> Dyson, L., Kleban, M. & Susskind, L. Disturbing implications of a > cosmological constant. Preprint <http://xxx.lanl.gov/abs/hep-th/0208013>, > (2002).

Most of this paper is way over my head. I need to read the ending much more carefully in order to understand its conclusions. But I wanted to make one point which IMO is really amazing and not often appreciated. I'm not 100% sure that it applies to the specific model considered in this paper, but it does apply in general. I think I got this idea from the Huw Price book on The Arrow of Time. The authors use the example of a box containing a gas, which starts in a low-entropy state with all the molecules in a small region. Then as time moves forward the molecules spread out and we get entropy increase, allowing for dissipating structures to form such as vortices, and in the general case even life. Then the gas reaches equilibrium, and all the dissipative states die out. All structure and order is lost, and in a sense, time is no longer passing, as far as causality is concerned. Causal time is something that only happens when there is entropy increase. After an extremely long interval, we may get a Poincare recurrence. (Actually, I'm not sure this is the right term for this; I think a Poincare recurrence is a more general thermodynamic effect. But I will use the phrase here to specifically talk about a low-entropy fluctuation out of a high-energy equilibrium state.) The gas will randomly happen to move back into a low-energy state, perhaps even the same state we started with, all the molecules in one corner. At that point we once again get dissipation, structures, the passage of time, and the possibility of life. This cycle can and will repeat indefinitely. The authors suggest, applying this concept to cosmology, "In the recurrent view of cosmology the second law of thermodynamics and the arrow of time would have an unusual significance. In fact they are not laws at all. What is true is that interesting events, such as life, can only occur during the brief out-of-equilibrium periods while the system is returning to equilibrium." The amazing thing is that this is wrong. Life and other dissipating events are not restricted to the period when the system is returning to equilibrium. Here is the surprise: these events also occur, to exactly the same extent, while the system is *departing* from equilibrium. That is, if we wait long enough for a Poincare recurrence of the kind described here, where the gas goes into a low entropy state and then goes through some kind of complex evolution back to equilibrium, we must pay attention to how exactly the gas goes into the low entropy state. And given the microscopic reversibility of the system, the most likely path into the low entropy state is a mirror of the most likely path out of it. That is, if we really assume that somehow this gas in the corner evolved life which then died out in the heat death of the universe, then the most likely path back into the corner is to evolve life backwards. We would see the formless void of space begin to cluster together to form structure. That structure would include the pattern of dead life-forms. These life-forms would come to life, and they would live their lives backwards. They would grow young and be un-born. Each generation would be replaced by its ancestors. Life would un-evolve back to a primordial state, and eventually to simpler dissipative structures and chemical reactions. The whole clock of the universe would continue to turn back until it reached the peak of the Poincare recurrence, the point of minimal entropy, and then it would start to run forward again. Now, this does not mean that we would see exactly the same path out of the low entropy state as in; but rather, that both paths would be governed by the same statistical constraints. The path out of the recurrence shows constant increases in entropy which guide its path. The path into the recurrence shows constant decreases in entropy which guide it in exactly the corresponding manner. I know this is pretty amazing; so amazing that I can hardly believe it myself. But it follows immediately from the time-symmetry of the laws of physics. If Poincare recurrences did not occur in this way, it would mean that physics had an absolute arrow of time. We could watch a movie of a low-entropy state forming and then dissipating, and the two phases would look different, showing that physics is not symmetric in time. One more point: during the entropy-decrease phase of the Poincare recurrence, what force pushes us backwards in time? Why does entropy continue to decrease? The answer is, there is no such force. At every point during the recurrence, it is *overwhelmingly* more likely to turn around and start heading towards higher entropy than to continue towards further decreases in entropy. It is no more likely for time to continue to run backwards during the first half of a Poincare recurrence than it is for time to turn around and begin running backwards today. So how come it happens, then? It is not a physical phenomenon, rather it is a selection effect. We choose to pay attention only to those Poincare recurrences which are interesting, that is, those which go back to what we consider a "beginning of the universe" state. Given enough time, enormous time, some recurrences will go back that far. So if we restrict our attention to that minute subset of events, and we ask what path did the universe follow in getting to this amazing low-entropy state, then what I have said above is true. The most likely path into the low entropy state runs along the same constraints as the most likely path out of it. Time runs backwards into the low-entropy state. I believe it follows, then, that if we are living in such a Poincare recurrence, it is overwhelmingly likely that the universe did not really go all the way back to the Big Bang. Rather, our past is an illusion. Time ran backwards far enough to form us; but among those recurrences where we formed, the overwhelming majority of them don't have time go back much farther than that. (My son is reading the Price book now and says that this idea goes back to Boltzmann, that our past is false and the universe no older than us, if our experience are explained by such a recurrence.) Hal Finney