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Layzer's Arrow and Dark Energy

  1. Mar 31, 2013 #1
    David Layzer wrote an article for Scientific American that explained the origin of order in the universe from the difference between actual and potential entropy. The graph he used showed actual and potential entropy increasing as straight lines with a growing gap between them over time. If we accept this theory, would the discovery of Dark Energy and the increasing rate of expansion change the straight line of potential entropy to a more sharply upward curving line with a corresponding similar change in the information curve?

    This link explains what I am asking about:

  2. jcsd
  3. Mar 31, 2013 #2


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    My understanding is that David Layzer was born in 1925 and as a professor at Harvard he was interested in philosophy and in teaching methods that encouraged students' self-expression and creativity while avoiding the use of things like midterm and final exams. His approach to cosmology may have been somewhat original/intuitive/speculative/philosophical. But in 1975, when he wrote his Scientific American article The Arrow of Time the field of cosmology was, I believe, much more freely speculative and philosophical (less constrained by observational data) than it is today.
    In any case I do not know very much about Layzer's cosmology ideas.

    When I looked at what seems to be a graph from his 1975 SciAm article, I saw it showing straightline conjectured increases in things that cannot so far be reliably measured namely the "potential entropy" and then subtracted off a linearly growing "negative entropy" (the formation of structure like galaxies etc.) giving another straightline growth of the conjectured real entropy.

    So it seemed that he was talking about stuff that we have not succeeded in measuring and which have extremely fuzzy meanings so far, if they mean anything. And if things like that were eventually measured and given rigorous meaning they might not turn out to be growing linearly with constant slope thru all history. So there is a kind of schematic philosophical non-quantitative simplification going on.
    However he could be seen as pointing to a quite valid area of modern investigation!

    I think the best way to treat his 1975 SciAm article would be to set it aside and look at current research into the same or related topics.

    In order to make progress along Layzer's lines, at a quantitative observational level, one would need to define the geometric entropy. (In other words, since the geometry of the universe is described by the gravitational field, the gravitational entropy.)
  4. Mar 31, 2013 #3


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    There's a related paper that came out this year. I started a thread about it:

    It's about the entropy of the gravitational field. People are still searching for a satisfactory definition of that, which will allow it to be measured and assigned a definite value.
    When that goal is achieved, the gravitational entropy will be a really major factor in the overall entropy--a key player.

    Here's a brief quote from the abstract of the Clifton Ellis Tavakol paper:

    "For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs."

    This is the opposite from what we ordinarily expect from the matter sector. Just looking at matter in a fixed geometry we associate entropy with disorder, the absence of structure. I think having assimilated Layzer's ideas you may already be well aware of what I'm saying, namely that we usually associated ordered STRUCTURE with negative entropy. But under the influence of gravity ordered structure in the universe's matter sector has GROWN.
    So this presents a seeming paradox, the structure formation paradox or puzzle. In order to resolve it we need a definition of entropy in the geometry sector according to which the formation of structure has the opposite effect! Namely the formation of structure must cause the gravitational entropy to increase!

    ==quote Clifton Ellis Tavako http://arxiv.org/abs/1303.5612 ==
    A key question in cosmology is how to define the entropy in gravitational fields. A suitable definition already exists for the important case of stationary black holes [1], but in the cosmological setting a well-motivated and universally agreeable analogue has yet to be found. Addressing this deficit is an important problem, as in the presence of gravitational interactions the usual statements about matter becoming more and more uniform are incorrect. Instead, structure develops spontaneously when gravitational attraction dominates the dynamics [2, 3]. This behaviour is crucial to the existence of complex structures, and indeed life, in the Universe. The question then arises, how can evolution under the gravitational interaction be made compatible with the second law of thermodynamics? If the second law is valid in the presence of gravity, such that entropy increases monotonically into the future, then the current state of the universe must be considered more probable than the initial state, even though it is more structured. For this to be true, the gravitational field itself must be carrying entropy.
    For a candidate definition of gravitational entropy to be compatible with cosmological processes, such as structure formation in the Universe, it needs to be valid in non-stationary and non-vacuum spacetimes. We will argue that an appropriate definition of gravitational entropy should only involve the free gravitational field, as specified by the Weyl part of the curvature tensor, Cabcd [4], and that a particular promising candidate...
    Last edited: Mar 31, 2013
  5. Mar 31, 2013 #4


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    To put it in basic intuitive terms, I think what Clifton Ellis Tavakol are saying is this: Total entropy consists of two parts, matter entropy and the entropy of the geometry that matter lives in.

