Re: Doomsday-like argument in cosmology
I've read the paper more closely and I think I understand it somewhat better. The paradox in the paper is actually closely related to the comments with which I concluded my earlier message. What they are saying is that if we are part of a Poincare recurrence, it is overwhelmingly likely that the past is false. And worse, it is overwhelmingly likely that the past is inconsistent; that we were or are on a trajectory that could not be continued all the way back to the Big Bang. That is because the entropy at the time of the Big Bang was very low compared to today, so the vast majority of today-like worlds have no plausible continuation back to a Big Bang. The specific example they give is, what if the cosmic microwave background was 10 degrees rather than 2.7 degrees? If we think about a Poincare recurrence in the process of forming, time running backwards, a hotter than usual microwave background will not cause any problems. You could still get planets being un-destroyed, life becoming un-extinct and running backwards, etc. Eventually you get back to the present day. And we look around and see a universe that's at 10 degrees. That's a big problem. There's no way our universe could have formed from a Big Bang if the microwave background was that hot. It means the Big Bang was completely different, we wouldn't see the elemental abundances we see today, galaxies wouldn't have formed properly, and so on. We would see a world which was inconsistent with its putative past. Yet we don't. Broadly speaking we seem to live in a universe to which we can ascribe a reasonably consistent model of the past. This contradicts what we would predict if we lived in a Poincare recurrence, hence we probably don't. Now you might say, so what, the whole idea that we formed in this way was so absurd that no one would ever take it seriously anyway. But the authors of this paper seem to be saying that if you assume that there is a positive cosmological constant (as the cosmological evidence seems to show), eventually we will get into this de Sitter state, and based on some assumptions (which I didn't follow) we really should see Poincare recurrences. Then by the anthropic principle we should be overwhelmingly likely to be living in one. Hence there may be something wrong with our cosmological theories. Another point, Tim is of course right that the time for one of these recurrences to happen is enormous. The formula they give is t = exp(S1-S2), where S1 is the entropy of the equilibrium state, which they estimate as 10^120 for the de Sitter universe, and S2 is the entropy of the state we are going to chance into, which they say would be about 10^10 for time near the Big Bang. So this means that the time until something interesting happens is about exp(10^120). The authors comment, This seems like an absurdly big time between interesting events, which by comparison last for a very short time. Nevertheless dismissing such long times as 'unphysical' may be a symptom of extreme temporal provincialism. As far as the de Sitter model, the references I have found agree that it has rapid, exponential expansion, with no beginning and no ending, and that it is a steady state model of the universe, which looks the same to all observers at all times. However some authors say that it has no matter, and others say that it has a constant density of mass-energy, and I'm not sure how to reconcile that. In this paper the authors do a coordinate change where the de Sitter model can be considered to have a constant volume and density, so that sooner or later recurrences should, well, recur. Hal Finney
Re: Doomsday-like argument in cosmology
On Saturday, August 17, 2002, at 11:37 PM, Hal Finney wrote: Now you might say, so what, the whole idea that we formed in this way was so absurd that no one would ever take it seriously anyway. But the authors of this paper seem to be saying that if you assume that there is a positive cosmological constant (as the cosmological evidence seems to show), eventually we will get into this de Sitter state, and based on some assumptions (which I didn't follow) we really should see Poincare recurrences. Then by the anthropic principle we should be overwhelmingly likely to be living in one. OK, let us assume for the sake of argument that we should be overwhelmingly likely to be living in one of these time-reversed cycles (which I distinguish from bounces back to a Big Bang state, the more common view of cycles). By the same Bayesian reasoning, it is overwhelmingly likely that any observer would find himself in a TRC in which other parts of the universe eventually visible to him (with telescopes) are incompletely reversed. Let me give a scenario to make the point clearer. It is 1860. Telescopes exist, but are still crude. The Milky Way is only known to be a nebula, a swirl of stars. The existence of galaxies other than our own is unknown. Professor Ludwig calls together several of us friends (perhaps on the Vienna version of the Everything List) and outlines his theory. We are very probably in a recurrence phase of the Universe, where a worn-out, gaseous phase of the Universe has randomly arranged us into this low-entropy, highly-ordered state we find ourselves in today. It took a very long time for this to happen, perhaps 1,000,000,000,000,000 million years, but here we are. (Reactions of his audience not presented here...maybe in the novel some distant version of me will write.) All that we see around us, our Sun, the planets, even the gas balls we call stars, were formed thusly out of a