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Entropic Accelerating Universe (Smoot et al)

  1. Feb 23, 2010 #1


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    I just posted this on the bibliography links thread. Thought it would be good to post for discussion as well.

    Entropic Accelerating Universe
    Damien A. Easson, Paul H. Frampton, George F. Smoot
    10 pages, 1 figure
    (Submitted on 23 Feb 2010)
    "To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-LemaƮtre equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the temperature intrinsic to the information holographically stored on the screen which is the surface of the universe. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on a surface screen. We consider an additional quantitative approach based upon the entropy and surface terms usually neglected in General Relativity and show that this leads to the entropic accelerating universe."

    Like it or not, Nobel laureate George Smoot (LBL Berkeley) has jumped in bed with Erik Verlinde and is describing an "entropic force" responsible for accelerating expansion. The Smoot et al reference #6 is to Verlinde's recent paper.
    [6] E. Verlinde, arXiv:1001.0785[hep-th].
    Personally I like this a lot.
    I also have a lot of respect for Smoot. In my view, he is the number one Observational Cosmology Nobelist at work today and really prominent and really influential.

    Plus this is a well-written paper. The quality is convincingly high. The kind of thing that helps allay nervous reluctance and kneejerk objections. So it changes the "entropic force" game slightly.
    Last edited: Feb 23, 2010
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  3. Feb 23, 2010 #2

    Physics Monkey

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    I hate to sound like a broken record, but I just don't see what the point of this paper is, like so many other of the entropic force papers. I would really like for anyone out there to tell me something we've really learned from this paper. I honestly can't think of anything, and I'm not trying to be difficult.

    Call me a cynic, but the kind of dimensional analysis carried out in this paper was on the blogs weeks ago, and now we're supposed to get excited because a Nobel prize winner put his name on something? Doesn't it seem a bit circular that we assume an accelerating universe to get a cosmic event horizon to get an entropic force to power the accelerating universe? It really seems to amount to dimensional analysis especially since even here the precise numerical factors still don't work out right. And after all this you still have the cosmological constant problem: naive estimates put it at 10^120 in "natural units" but now we're back to requiring that it's exactly zero and everything is "entropic force"?

    And what's worse in my opinion is that none of this is discussed in the paper. Frankly, I don't agree with marcus that it's well written or clear or that it adds much to the discussion.

    Haha, that was an unusually harsh post for me!
  4. Feb 23, 2010 #3


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    Well you are one of the most knowledgeable of us here. I like your posts and usually find them quite interesting. So that makes your reaction extremely interesting. I'm glad to have it and others surely will as well.

    My point of view is different, of course. From my perspective it is early days and I would not bet either right or wrong at any odds. It's too early to be guessing winners. But I think it's also too early to be declaring losers: saying that the idea is vacuous or will never work or is absurd.

    That was the kind of talk I heard from string theorists, about Loop gravity, back in 2003 and 2004. There was even a list of 10 reasons why it would be impossible for Loop to be of any value, published in Wikipedia, since withdrawn :biggrin: The String War started long before Woit or Smolin books, with contemptuous dismissal attacks on alternatives.

    I think the question is simply: is there something here worth investigating.

    Ted Jacobson thought so in 1995.
    Then Padmanabhan.
    Then Verlinde.
    Then Smolin.
    Then Kowalski-Glikman.
    And now Smoot.

    My guess is that your PhD advisor (you mentioned his name earlier) will probably get on board before very long. If he hasn't already.

    On the other hand, Peter Woit is vehemently against the idea and has written several bitter attacks on the entropic force idea. You would probably agree with a lot he says.

    I find people's reactions add an instructive extra dimension to this business.

    My impression that this line of investigation is very much worth pursuing (whether or not it hits paydirt) is not based on my respect for a few of those involved. It is based directly on my finding it intuitive and imaginable that nature could work that way. I've known about Jacobson's paper for something like 4-5 years, I forget, but a long time, and always wondered about it, would it lead to something.

    BTW Smoot's nobel was about that oval blue and red splotchy "snapshot" mapping a distant surface called the "surface of last scattering". As you surely know. I wonder whether he draws some kind of private analogy.
    Last edited: Feb 24, 2010
  5. Feb 23, 2010 #4


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    The main person behind the specific idea of this paper should be Raphael Bousso (the math is even simpler than Verlinde`s). It is a pity he was not cited, because each of his papers on this got over 250 citations... (and I knew of the 1st of them since the very day it was posted, in 1999, while I was in the first semester of my physics course. Its paper promptly made me print it, because I was hugely excited by it, even though I didn`t understand much... and I read it over and over for a few years after...)

