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Quantum Entropy version of Second Law (Bojowald Tavakol)

  1. Mar 31, 2008 #1


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    An important issue here. In 2001 Bojowald discovered that quantizing the basic (Friedmann) model of cosmology got rid of the classical singularity and typically replaced it by a bounce. A prior contracting phase leads up to the start of expansion.

    In the years that followed Penrose raised the question of how one can reconcile the bounce cosmology with the Second Law. The entropy approaching crunch is very large and suddenly, after the bounce, the entropy of the born-again spacetime is very low. somehow it appears to be reset to zero. Penrose obviously found the bounce cosmology picture extremely interesting except for what he considered to be this terrible flaw---violating Thermodynamics. Since 2005 several of his lectures have focused on this issue.

    What Bojowald and Tavakol have done is very creative. They seem to have found a way around Penrose objection to the bounce.

    In doing so they have found a way of defining quantum entropy

    Recollapsing quantum cosmologies and the question of entropy
    Martin Bojowald, Reza Tavakol
    23 pages, 2 figures
    (Submitted on 31 Mar 2008)

    "Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in presence of a free scalar field with, in turn, a negative cosmological constant and spatial curvature. Effective equations shed light on the quantum dynamics around a recollapsing phase and the evolution of state parameters such as fluctuations and correlations through such a turn around. In the models considered here, the squeezing of an initial state is found to be strictly monotonic in time during the expansion, turn around and contraction phases. The presence of such monotonicity is of potential importance in relation to a long standing intensive debate concerning the (a)symmetry between the expanding and contracting phases in a recollapsing universe. Furthermore, together with recent analogous results concerning a bounce one can extend this monotonicity throughout an entire cycle. This provides a strong motivation for employing the degree of squeezing as an alternative measure of (quantum) entropy. It may also serve as a new concept of emergent time described by a variable without classical analog. The evolution of the squeezing in emergent oscillating scenarios can in principle provide constraints on the viability of such models."
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  3. Mar 31, 2008 #2


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    I've been reading pages 15-19, the section 3.4 on entropy. I may have not understood how far they have gotten. They may not yet have resolved the paradox of the resetting to zero at the bounce---but in the Conclusions section they seem to have a shot at that one too. The first thing is to resolve the paradox about entropy continuing to increase even after the universe reaches maximum size and begins to collapse. so that going in to a crunch it can have very high entropy. No reversal of time's arrow as some have speculated.
    In any case I think they've got something interesting going here and hope to hear reactions from others who have read the paper.
  4. Apr 2, 2008 #3


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    I don't have any meaningful comments in the intended context of quantum cosmology so I apologize for that but I have some general conceptual problems to fully see the questions asked.

    From the paper:

    "A central question in cosmology is how to successfully define a notion of cosmological entropy...
    ...The notion of entropy is connected to that of information associated with the degrees of freedom considered."

    Taken as fuzzy questions this seems to be in a nutshell part of the issue. And I can understand this. But before one rushes further into this and adding even more things, I would like to reflect over what this means. As I see it, they are seeking to construct a measure, which we would very much like to name "entropy".

    How do we know when we have a satisfactory construction of such a measure, in this particular case but also in the general case? Clearly "entropy" isn't just a name, it implies that we want this measure to have certain properties. What properties? and relative to what are these desired properties described?

    Often entropy measures are constructed by adding some desired properties are constraints. So we are seeking a measure with certain properties, that further has meaning in some larger context?

    They say that this entropy is supposed to serve as a measure of information (or missing information, depending on how you see it) associated with some considered degrees of freedom.

    How can we find out exactly what degrees of freedom to consider? Usually in a theoretical example one simply defines the problem but it's degrees of freedom. But how does "natural" problems as opposed to textbook problems select the degrees of freedom? And does that process by any chance have any impact here?

    IMHO, the choice/construction of the measure we seek seems difficult to distinguish from the choice/construction of the degrees of freedom?

    So the question is still - what are we really looking for here? Is there a way to reformulate this quest that removes this apparent but possibly vague distinction between choice of degrees of freedom and choice of measure?

    Perhaps the distinction between the measure, and the degrees of freedom is part of the confusion. And I am personally confused by that nowhere is an observer mentioned, even in principle. How can we establish a physical starting point?

    Edit: To speak for myself, a starting point along the lines of "this is the state vector of the universe" simply knocks me off the chair - it just doesn't fit in my head. Regardless of wether we know what the state vector of the universe is, the first question seems to be if we even know what the state space of the universe is? And if I don't know that either, is there a strategy how we can someone find out? I can't wrap my head around where the observer has gone and where the scientific method is in this.

    Last edited: Apr 2, 2008
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