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Lee Smolin predicted dark energy back in 1995

  1. May 24, 2003 #1


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    I was just reading a 1995 paper by Lee Smolin
    "Linking topological quantum field theory and non-perturbative quantum gravity"

    not such a catchy title, but contains some surprising things

    We all know the story about how Einstein put Lambda (cosmological constant) in the quations in 1916 and then
    found it embarrassing to have done so. And Lambda went into eclipse for many years.

    The standard story is that in 1998 it suddenly made a comeback because of supernova Type Ia data which showed accelerating expansion.

    then positive Lambda became necessary to make things fit the data. Cosmology underwent a revolution and came out looking quite different.

    Before 1998 people would put Lambda in sometimes and try the model but it wasn't showcased, it was just an optional doodad.
    Or so the story goes.

    But it turns out that Smolin developed a "spin-networks" QG approach in 1995 that absolutely depends on positive Lambda.
    Indeed Lambda is quantized and (in natural units c=G=hbar=1) its reciprocal has to be a positive integer divided by 6pi.

    You remember how the present radius of the observable universe is about 40 billion light years (about 3 times 13.8 billion). the area of that horizon is also quantized, in units of the planck area. It sounds incredible I know. The mind reels. But this paper is turning out to be an important one. The conclusions are seemingly still valid and play a role today.

    Both the event horizon of a black hole and the expanding boundary of the observable universe are quantized areas and the number of planck area units comprised has some information theoretic meaning. Very hard to comprehend.
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  3. May 24, 2003 #2


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    A few weeks ago I calculated the dark energy density in natural units---it was 1.3E-123

    turns out to be an important number which people want to explain and its reciprocal may be an integer (or integer divided by 6 pi)

    Also I happened to calculate that the Hubble time is 8.06E60 in natural. So the current distance to the farthest objects whose light can have reached is is about 3 times that or 24E60----the current distance to the horizon----the radius of the observable.

    So lets get the area, which Smolin was talking about
    by 4pi R^2, 7.3E123

    Oh oh

    6pi times the reciprocal of Lambda is 14.5E123
    (Lambda is 1.3E-123 and you divide 6pi by that and
    you get 14.5E123)

    It is very very strange that
    1. smolin should say the area is an integer
    2 he should also say 6pi/Lambda is an integer
    3. one integer turns out to be twice the other

    normal polite english cannot express how strange this is and how I feel just having uncovered the fact---which smolin doubtless knows, though he said nothing in his 2003 review of QG.

    The present surface area of the observable universe, containing thos objects whose light has reached us, is a certain whole number

    if you multiply that whole number (which BTW we know only approx) by two
    then you get a kind of reciprocal dark energy size, also according to loop q. gravity supposed to be a whole number.

    If that is not a coincidence, but the two are linked, then Lambda is getting smaller as the horizon area expands.

    that would mean that, yes expansion is accelerating, but the acceleration itself is gradually diminishing towards zero
  4. May 24, 2003 #3


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    quotes from Smolin's QG survey

    Smolin's 2003 survey article "How far are we from the quantum theory of gravity?"


    Page 11---he is listing a dozen or so things that a successful QG theory must be able to do---predict certain things, certain logical requirements like background independence.

    Point 5 "Be compatible with the apparently observed positive, but small, value of the cosmological constant. Explain the entropy of the cosmological horizon."

    OK, we hear that. Now on page 24 he is summarizing the 22 main results proven in LQG----it takes four pages and is really impressive, but anyway on page 24 he goes:

    Point 15. The inverse cosmological constant turns out to be quantized in integral units, so that
    k = 6pi/GΛ is an integer. [In natural units G drops out so it is simply that 6pi/Λ is an integer]

    Also there is an interesting treatment of horizons in general including both the cosmological horizon (presumed spherical surface of 40 billion lightyear radius) and black hole horizons (commonly the spherical event horizon surface tho other shapes are possible). there is a Bekenstein entropy formula that depends on the surface area----and it is related to the dimensionality of a hilbert space---measure of information---and these areas are integer multiples of planck area. This paper is a must-read

    Last edited: May 24, 2003
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