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Cosmic coincidence spotted

  1. Feb 20, 2008 #1


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    An absurdly large number could hold the key to universal mysteries.

    The secret of the Universe is not 42, according to a new theory, but the unimaginably larger number 10^122. Scott Funkhouser of the Military College of South Carolina (called The Citadel) in Charleston has shown how this number — which is bigger than the number of particles in the Universe — keeps popping up when several of the physical constants and parameters of the Universe are combined1. This ‘coincidence’, he says, is surely significant, hinting at some common principle at work behind the scenes.

  2. jcsd
  3. Feb 20, 2008 #2
    I wanted to ask a separate question about large number coincidences - I hope it's OK to add it to this topic.

    I am a total layman, but have an interest in cosmology. I have been reading about large number coincidences in some books (by Paul Davies, Leonard Susskind and Martin Rees). Each of them lists a number of evidences of "fine-tuning" (e.g. the cosmological constant, the strength of the strong interaction, the ratio of gravity and expansion energy, etc), although they provide differing explanations.

    I also came across on the web a book by Roger Penrose (The Emperor's New Mind) where he discusses the fine tuning of the initial phase space volume to produce a low entropy universe, and calculates the fine tuning to the extraordinary figure of 1 part in 10^10^123 (almost your 122 again, SF).

    Now my question is this. Penrose is a very well-respected mathematician and cosmologist, yet none of the other books mention his calculation (which if correct would add weight to the case each book builds) and entropy is only mentioned briefly. Does anyone know why this is please? Has Penrose's calculation or concept been shown to be in error, or have I totally misunderstood it as having relevance to the question?

    Thank you.
  4. Feb 20, 2008 #3


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    How can it be in error AFAIK no can test it.
  5. Feb 20, 2008 #4


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    Here is a paper by Scott Funkhouser that passed peer-review and is due to be published this year
    A New Large-Number Coincidence and a Scaling Law for the Cosmological Constant
    Scott Funkhouser
    8 pages. Accepted for publication in PRSA
    (Submitted on 12 Nov 2006)

    "An ensemble of pure numbers of order near 10^122 is produced naturally from the fundamental parameters of modern cosmology. This new large-number coincidence problem is resolved by demonstrating implicit physical connections that follow from the standard cosmological model. However, the occurrence of the new large-number coincidence combined with the known coincidence among pure numbers of order near 10^40 poses a distinct problem that is resolved with a scaling law for the cosmological constant that was originally proposed by Zel'dovich."

    I'll reserve comment on this one.
    Last edited: Feb 20, 2008
  6. Feb 20, 2008 #5


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    Sounds like a reprisal of the Dirac Large Numbers Hypothesis
  7. Feb 20, 2008 #6
    The large number 10^123 can be obtained in the quantum cosmology near initial conditions utilizing three copies of the Monster Sporadic Group. At the end of the Planck epoch at 10^-44 seconds the entropy is an orderly: S = pi*22*196883^3 and is determined from the running gauge. The growth of 4D is due to K3xK3 at this point and the 8.07 *10^56 matter fields are designated as vacua since ordinary matter is yet to exist. The 8.07 *10^56 vacua is calculated from a 10^40 relation: hc/2piGmn^2 = 1.6889 *10^38 utilizing the Planck cutoff: hcMpl/epiGmn^2 = 2.7048 * 10^33 g = Mn where the number of vacua = Mn/2mn where mn is the neutron mass (representing the gauge fields). These numbers are available in a calculation of the Monster symmetry below.

    In Planck units we obtain: 196883^3 x 22 > 196883 x 22^3 [8.07*10^56 x 8.07*10^56] = 1.37 *10^123 vacuum density This is due to three copies of the Monster on a 22 dimensional manifold.

    The large number 10^40 is related to the symmetries of the monster (about 8 x10^53) in the following manner.

    The symmetries of the monster can be calculated using the Planck scale as the cutoff:

    (4/a^2)(Mpl^2/me^2)[((Mpl^2/mn^2)^1/65536 -1.00)^-1]^1/2048 = 8.08017424…*10^53

    a = fine structure constant, mn = neutron mass, Mpl = Planck mass
    The neutron provides for the appropriate (quark-gluon) thermal gauge fields.

    The third product term contains an electroweak gauged 4D black hole:

    ((Mpl^2/mn^2)^1/65536 -1.00)^-1 = (((emn)^2 SbhG/2hc)^1/65536 -1.00)^-1

    Where the Bekenstein Hawking entropy Sbh is that of a 4D Schwarzschild mass: Mn = hcMpl/epiGmn^2 = 2.7048 * 10^33 g Also: Sbh = Ss = piMn^2/Mpl^2
    And one can get: Mn/2mn = 8.07 *10^56 binaries
    From this one obtains a Bohr correspondence of semi-classical and classical fields with quantum numbers going large in the N limit where N = 8.07 *10^56
  8. Feb 22, 2008 #7

    I don't think this is the only explanation, as Rees & Susskind admit that their whole idea of a multiverse is speculative and probably never able to be tested.