    Last edited: Feb 23, 2010
  6. Feb 24, 2010 #5


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    Basically I think we should be focusing on the socalled CEH---the cosmic event horizon.

    The best current information on the CEH that I know of is in Egan Lineweaver
    which incidentally is cited by Smoot and friends.

    The Radius of the CEH is estimated at 15.7 billion lightyears. It is expanding out towards an asymptotic limit of 16.4 billion lightyears.

    I don't recall seeing an estimate of the CEH temperature, except for the one Smoot et al gives.
    4 x 10-30 kelvin. I'll keep looking for corroboration of this.

    I've been trying to check up on Smoot etal numbers. Lineweaver is a major authority and he says that the entropy of the spherical shell, the CEH, is currently
    2.6 x 10122kB, measured in units of Boltzmann constant, the natural unit to use.

    Presumably that entropy would be increasing towards some asymptotic limit likewise.
    Yes, as time goes to infinity the horizon entropy goes to 2.88 x 10122kB

    Ahah! I see that Lineweaver 2009 has a reference to something that Bousso published in 2007!
    So Bousso may not necessarily seem to everybody to be a central figure here, but he is not getting entirely left out!
    The Bousso paper cited by Lineweaver is Bousso, Harnik, Kribs, and Perez 2007,Phys.Rev.D,76,043513

    Apparently Bousso also estimated the entropy of the CEH (cosmic event horizon).

    If anybody is happening to read this and is unfamiliar with the terminology, the CEH is NOT THE SAME AS THE HUBBLE RADIUS.
    The hubble radius is the distance to stuff that is receding at the speed of light---around 13.7 billion lightyears.
    The particle horizon is the current distance to the farthest stuff we would be seeing under perfect visibility conditions (no scattering)---it is around 46 billion light years. The CMB (microwave background ) comes to us from matter which now is nearly that far away.
    The particle horizon is often considered to be the radius of the observable universe because we can see light that was emitted by matter which (although it used to be much closer) is NOW at a distance of nearly 46 billion lightyears.

    However I think Smoot is not talking about the particle horizon and he is not talking about the Hubble radius. He is talking about the CEH.
    The CEH is very interesting. It is the distance of a galaxy which if today we sent a message it would never get there. Or which if today the galaxy had a supernova we would never see it. If the galaxy was just a bit closer then our today message could reach it, or their today supernova we would eventually see in a finite time. That is the distance of 15.7 going to 16.4 as time goes to infinity.

    And yes the CEH does have a temperature, just the way a black hole event horizon has! Lineweaver and others have pointed this out. Maybe Bousso did too. It is a fascinating business. :biggrin:

    But that paper you linked by Bousso is only his covariant entropy bound. That is well-known and all, but it is not talking about the CEH and about cosmology. It is very abstract. Basically it is going along in the same vein as Bekenstein Hawking and all that. The area divided by 4. Later generalized to the 'holographic principle' that 't Hooft first stated in 1993. That general theory stuff is always in the background. But for cosmology we need definite numbers about the temperature and entropy of particular horizons.
    Last edited: Feb 24, 2010
  7. Feb 24, 2010 #6


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  8. Feb 24, 2010 #7
    I shouldn't be posting in this forum, where the really knowledgeable people live, but I seem to have survived into exciting physics times and the sounds of a logjam that may be easing are more than I can resist commenting on.

    Physics Monkey: I have consulted several of the (Vervet) monkeys who are often to be seen swinging in the trees on our farm, and their consensus gabble is that the Smoot et al. article, although simply and perhaps too casually written, may just be another signal of a long-needed sea-change in cosmology. Instead of an ad hoc invention with 70% of everything being mysterious dark energy of an unknown kind, Smoot et al. and folk like David Wiltshire are trying to find a physical reason for the apparent deviation from linearity of the observed Hubble plot at high z. I agree with Marcus that there is "something here worth investigating". Be great if the invention proved to not to be needed -- the only second Nobel after transistor days and a million-dollar quiz win? Turns one green with envy of Smoot.

