Sunday, September 04, 2005

Dark matter and 3 extra dimensions

Philip Ball describes in the New York Times as well as

a recent speculative preprint

in which Bo Qin, Ue-Li Pen, and Joseph Silk study some quantitative features of Spergel and Steinhardt's model of self-interacting cold dark matter - one of the popular models that can explain that the dark matter halos don't seem to be cuspy, which is a wrong prediction of the older models of cold dark matter theories.

It is argued that the observed data are exactly matched if there are three extra large ADD-like dimensions whose size is 1 about nanometer. Below this distance scale, the gravitational force would intensify from the 1/r2 behavior to 1/r5. This would be pretty hard to measure with the tabletop experiments. ;-)

In these extra large dimensions scenarios, you must think about the ADD braneworlds. For example, type IIA on a six-torus with orientifolds and D6-branes - something that you can learn from Barton Zwiebach's textbook - could, in principle, allow you for such a strange arrangement of the dimensions in which three of them are large.

They also advocate the mass of the dark matter particles to be 0.3 microelectronvolts (the Compton wavelength is around a meter), a fine value for axions. You may think that this is very light; but because the sub-nanometer gravity is so strong in their model, the (purely gravitational) self-interaction cross sections are large enough. On the other hand, at galactic distances, the self-interaction becomes weak which solves some difficulties of Spergel and Steinhardt's model to account for the absence of certain gravitational lensing observations, and for some galactic X-ray data. Three large extra dimensions seems to be the unique discrete number in which all things may be resolved, the new guys argue.

Silk et al. explain that they may thus be capable to almost prove string theory by hardcore data which may be more straightforward than the arguments based on uniqueness of quantum gravity and the incredible mathematical beauty of string theory. ;-) Their proposed scenario, if true, would probably imply a lot of new physics to be seen at the LHC, too.

Can you actually construct a stringy model that has such a light axion?


  1. Dear Lumo,

    Have you seen yet?

    I'd be glad for a comment by you.

    Best wishes,

  2. Dear Nigel,

    that article involves many ideas. The holographic principle is correct in quantum gravity, at least in some contexts.

    Maldacena's correspondence is correct - and even more reliable and it's one of the reasons why the previous paragraph is true.

    Neither the holographic principle nor anything else leads us to modify the rules of quantum mechanics.

    No consistent deformation of the quantum mechanical postulates is known and there are many reasons to think that none is possible mathematically.

    I did not understand how these things should be related to kinetic theory of radiation.


  3. Dear Lumo,

    Thanks for your comment. I've summarised the idea in this illustration:

    I agree that the rules of quantum mechanics do not need modification. What seems to be needed however is a clear, testable way to bring in gravity.

    It seems that the spacetime fabric can be viewed physically as a form of radiation, pushing masses. Where shielded from this by another nearby mass, you get pushed towards that mass by the asymmetry.

    Best wishes,

  4. Nigel, I saw your page I am amazed about how one can delude himself into believing that a result with an adjustable parameter is a prediction. I refer to equation 6, where Newton Constant is derived from Hubble constant AND a undetermined "r local" (plus an unexplained use of e^3)

    I am even more surprised by searching in google and noticing that you have already been around for years with this kind of equations and nobody has asked you to clarify the derivation.

  5. dear Leucipo,

    I find it easy to "delude" myself into accepting that the base of natural logarithms is not an adjustable constant.

    The easy way to remember it to 9 decimals is as 2.7 followed by 1828 twice:

    e = 2.718281828......

    The local density of the universe is also easy to determine from the measured masses and separation distances of galaxies. I'm well aware that some data for density requires the Hubble constant. This is why I choose to test the model using consistent data for both Hubble and density of the local universe.

    By the way, the early universe was denser (like my earlier critics!), and we see the earlier universe as a function of distance because of spacetime.

    If you want to consider the quality of responses to my model, consider the guy who disproved pushing gravity by claiming that an unbrella is so solid it stops space pressure pushing down. He didn't even know that the radius of a nucleus is 10,000 times less than the whole atom, thus the nucleus has an area 100,000,000 times smaller in cross-sectional area than the whole atom, or that quarks are very much smaller than nucleons in the nucleus.

    The moderator of the argument then closed it down, saying that the unbrella disproved the model.

    You will not find that you win a Nobel Prize by a disproof of a new idea using a false argument, however ingenious it it. Maybe if you can do something a little more constructive (and much harder) than sneer, you might. I won't because I'm not interested in prize funds based on profit making in the Crimean War.

