Tuesday, March 16, 2010

Dark Energy As An Entropic Force.

(Skip to summary below if you want to cut to the chase and ignore the draining explanation.)

We are going to take time out of our series on the prejudices against dark energy paper and talk about... another paper on dark energy. :)  This is justified because this paper is cool.

Easson, Frampton, and George Smoot (Yes the Nobel Prize winner Smoot who headed the COBE project) recently released an interesting paper showing that one can do a pretty good job explaining dark energy from entropy.

We often assume our universe either doesn't have a boundary, or that if it does its "at infinity" and doesn't really effect us.  These authors took a step back and asked what entropy would do to our universe if it had a consequential boundary.   If it does, we need to add the boundray term we usually ignore to the Lagrangian:

Here R is the term that gives gravity, L is the term that contains the matter of the universe and K is the curvature of our new boundary term.  M is our manifold (space) we live one and the "backwards 6" M means the boundray of the manifold.

Interestingly, if a system has a boundary, the maximal entropy the system can have is directly related to the size of the boundary.  (Thank Steven Hawking for this.)  Because entropy wants to increase, a pressure is exerted on the system to get the boundary to increase.  They calculate the pressure for the given universe and find:

In case you missed it, the pressure exerted on the universe is the same as would be exerted by a cosmological constant making up 2/3 of the total energy of the universe.  Given the cosmological constant is measured at making up ~70% of the universe, this is a remarkable result.

Furthermore, as the boundray increases, so does the pressure.  This causes, not only an expansion of spacetime, but an accelerated expansion!  In fact, the accelerated expansion predicted fits the supernova data (that we use to gauge such an acceleration) remarkably well!  See the plot above.  Hence we read (from the paper above):
Thus, the acceleration of the universe simply arises as a natural consequence of the entropy of the universe, via the holographic principle....  We have discussed a theory underlying the accelerated expansion of the universe based on entropy and entropic force. This approach provides a physical understanding of the acceleration phenomenon which was lacking in the description as dark energy.... The accelerated expansion rate is no longer surprising. It is the inevitable consequence of the holographic information storage on the surface screen of the universe.
If you missed It behind the equations and bad writing:
1.  Assume the universe does have some type of boundary.
2.  Entropy will increase if the boundary can expand. 
3. This induces a pressure trying to cause the universe to expand, incresing the size of the boundary. (And hence entropy.)
4.  The pressure pushing the universe to expand is the same as cosmological constant making up 66% of the energy density of the universe. (It is currently measured at ~70%)
5.  As the universe expands, the pressure actually increases causing an acceleration that matches the cosmic acceleration we observe.

Pretty cool huh? Even if it is not true, at least it is cool.


  1. That's a snazzy approach.

    One thing troubles me: it seems the authors have implicitly placed the expanding boundary in some space-like arena. Yet, unless carefully done, that would include considering space outside the boundary of the universe, which makes as little sense as talking about time before the big bang.

    It's like imagining a universe consisting of just a rubber ball, and then saying that the ball is expanding or moving. Compared to what? Scale and motion become meaningless unless you reintroduce Newtonian absolute space, which I am loathe to do.

    Even so, I like the creativity having to do with the holographic principle, though Ulf Danielsson says it's not a new approach:

  2. Ben,

    Thanks for the link to the Danielsson paper. I knew (as this always happens) people will find ways to attack such ideas.

    A problem, for better or worse, is it is:
    1. It is hard to come up with a genuinely new idea.
    2. It is hard for new ideas to not suffer from major issues once scrutinized.

  3. So applying this to real life, as entropy increases in my teenage daughters room, the pressure to increase the size of her room increases so entropy can continue to increase, otherwise entropy reaches an uncomfortable equilibrium? Woah, that's cool.

  4. Stan,

    Yep, theoretical physics is very practical to help you deal with life's problems like that.

  5. I'd say that entropy creates dark energy and thus pressure. But, for a significant amount of dark energy to be created, one needs to have loads of particles at a high temperature, for the process creating the dark energy with entropy seems to depend on temperature.

  6. I am a little bit late to the discussion because I was wondering about this on the way to work.  I had not remembered Steven Hawking's holographic principal.  Cool stuff.  I just looked this up on google and there you were.  How much room is there in the statistics of what we know about the universes expansion? I recently read that they are beginning to suspect that there are distinct types of 1a supernova explosions.  Tycho's remnant is one possible example of a more powerful type of 1a supernova.  If this is the case would it explain the deviation


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