    I also don't quite follow your objection:
    , since it seems that the "entropic force" referred to is not necessarily associated with an event horizon, only with an "information screen" (a concept that I do find a bit baffling) --- which could be at any radius, perhaps anywhere?:
    What about acceleration and entropic force going together like a horse and carriage, as in Newton II?
  9. Feb 24, 2010 #8
    It intrigues me to think that the expansion of the universe may be the cause of structure in the universe. Is it that the information content on the surface of the event horizon is shrinking because the universe is accelerating in its expansion? Does this shrinking event horizon and corresponding decrease in the information on its surface cause a corresponding decrease of information content inside the event horizon? Could gravity that pulls all things together contrary to entropy making things dissipate itself be caused by the decrease in information inside the shrinking surface of the event horizon? Could other structures like life also be the result of the accelerating expansion of the universe? I wonder.
  10. Feb 24, 2010 #9
    Maybe some of you experts would be so kind as to comment on the following which I believe is closely related to and may underly Marcus' post topic.

    When I began reading about the holographic principle I did wonder about energy relationships...but got no further....how does information move from boundary to boundary...

    Regarding Landauer's principle,

    Charles Seife in DECODING THE UNIVERSE (pages 81,85) says the following
    have computer problems, back in a few...

    How do you interpret this??? and does it apply to a holographic boundary (screen)....all this and temperature, to boot, is hard for me to piece together in a few coherent statements. I have learned over the years that if I can't explain the basics in a few sentences I don;t know what I am doing....
  11. Feb 24, 2010 #10


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    friend and Naty, I can't comprehensively respond to all the questions you raise, and I don't want to risk diverting the discussion but I will mention a little background about the CEH. Intuitively it has a temperature for the same reason Hawking said BHs radiate
    Current radius RCEH is 15.7.
    If an event occurs farther than that it cannot ever affect us. If an event occurs closer than that, it can affect us.
    At exactly that distance, are a lot of photons aimed directly at us and not making any headway, in fact being slowly swept back as the CEH expands. The asymptote RCEH is 16.4.

    The CEH can make Hawkinglike radiation (one can imagine for rough intuition sake) by a Hawkinglike mechanism. A pair of particles appears near the horizon, one buddy comes towards us (and eventually makes it) and other buddy goes away from us and disappears over the horizon and is out of our causal world. He can never affect us so he in some sense does not exist. The CEH glows with the ridiculously low temperature of 4 x 10-30 kelvin.

    I will sift in some more background, or I hope to anyway, later. But don't want to dilute the debate on the issues. Very interested in PhysicsMonkey's point of view and also in what Oldman just said.

    MTd2, I've taken a look at Bousso http://arxiv.org/abs/hep-th/0203101 which is certainly a very impressive paper about the covariant entropy bound. However I do think that the holographic principle as such goes back to 't Hooft 1993. As we all realize what is going on here uses holo principle as an assumption but advances beyond it.

    BTW isn't it kind of cute that while stuff (galaxies etc) is constantly falling thru the horizon (and out of causal touch with us) the horizon area keeps expanding. It resembles a BH horizon in that respect. As stuff falls in thru the BH horizon, that horizon also increases in area. No direct connection. Maybe just an accidental similarity.
    Last edited: Feb 24, 2010
  12. Feb 24, 2010 #11


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    Yes, it does go back all the way. But we are talking about general relativity, and not in Newtonian Gravity anymore. And indeed, holography is used as a principle, but this is a small step no one had the courage to take up to today (Even I thought of using that as a principle, so pretty much lots of people also thought of that).

    Indeed, it is cute. But in the case of a black hole, the matter flux is strongly biased to the black hole. In the case of an apparent horizon, everything goes one calmly. So, it is like the total universe balanced the distribution of matter like the amoeba does with its cell contents.
    Last edited: Feb 24, 2010
  13. Feb 25, 2010 #12
    I guess I still have some expansion confusion. I'm understanding that if the expansion of the space accelerates, then the distance to where things are receding at the speed of light will get closer to us. That would mean that the horizon would be getting closer and shrinking in surface area. Is this correct? Or are things more complicated when talking about spacetime and not just space?
  14. Feb 25, 2010 #13


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    Yes, it will shrink until the Big Rip.
  15. Feb 25, 2010 #14
    I agree with Marcus that the new article is very much worth investigating and that Verlinde's idea may be a much more elegant way to explain dark energy. But I also think the article is not very clear, at least I have two questions:

    He claims that the pressure in eq (17) decreases if the screen is placed at smaller radii, but as far as I can see the entropic force is a constant (-1 in natural units), such that F/A increases at smaller areas. Can anyone clarify why the pressure decreases?