    In a fixed geometry we are used to thinking of matter entropy as being low if it is clumped together and increasing as it spreads out. Entropy increases as the matter becomes more uniformly spread out.

    But with changing geometry, they suggest that geometric entropy measures how messed up the geometry is. How wrinkly and glitchy and clumpy. So low entropy geometry corresponds to very smooth even geometry.
    What astronomers call "structure formation" increases the geometric entropy.

    Now this much is just verbal imagery and could have been arrived at many decades ago. What is new about the CET paper? I think it is just that Clifton Ellis Tavakol are proposing a specific way to measure how messed up geometry is---they have a specific quantitative way of defining the gravitational entropy.
  6. Apr 1, 2013 #5
    Where I am going with my question...

    Thanks, Marcus. I will spend some time looking at the links and rereading what you have posted.

    I am very much aware of the role of gravity in negative entropy. My understanding is that after the initial expansion and cooling from the Big Bang the universe was particles, hydrogen, and oxygen with little structure. Gravity was what caused the initial structures, large hydrogen and helium burning stars, to form. From these came the other elements, the next generations of stars, and eventually galaxies and mega-clusters. This led to a very active period of star creation which is now slowing down. This is largely driven by gravity.

    Our solar system formed shortly after the period when Dark Energy begins to accelerate the expansion of the universe about 5 billion years ago. Our solar system is , of course, a case of one but is it a coincidence that life, another example of negative entropy, came into existence on our planet during this period? In other words, could there be some relationship between the increasing growth of negative entropy (about which I am asking) and the ability of life to come into existence?

    I know this is complete speculation but this would imply that the ability for information to accumulate in matter (a definition of life) is tied to properties of space that are evolving as the universe ages.

    A more mundane explanation would simply be that our solar system and Earth with life came into existence after much of the turbulence and violence of our galaxy had diminished. So the timing is perhaps not so unusual.
  7. Apr 1, 2013 #6
    Not sure I am quite following...

    The distinction between geometric and matter entropy.

    If matter entropy get lower under influence of gravity, then geometric entropy get greater?

    Wouldn't that be Dark Energy?
  8. Apr 1, 2013 #7


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    Nope. The geometrical entropy gets greater when matter collapses in on itself when dark energy is small. It gets greater when matter spreads apart and becomes diffuse when dark energy is large.

    So dark energy critically influences the behavior of geometrical entropy. It doesn't make sense to think of dark energy as a result of gravitational entropy.
  9. Apr 4, 2013 #8

    I definitely mangled my comment but I think you misstated something in yours.

    You say:

    The geometrical entropy gets greater when matter collapses in on itself when dark energy is small.

    It (geometrical entropy?) gets greater when matter spreads apart and becomes diffuse when dark energy is large.

    This seems to be saying geometrical entropy gets greater both when matter collapses and when it spreads apart, when dark energy is small and when dark energy is large.

    Is that what you meant?
  10. Apr 4, 2013 #9


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    Yes. What I meant was that whether entropy increases as a gravitational system changes depends upon the relationship between the matter density and the dark energy density. A large amount of matter density compared to the surroundings and not much dark energy density means it will tend to collapse (and entropy will increase as it does so). A small amount of matter density compared to the surroundings and a large amount of dark energy density (by comparison) will cause the matter to spread apart, and the entropy will increase in that case as well.

    Though I suppose I wasn't entirely thinking correctly: it is clear that the total entropy must increase with matter that becomes less dense in the presence of lots of dark energy, but the entropy of the matter is increasing. It's conceivable that the entropy in the gravitational field is decreasing in this case, just not enough to overcome the increase in entropy of the matter. But either way, the total entropy increases.
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