaller.
  4. May 2, 2012 #3
    I am not very familiar with functions like this. That makes more sense

    So what is μ?
  5. May 2, 2012 #4

    Jonathan Scott

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    The MOND scheme only specifies how the interpolation function behaves for large and small x, without giving a specific form.

    For illustration purposes, you could for example use μ(x) = x/(1+x).

    The whole idea of a function which effectively cuts off the effect at a certain acceleration is very odd anyway. MOND is typically used to describe how stars move when in a very weak gravitational field at the edge of a galaxy, but if you consider the atoms within the star, they are all subject to much greater accelerations due to the star itself. This seems to require some sort of magic whereby the motion of the star as a whole is not the same as the average motion of its component atoms.
  6. May 2, 2012 #5
    The tooth fairy. Seriously.....

    The idea behind MOND is to insert a fudge factor into the gravity equations and see if you can get the observed behavior of galaxy rotation curves. Now if it turned out that there was some pattern in that fudge factor, you could then start thinking about what that fudge factor could be.

    But it hasn't worked out. It turns out that every galaxy seems to have a different fudge factor, which makes dark matter a more convincing explanation for what is causing the rotation curves.

    There's something one of my advisors called the "tooth fairy rule." Which is that in any theoretical astrophysics paper, you are allowed one wave of the tooth fairy's magic wand. If you assume one crazy thing and if everything works, you win. Dark matter is another tooth fairy, but you just wave it once and lots of problems disappear.

    The problem with MOND is that right now you need to wave the magic wand several times.
  7. May 2, 2012 #6
    Okay, I'm going to look at this again.
  8. May 2, 2012 #7
    That much I understood, it would be interesting to see (on average) how much that 'fudge factor' is. If it does somewhat represent the actual observations for the speed of stars (which to some degree it does) then it is at least a place to start to help understand how gravity works on the galactic scale.

    The dark matter theory seems a little shaky too though with it's "halo" and in essence is just another 'fudge factor' is it not to preserve Newtonian Mechanics?
  9. May 2, 2012 #8


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    Except that as has been pointed out the value is always different and there doesn't appear to be any pattern at all.

    What does newtonian mechanics have to do with anything? And as twofish stated, one wave of the wand is ok, but many many waves is obviously not working. Dark matter explains the most amount of observations and is the one that makes the least amount of wand waving, so currently there's not much of a reason to think it's mistaken entirely.
  10. May 2, 2012 #9

    Jonathan Scott

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    Where did you get that from?

    The really weird thing about MOND is that it actually works for a huge range of different galaxies using the same a0 value, and correctly predicted the results for Low Surface Brightness (LSB) galaxies before any measurements had been made on them.

    However, it doesn't work at larger scales (such as galaxy clusters and interacting galaxies) nor at smaller scales (globular clusters within galaxies) without further tweaking.
  11. May 2, 2012 #10


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    http://www.scilogs.eu/en/blog/the-dark-matter-crisis/2011-03-21/question-c.ii-mond-works-far-too-well [Broken]

    Pavel Kroupa is highly enthused over MOND.

    Respectfully submitted,
    Last edited by a moderator: May 6, 2017
  12. May 2, 2012 #11
    I thought MOND was supposed to be a better predictor than the dark matter theory for star velocities in galaxies without screwing up mechanics for smaller systems?

    I thought that was the point of introducing the dark matter into the system, so the laws of gravitation still work without re-inventing the wheel like in quantum mechanics.
  13. May 2, 2012 #12

    Jonathan Scott

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    As far as I know, MOND is extremely successful on the scale of galaxies. The problem is mainly that it is simply an arbitrary rule which has been found to work experimentally, while attempts to find an underlying theory behind it have not been very convincing; even though progress has been made, for example with TeVeS, some of the concepts still seem to violate fundamental physical principles.