random rearrangement of gas molecules. My young mathematician friend in Paris, Msr. Poincare, says this sort of recurrence is inevitable in any sufficiently rich phase space. Now, if this is correct, it is overwhelmingly likely that of all of the time-reversed cycles, or TRCs, the TRC we find ourselves in will have only reversed time (or created low entropy structures) in our particular region of the Universe. In a hugely greater amount of time, even more regions of the Universe we will be soon be able to observe would be subject to this reversal, but the times involved are even more hideously enormous than the very long times needed to create our own TRC pocket in which we find ourselves. So, overwhelmingly, observers who draw the conclusions I have reached will find themselves in a Universe where only a region sufficient to have built them and their supporting civilization will have the low entropy order of a TRC. Thus, gentlemen, by a principle I call falsifiability, I predict that when the new telescopes being built now in Paris and London become operational, we will see nothing around our region of the Universe except gas and disorder. And, of course, within his remaining lifetime Professor Ludwig was astonished to learn that distant galaxies looking very much like nearby galaxies existed, that if a Poincare recurrence had in fact happened, it must have happened encompassing truly vast swathes of the Universe...in fact, the entire visible Universe, reaching out ten billion light years in all directions. The unlikelihood that an observer (affected causally only by events within a few light years of his home planet) would find himself in one of the comparatively-rare TRCs which affected such a big chunk of the Universe convinced Professor Ludwig that his theory was wrong, that the new ideas just being proposed of an initial singularity, weird as that might be, better explained the visible Universe. --Tim May (who also thinks the difficulty of time-reversing things like ripples in a pond, radiation in general, and all sorts of other things makes the Poincare recurrence a useful topological dynamics idea, but one of utterly no cosmological significance)
Re: Doomsday-like argument in cosmology
Tim May writes: OK, let us assume for the sake of argument that we should be overwhelmingly likely to be living in one of these time-reversed cycles (which I distinguish from bounces back to a Big Bang state, the more common view of cycles). By the same Bayesian reasoning, it is overwhelmingly likely that any observer would find himself in a TRC in which other parts of the universe eventually visible to him (with telescopes) are incompletely reversed. Let me give a scenario to make the point clearer. [Example elided] Yes, that's a good point, it seems completely correct. It is consistent with the basic argument in the paper, a better example than the one they gave about the microwave background being too hot. These kinds of considerations were summed up by Wei Dai in his original comment: This is a variant on the Doomsday argument. The core argument of the paper is this: If we live in a world with a true cosmological constant, then the observers whose observable universe is macroscopically indistinguishable from ours are a tiny fraction of all observers. Therefore the only reasonable conclusion is that we do not live in a world with a true cosmological constant. When Wei writes about universes macroscopically indistinguishable from ours, I believe he means ones that don't suffer from the kinds of flaws that Tim describes. Clearly the vast majority of observers spawned in time-reversed universes would have the smallest possible time-reversed region sufficient to generate life, and the rest of the universe would still be chaotic. The fact that we observe a huge, complete universe, rich in structure, which appears to have a consistent history, means that we are very special and unusual in a universe dominated by recurrences. I think I see Wei's point that this is similar in flavor to the Doomsday argument. The paper's cosmological theory predicts that the vast majority of observers would see a universe more like Tim describes, and not what we see. Therefore, either we are very special, or the theory is wrong. In the Doomsday argument, the theory that life will go on far into the future predicts that the vast majority of observers would see a history very different from what we see. Again we can conclude that either we are very special, or the theory is wrong. I haven't yet tried to understand Wei's use of the Self Indication Axiom and how there can be a universe model which is supported by the Doomsday type argument but not contradicted by the SIA. Hal Finney
Re: Doomsday-like argument in cosmology
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
Re: Doomsday-like argument in cosmology
On 17-Aug-02, Hal Finney wrote: 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
Re: Doomsday-like argument in cosmology
On Sat, Aug 17, 2002 at 04:55:59PM -0700, Brent Meeker wrote: I think what the paper says is that when matter/energy have thinned out enough so that we have essentially empty space again, a de Sitter universe, a vacuum fluctuation can start a new universe. You're not understanding the paper correctly. A de Sitter universe never thins out to essentially empty space. It thins out to a certain density and no further (I think because new vacuum energy is created as the universe expands.) So at any given moment there is always a minimal chance that the very sparse matter/energy can come together and recreate the present.