    I thought that a high pressure (hence high acceleration) may produce a model for inflation at small times where A is still small, or is this idea too crude?

    PS: @Friend, I think the evolution of the CEH depends crucially on omega, but from Lineweavers article it becomes clear that it will increase in time. Note also that the CEH is not the distance where particles are moving to us with the speed of light, since due to the accelerated expansion later on these particles will not reach us.
  16. Feb 25, 2010 #15


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    If the horizon logic is applied to the Beckenstein horizon experienced by the accelerating observer does it predict a force acting in the direction of the horizon, i.e. back, from the observers POV ?
  17. Feb 25, 2010 #16


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    Actually no, there is a subtlety that comes in. It is not correct. Wilke made a good point about reading the Lineweaver article. RCEH increases with time, in the standard cosmo model, from 15.7 billion lightyears now, to 16.4 later.

    One way to see it is to think about what accelerated expansion means. It doesn't that the Hubble H(t) increases. It means that a'(t) increases. a'(t) is the time derivative of the scale factor. That's a case where words are confusing. The astronomers discovered that a'(t) is increasing and they couldn't think of how to say it clearly. There was some kind of acceleration going on, obviously, so when they had to translate it to the public they said vague things like "the universe" is accelerating.

    To make sense of it, you have to study and consider what the scalefactor a(t) is.
    Intuitively something like "the average distance between galaxies".
    And then you have to study and realize that the Hubble H(t) = a'(t)/a(t)

    And then see why H(t) is destined to decrease, because the denominator is so large and already growing so fast! While the actual change in the numerator is piddling. The acceleration is comparatively slight. So this big growing denominator dominates and makes H(t) decrease (even with "acceleration")

    And then you have to realize that what you asked about, namely "the distance to where things are receding at the speed of light" is simply the reciprocal of H(t) or more exactly it is c/H(t). So as H(t) decreases, that distance has to increase.

    It's a good question, friend. There is an unintuitive quirk to the answer because it has to do with the actual mathematical meaning versus the somewhat vague translation into ordinary speech.
  18. Feb 25, 2010 #17


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    But the standard cosmo model has no "Big Rip" :biggrin:

    The standard model fits the data well, so far, so there is no basis for assuming a big rip.
    The model might eventually prove wrong, and a rip scenario might prove right! But so far the standard is consistent enough that it is generally accepted and is normally the context our discussions.

    In the standard picture, the Cosmic Event Horizon does not shrink down. It stabilizes at around 16.4 billion lightyears.

    Galaxies that are not bound to us in our own local group will gradually drift out towards the horizon. And they will pass over the horizon. But we will not see them pass over. We will see them redshift and redshift until they are no longer detectable. The news of their events will come to us more and more spread out in time, so that events in them seem to slow down.

    They will long ago have said goodbye and passed over the horizon but we will see them frozen at the horizon in a slowed down time, gradually getting redshifted into invisibility.

    That's the standard cosmo model scenario, but no "big rip".

    Larry Krauss is a world-class cosmologist and he has a nice perspective piece on this which is at arxiv.
    It is accessible, written for general audience.
  19. Feb 25, 2010 #18


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    That's a good question. I'll try to respond. (Maybe others will as well.) I think that he calculates the entropic force at a distance of Rceh and it comes out to be the natural force unit c4/G
    at that distance. But at a closer distance I think it would not come out to be that. Have to take a look.

    I took a look back at equation (15)-(17) and it looks to me as if the estimates of the entropy at the Rceh screen, and the area, and the change in the entropy all depend on it's being the CEH, not some other screen.

    And the temperature estimate too, seems to depend on radius. So it looks to me like
    the force is c4/G only in this one case.

    That's how it looks. I don't have time to go thru every detail involved, but I don't think that if you took a smaller nearer screen you would get the same force, or a higher pressure.

    It is a good question though, we ought to be checking these things out.
    Last edited: Feb 25, 2010
  20. Feb 25, 2010 #19


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    Where did you get that I am talking about standard cosmology? If the CEH is emitting radiation, it will shrink until every point becomes non local or the energy density becomes equal to that of a black hole.
  21. Feb 25, 2010 #20


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    I would like to understand better what you are talking about, MTd2.

    I am talking about standard cosmology, and that is what we normally are discussing here in this Forum. It is kind of the "home base" which you assume unless clearly otherwise stated.