    Does anyone else know anything about the Penrose computation please (see my original post #2)?
  9. Feb 22, 2008 #8
    Hello, all. The nature article was in reference to the paper
    which was recently accepted for publication.
    I was not aware of Penrose's mention of the large number 10^123 but
    I'll check out the emporor's new mind to see if there is any connection.
    --Scott Funkhouser
  10. Feb 22, 2008 #9


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    Hello Scott!
    We realized that the news item was about your 0611 paper and that it had been accepted by PRSA, see post #4 above. Congratulations!
    Please make yourself at home and feel free to start threads discussing your ideas. We don't necessarily argue or debate. Sometimes a thread will be mostly exposition or motivation for reading a paper. Stuff that has not passed peer-review can sometimes be weeded out, the forum follows mainstream cosmology primarily. But your conjectures have been accepted so that's not an issue. For me personally, you would have to do a fair amount of motivation-talk, at a general audience or non-specialist level, before i was interested enough to delve into your 0611 paper.

    I remember some years back calculating Lambda in terms of the reciprocal Planck area
    and also sqrt(Lambda) in terms of reciprocal Planck length. And getting numbers like 10-123 and 10-61.
    So I am moderately on the look out for numbers like that. But I am also open to the idea that Lambda is not a constant but that the observed effects arise from some other process, or that its value runs with scale and that there is some more fundamental "bare" value of Lambda. So I might need more of a persuasive introduction to your proposed largenumber relationships. Others might be more ready to hop on and ride with you.

    But it would be all to the good if you would take the opportunity of this thread to make a pitch for your idea (or start a new thread with headline of your own choice.)
    Last edited: Feb 22, 2008
  11. Feb 22, 2008 #10


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    Here is a nice series of Penrose lectures at Princeton. Scroll down to Oct 17-22, 2003. I don't remember exactly where he came up with the number, but he was computing the magnitude of the phase space of the BB singularity based on an estimated total baryon number, IIR.


    A more condensed version is at the top of this page.
    Last edited: Feb 22, 2008
  12. Feb 22, 2008 #11
    Funkhouser’s scaling equation (22) is remarkable in that it is possibly directly related to the cosmological scalar roll down from t = 0 ending in the Electroweak epoch at t = 2.52 x 10^-9 s where electroweak gauge symmetry breaks.

    His equation: (h^4 L/G^2c^2)^1/6 ~ nucleon mass (where L is lambda) suggests that there are 6 regions generated by the inflaton potential coming down from the Planck scale. This includes 7 points that bound the scalar which create a Higgs sector of 5 regions and a unification sector next to Planck.

    I think that this is related to the spectral curve generated from a running gauge theory going from electroweak to the Planck energy involving the moduli space of the hidden symmetries of the Monster. (I talk about the symmetries generation of the 3 Monster copies after the Planck epoch in post #6 above and will not reiterate.)

    We can show how (22) above is a scaling argument for the running gauge:

    Before we obtained 1.367 *10^123 (Planck units). At cosmological reheat (a parametric resonance of transition(s) from super cooled to hotter) a single copy of the Monster group degenerates to where it goes from tensor 196883 x 196883 x 196883 196883^2/3 x 196883 x 196883. Where 196883^2/3 is no longer a faithful representation of the Monster. This leaves two tensored copies preserved as a Hilbert space. We can now calculate the absurd QFT vacuum density value:
    196883 x 22^3/(196883^1/3)*22 > 196883 x 22^3 [8.074*10^56 x 8.074*10^56] = 1.0678 *10^120 (Planck units) Again [8.074*10^56] are the matter fields related to the gauge action of a mass obtained from the theory: hcMp/epiGmn^2 = 2.704 X 10^33 g = Mn where since we have neutron mass: Mn/2mn = 8.074*10^56 binaries.
    Whereas at the Planck epoch we had 3 copies of the Monster on a 22 dimensional manifold now we have 2 tensored copies of the Monster on separate 22 dimensional manifolds. This is a Hilbert space in the supersymmetric potential carrying chiral gauge groups from a thermal neutron mass potential. The current vacuum density rho or lambda is calculated from the Planck energy density cutoff (and also be sure to include 8pi back to Planck units from the field lagrangian):
    P = (Mp/lp^3)(1/8pi x 1.0678 *10^120) =1.922 *10^-28 g/cm^3
    If we place this as L in Funkhouser’s equation (22) we retrieve the nucleon mass as the neutron mass mn off by a factor of 4 (not an order of magnitude). In the gauge theory the neutron mass provides the thermal gauge content for 7 QFTs. Each QFT is defined as a spectral peak on a black body curve with 6 regions bounded each of which is related to Funkhouser’s scaling action of (22). See attachment of spectral curve showing 7 transitions or QFTs of the thermal gauge history.