    Calculations on the scale of galaxies are typically done using mainly Newtonian gravity theory, with the occasional check to ensure that General Relativity effects are small enough to ignore in specific cases.
  14. May 2, 2012 #13


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    I apologize, I think I misunderstood what MOND was and was thinking of something else. I'll remove myself from this thread now! :biggrin:
  15. May 2, 2012 #14
    No worries. Let's continue the discussion,

    Anyone know how to run the calculations for MONDS?

    In DMT (dark matter theory) it looks like they are just using a certain mass of dark matter outside the galaxies to account for the discrepancies in velocities of the stars and to preserve the laws of gravitation. Does that sound right?
  16. May 2, 2012 #15
    I'm not sure I am getting this, how do the atoms in the star affect the overall velocity of the star? Or are you saying this just a way of looking at the effect of gravity on the scale of the very large vs small and that it seems silly to have different rules for both systems?
  17. May 2, 2012 #16
    In essence, yes. It's just that there is a *lot* less fudging that you have to do to fit the observations. You wave the magic wand once, and not only can you fit galaxy curves, but observations of CMB, and various cosmological quantities make sense.

    But things can change.
  18. May 2, 2012 #17
    True, and looking just at the data that he is looking at, I probably would be too.

    The trouble is that the main reason people think that there is dark matter has to do with large scale cosmology which Kroupa doesn't talk about. Basically in order to get the right lumpiness factor and deuterium abundances, you have to assume dark matter.

    Modified gravity theories don't quite work in that context. One reason for this is that things go in the wrong direction. With dark matter, the denser things are, the weirder things get, whereas with modified gravity, you end up with things getting weirder the less dense things get. This matters for things like deuterium abundances.

    Look at point 9) that Kroupa makes. In order to get the CMB distributions with MOND he has to assume a 11eV sterile neutrino. That's fine, but 1) sterile neutrinos are dark matter and 2) that's another wave of the magic wand, and it's not a small wave. Once you put in a new particle, then you have to recalculate all of the big bang nucleosynthesis numbers.

    What Kroupa is saying is that MOND + a hypothetical particle makes everything work. Trouble is that you can get everything to fit by dropping MOND and just assuming a hypothetical particle, and you save one wave of the magic wand.
    Last edited by a moderator: May 6, 2017
  19. May 2, 2012 #18
    Not quite. The thing about dark matter is that you wave that magic wand once and lots of seemingly unrelated things make sense. For example, there seems to be more deuterium than you would expect if the universe were all "normal matter" and you can calculate the "lumpiness factor" of the universe.

    Galaxy rotation curves are only one "weird thing", and frankly, if galaxy rotation curves were the only "weird thing" that we see, then MOND would make more sense to me than dark matter.

    Also the possibility exists that both are correct (i.e. that there is dark matter and gravity doesn't behave the way we think it does).
  20. May 2, 2012 #19
    I was misremembering something that you seem to have remembered correctly.....

    When people saw that this was like *wow* there might be something here. It's this particular observation that gave MOND quite a bit of credibility for a time.

    Yup. The trouble is that the more "tweaking" you have to do to get things to work, the less strong the theory is. Both dark matter and modified gravity require tweaking to get the right fit with observations, but at this point dark matter seems to require a lot less tweaking than modified gravity, but this is one of those things that could change quickly.

    One other thing about arguments toward elegance is that different people can weight things differently. If someone looks at the data that modified gravity requires less tweaking than dark matter, it can be hard to argue otherwise because these are somewhat subjective.
  21. May 2, 2012 #20
    The other problem is that Krupa seems to misunderstand the applicability of LCDM. The idea behind LCDM is that the big bang produced large scale clumps and that these clumps influences where galaxies form. How galaxies actually form is outside of the theory, so LCDM really says nothing about things at small scales.

    No one has been able to reproduce the cosmological observations with only modified gravity (lots of people have tried). Once you assume that some dark matter is necessary, then it becomes easier to assume (unless you have some reason otherwise) that it's all dark matter.
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