    And Smoot is talking about standard cosmology too, right? This all comes from classical GR and thermo. Plus a little semiclassical stuff like Bekestein or Unruh horizon temp.
    The Smoot paper seems very standard to me. They just want to find a better and simpler explanation of the "dark energy" effect.

    If it works it would be an improved version of the standard cosmo. Same behavior, but with a simpler explanation, streamlined mathematics.

    I don't think this is right. Smoot does not say this. It is your idea and you have not offered any explanation why the cosmic event horizon should come in towards us at the same time as it radiates radiation at us.

    Notice it is the space OUTSIDE of the cosmic horizon which is analogous to the space inside of a black hole. When a black hole radiates the BH horizon shrinks back away from us. The analogous thing with CEH is when it radiates it would expand back away from us (so the area increases). But I think there is no analogy at a physical level.
  22. Feb 25, 2010 #21


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    He used a great deal of simplification in eq. 12. Note that he either assumed H to be constant, first solution, or its temporal linear approximation. This is why he gets the standard cosmological solution. Otherwise, this equation would be highly non linear.

    And he indeed says that in a future paper, this work give support to the cyclic model and inflation. Look at the 2 last paragraphs of the appendix. He will talk about this in future work.

    BTW, I told you LQC supports a bounce at the big rip. If this entropic force does indeed relate to LQG, like Smolin said, you will see later that this is the case.

    In our referencial, the CEH would lose energy, just like the horizon of a black hole. So, both of them shrink.
    Last edited: Feb 25, 2010
  23. Feb 25, 2010 #22


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    Let me think in terms of what Fra would like. Every observer have a quote of what he can measure and interact. That quantity quantity includes the "potential energy" necessary to build enough room to that happen. But, even that room decays, in the form of cosmological constant, dark energy, or entropic force.
  24. Feb 26, 2010 #23
    What about the observed flat spatial geometry of the universe?

    As I see it dark energy serves two major purposes in standard cosmology -- 1: it exerts a negative pressure and explains the apparant acceleration deduced fron S1a observations --- 2: it bears the main (74 %) responsiblity for flattening the universe's spatial geometry.

    If the Smoot paper turns out to be correct, would purpose 2 be as well served as purpose 1?

    If so, would this be because the "entropic force" can be thought of as an all-pervading negative pressure stretching all the way out to the CEH, acting across any imagined "holographic screen" surface, of any radius?
  25. Feb 26, 2010 #24
    I also thought about that, and basically it is the only sensible solution, but wasn't able to work out the details. Some remarks I think relevant:

    dS/dr ~ R (with R radius screen, this follows unambigious from holographic principle)
    P = F/A ~ T / R (since dS/dr ~ R and A ~ R2)

    It is quite difficult to interprete the temperature in this case, but I guess it should coincide with Verlinde's idea: being proportional to acceleration. Assuming a constant mass density this would be proportional to R (in Newtonian gravity, M ~ R^3, so a ~ R). This would give a constant pressure, which I think makes sense: in the current models dark energy has a constant negative pressure throughout the universe, causing an accelerated expansion in accordance with Hubble's law.

    This picture is not entirely equivalent to the one presented in the article though, what do you think? Do you think a constant pressure makes sense?

    Kind regards,
  26. Feb 27, 2010 #25
    Which would also make "entropic force" the chief universe-flattening agent.

    Two other points I'd like to mention:

    1. There must also be some very good reason why the proposed entropic forces, together with dark and visible mass/energy, form a Goldilocks combination that makes Euclid's spatial geometry the universal average.

    2. The arguments made by Easson, Frampton and Smoot are presented in the context of the standard model of an idealised uniform cosmic fluid, in which a spherical holographic screen may be imagined to be centered anywhere, in order to have the same negative pressure throughout the universe. If Verlinde's suggestion that Newtons law of universal gravitation is a manifestation of entropic force is correct, then in an ideal, uniform fluid this law must also be the same everywhere.

    But the real universe is lumply in a hierarchical way. It's built of blocks large enough to be shaped by gravity alone, like galaxies, huge voids and galaxy clusters. Would the strength of gravity-as-an-entropic-force change at all if an imagined holographic screen or CEH was centred on a galaxy or on a void? For relatively small R the assumption of constant density then fails. And if G depended at all on where the screen was centred, approaches that
    could still be interesting.
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