    Attached Files:

    Last edited: Feb 23, 2008
  13. Feb 22, 2008 #12

    Thanks. The reference is pages 441-446 (in the version online at Google Books - but I'm too new to be allowed to post a URL for you). If you get an answer, remember I'm a layperson! : )
  14. Feb 22, 2008 #13


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    ercatli, if you wish, send me the url by PM (see the private messages link in the upper right corner of the screen).
    I will be happy to post the url for you, since it is for something by Penrose.

    I think the limitation on new members posting url is just a pratical way to discourage people who join just so they can advertise their own sites and aren't interested in participating.
  15. Feb 25, 2008 #14
    If you apply a simple dimensional analysis to Funkhouser’s equation (22) from the fore mentioned paper it is difficult to see how one arrives at the scaling argument for the nucleon mass. I believe the relation holds but it is not approximate for the nucleon mass. It is more than likely to be scaling for the Intensity (I) of spectral radiation. For the mn looks like to be very near to the nucleon mass Zeldovich or others took it to mean just that. This is pure coincidence. In my thread #11 above I stated that I was able to obtain the mn as the neutron mass x4 (almost a factor of 4). Large numbers are easy to obtain but the difficulty is navigating the terrain and it is dangerous. I took another look and noticed that the reduced Planck constant (hbar) is what should be used in (22). This still does not change the value that much but it comes out more plausible. If I apply Planck’s law of black body radiation to the area where cosmologic reheat occurs (in my theory at 1.64 *10^16 GeV) I obtain the spectral peak intensity I = 2.77599 x 10^142 (in cgs units). The units are complex which lead me to think that they may be obtainable from relation (22). If one then takes the inverse which is 3.60232 x 10^-143 and takes the 1/6th power:
    (3.60232 x 10^-143)^1/6 = 1.81732 x 10^-24 (cgs complex units)
    This numerical value is very close to the numerical nucleon mass value. The scaling equation using reduced Planck’s constant is:
    (h^4 L/((2pi)^4)G^2c^2)^1/6 = 1.81732 x 10^-24 (cgs complex units)
    This is not a mass value according to dimensional analysis. If we separate L (lambda or rho) from this we get: L = 1.6608 x 10^-28 g/cm^3. This is still superbly close to the value I obtain for the vacuum density 1.9218 x 10^-28 g/cm^3 from the use of Monstrous symmetries in the early cosmology between super cooling and reheating.

    Mark A. Thomas
  16. Feb 25, 2008 #15


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    With a little coaching, I was able to find a large portion of The Emperor's New Mind online as a free sample at Google Books. I had not tried this before and was impressed to see how much is available.
    http://books.google.com/books?id=oI0grArWHUMC&pg=PR14&dq=penrose+emperors+ new+mind&sig=qwSAHnUiAQ_WKYGOnHZFO0yQtX8#PPA443,M1

    To paraphrase Ercatli, go to Google Book Search and search for "penrose emperor's new mind" and then go to "popular passages" and select either p441 or p445.

    This book of Penrose is probably a mixed bag. I happened to read parts having to do with entropy, thermodynamics, cosmology and the arrow ot time. It seemed enlightening and well-written. If I had read parts about the brain and the mind, I might have a different impression.
    Last edited: Feb 25, 2008
  17. Feb 27, 2008 #16
    Just a little more info on the Penrose estimate.

    I came across a reference to it in "The Appearance of Design in Physics and Cosmology" by Paul Davies, in "God and Design" (ed. Neil Manson; Routledge, 2003). You can again read the relevant section on Google books. I can't give you the full URL (I understand why and I agree with that), but here it is without the h.... bit:


    ..... and go to page 157.

    This reassures me. As recently as 2003 Paul Davies thought the Penrose calculation was relevant. But I can't say I fully understand what Penrose is getting at - he seems to be claiming that we live in a minimum entropy universe and that this is important for the evolution of life. I'll have to read more.
  18. Mar 17, 2008 #17
    funkhouser's large numbers

    It strikes me that funkhouser's work gives us a very strong reason for believing that the cosmological constant is not fundamental but is instead scaled to the sixth power of the nucleon mass. Most of the press/blog reviews of his work fail to address that point. He was not the first to suggest sucg a relationship. According to funkhouser's paper, zeldovich and mena-marugan and carneiro have suggested it also.

    I also commend funkhouser for taking a bold stand against political bias on college campi. It takes guts to fight back against faculties that deem people unfit for being a professor if they are not zocialist/marxist/communist.
    hear hear...richard g.
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