    Best wishes,

  6. Nigel, Your parameter is adjustable in three ways:

    - r_local itself. How do you choose its value?
    - base and exponent in the e^3 expression. Why not pi^7 or 3.3^46.4? if you have a theory to justify it, it is not explained there in the webpage.

  7. Hmm Ok I noticed a better (less coloured) explanation and it is true that e^3 is not random after all. You should be more careful with colours in your main page, I missed it and some others could miss it too.

    Still, what about r_local?

    I won't because I'm not interested in prize funds based on profit making in the Crimean War.

    As anarchist, I am not morally justifyed to raise objections to the invention of the dynamite. Albeit I can agree on your objection agains Guvernment waged wars such as Crimean one.

  8. Dear Leucipo,

    "Leucipo said...
    Hmm Ok I noticed a better (less coloured) explanation and it is true that e^3 is not random after all. You should be more careful with colours in your main page, I missed it and some others could miss it too.

    "Still, what about r_local?"

    The local density of the universe, symbol rho, is the density of the universe within the local supercluster.

    As you look further outward beyond that, the density gets higher. The problem is that most of the matter exists at the furthest distances. To get a simple value of this higher density is not a simple matter.

    The first approach was to set up an equation for the variation of density with distance (see notes in: Nigel Cook, ‘Solution to a Problem with General Relativity’, CERN Document Server paper preprint EXT-2004-007).

    You would then have to calculate the inward pressure contributions from a sequence of shells surrounding you, each at progressively higher density.

    An easier way to obtain the same result is the mass continuity equation, based on Green's theorem (related to Gauss's law).

    As matter disperses outward, the density fall is related to the amount of matter crossing a given spherical surface area. You can plug the Hubble law (v = HR) into the mass continuity equation.

    Since it is the nearby (local or near 15 Gyr after big bang) density of the universe which is estimated by astronomers, not the density at an arbitrary distance (time in the past), we have to multiply the local density up by the right factor to get the higher density which applies to the large distances where most of the gravity pressure is generated.

    The result of e^3 agrees with the result from detailed calculations.

    Best wishes

  9. I hate astrophysics. Not that I do not enjoy particular papers, as Phys Rev 73 pg 803 (Alpher Bethe Gamow) or some bound extracted from observations, but I am not able to sail confortably across astro-ph world.

    Said that, I notice that lists a quantity rho_c=3 H^2 / 8 pi G, named the critical density of the universe. I guess it is the density corresponding to flatness, but whatever, the point is that your result can be recasted as
    rho_c = 2 e^3 r_local
    r_local/rho_c = .5 e^-3 = 0.02489...
    and it seems to me that this is the apropiate way to discuss it, instead as of a prediction for G_N or H_0.

    Your concept of "local" is also very confusing for a casual reader. The point where you stop seems a bit arbitrary. Note that the pdf page above quotes a baryon (aka visible?) density quotient against rho_c of 0.044, far from your estimate.

  10. Dear Leucipo:

    I've changed the page to make it less confusing to the casual reader. The critical density in general relativity is the 3/8 factor you mention, which creates the unconfirmed "dark matter" prediction for density.

    Notice I have a list of predictions near the top of the page, which includes the fact that the critical density (based on the assumption that there is no mechanism of gravity) is out by 0.5e^3 which is a factor of 10.

    What general relativity does is to omit a mechanism. This assumes that the furthest galaxies, receding at light speed, are being pushed back towards us (slowed down by gravity).

    In 1996 via Electronics World I pointed out that the furthest galaxies are not going to be slowed down, because the push of gravity requires that you are surrounded by a large amount of receding matter. The universe is like a 10^55 megatons space burst nuclear explosion, so far as gravity is concerned.

    The 'warped space' comes from the radial contraction of masses due to this space pressure, not from mathematical equations, which are just modelling what occurs. Popular accounts of general relativity tend to use non-causal interpretations. I have pointed out that space fabric does not expand. What happens to it in the big bang? It moves inwards, pushing things together, gravity.

    The furthest receding matter or radiation is not slowed down by gravity because gravity is not a pulling effect. It is purely pushing, and that requires that you have an expanding universe around you, which doesn't apply to the outer most edge of an space burst explosion.

    Thus, the most distant supernovae continue unimpeded. This was discovered experimentally by Dr Perlmutter in 1998, about a year after the prediction. However, the scientific journals still wanted to ignore the mechanism.

    What has happened is that instead of admitting that gravity doesn't slow down the most distant expansion, they have instead invented a new force that offsets the supposed gravity pull back, allowing the supernovae to continue as if there were no gravity.

    In the same way, when the Earth centred universe failed to account for the motion of planets, epicycles were invented to "fix" the problem.

    Best wishes,