Re: Doomsday-like argument in cosmology
On 17-Aug-02, Wei Dai wrote: On Sat, Aug 17, 2002 at 04:55:59PM -0700, Brent Meeker wrote: I think what the paper says is that when matter/energy have thinned out enough so that we have essentially empty space again, a de Sitter universe, a vacuum fluctuation can start a new universe. You're not understanding the paper correctly. A de Sitter universe never thins out to essentially empty space. It thins out to a certain density and no further (I think because new vacuum energy is created as the universe expands.) So at any given moment there is always a minimal chance that the very sparse matter/energy can come together and recreate the present. My understanding was from Weinberg, Gravitation and Cosmology. He takes the Einstein cosmology with cosmological constant, sets k=alpha=0 and says, In the de Sitter model space is essentially empty and flat...there is no matter. Maybe by vacuum energy you mean the closed loop Feynman diagrams of QFT. However, I think the bosonic closed loops give a positive vacuum energy, while the fermionic loops give a negative term - so the speculation is that they cancel and that is why the (or a) universe can pop out of the vacuum and not violate conservation of energy. Brent Meeker I am very interested in the Universe - I am specializing in the Universe and all that surrounds it. --- Peter Cook
Doomsday-like argument in cosmology
- Forwarded message from Wei Dai [EMAIL PROTECTED] - Date: Thu, 15 Aug 2002 13:28:43 -0700 From: Wei Dai [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Nature Article On Thu, Aug 15, 2002 at 12:45:17AM -0400, [EMAIL PROTECTED] wrote: Dyson, L., Kleban, M. Susskind, L. Disturbing implications of a cosmological constant. Preprint http://xxx.lanl.gov/abs/hep-th/0208013, (2002). This is a variant on the Doomsday argument. The core argument of the paper is this: If we live in a world with a true cosmological constant, then the observers whose observable universe is macroscopically indistinguishable from ours are a tiny fraction of all observers. Therefore the only reasonable conclusion is that we do not live in a world with a true cosmological constant. Compare this with the Doomsday argument (see http://www.anthropic-principle.com/primer1.html): If we live in a world without a doomsday in the near future, then the observers whose birth ranks are similar to ours are a tiny fraction of all observers. Therefore the only reasonble conclusion is that we do not live in a world without a doomsday in the near future. So you should accept the conclusion of this paper only if you think the Doomsday type of argument is sound. - End forwarded message -
Re: Doomsday-like argument in cosmology
I think that the difference is that invoking the SIA does not affect the conclusion of the paper. Saibal Wei Dai wrote: On Thu, Aug 15, 2002 at 12:45:17AM -0400, [EMAIL PROTECTED] wrote: Dyson, L., Kleban, M. Susskind, L. Disturbing implications of a cosmological constant. Preprint http://xxx.lanl.gov/abs/hep-th/0208013, (2002). This is a variant on the Doomsday argument. The core argument of the paper is this: If we live in a world with a true cosmological constant, then the observers whose observable universe is macroscopically indistinguishable from ours are a tiny fraction of all observers. Therefore the only reasonable conclusion is that we do not live in a world with a true cosmological constant. Compare this with the Doomsday argument (see http://www.anthropic-principle.com/primer1.html): If we live in a world without a doomsday in the near future, then the observers whose birth ranks are similar to ours are a tiny fraction of all observers. Therefore the only reasonble conclusion is that we do not live in a world without a doomsday in the near future. So you should accept the conclusion of this paper only if you think the Doomsday type of argument is sound. - End forwarded message -
Re: Doomsday-like argument in cosmology
On Thu, Aug 15, 2002 at 11:28:28PM +0200, Saibal Mitra wrote: I think that the difference is that invoking the SIA does not affect the conclusion of the paper. Why do you say that? I think SIA affects the conclusion of the paper the same way it affects the Doomsday argument. It's kind of funny that the authors of this paper is playing the role of the presumptuous philosopher (in the thought experiment I just discussed in a previous post), except they're physicists, and they're making the opposite argument (in favor of the hypothesis that implies fewer observers rather than the one that implies more observers).
Re: Doomsday-like argument in cosmology
I haven't read the paper in detail, so I could be wrong. Consider the two alternatives: 1) true cosmological constant 2) no true cosmological constant We also assume SIA. Is it the case that there are much fewer observers in case of 2) than in case of 1) ? I haven't seen such a statement in the paper (but again, I could have missed it). So, I would say that given our observations of the universe a probability shift takes place, such that 2) is favored (assuming that 1) and 2) have a priory probabilities of the same order). Saibal - Oorspronkelijk bericht - Van: Wei Dai [EMAIL PROTECTED] Aan: Saibal Mitra [EMAIL PROTECTED] CC: [EMAIL PROTECTED] Verzonden: donderdag 15 augustus 2002 23:46 Onderwerp: Re: Doomsday-like argument in cosmology On Thu, Aug 15, 2002 at 11:28:28PM +0200, Saibal Mitra wrote: I think that the difference is that invoking the SIA does not affect the conclusion of the paper. Why do you say that? I think SIA affects the conclusion of the paper the same way it affects the Doomsday argument. It's kind of funny that the authors of this paper is playing the role of the presumptuous philosopher (in the thought experiment I just discussed in a previous post), except they're physicists, and they're making the opposite argument (in favor of the hypothesis that implies fewer observers rather than the one that implies more observers).
Re: Doomsday-like argument in cosmology
On Fri, Aug 16, 2002 at 12:26:10AM +0200, Saibal Mitra wrote: I haven't read the paper in detail, so I could be wrong. Consider the two alternatives: 1) true cosmological constant 2) no true cosmological constant We also assume SIA. Is it the case that there are much fewer observers in case of 2) than in case of 1) ? I haven't seen such a statement in the paper (but again, I could have missed it). You're right, we need to look at the alternative hypothesis. But there's not just one alternative, there are several. 1) True cosmological constant, therefore heat death and endless Poincare recurrences. 2a) The universe ends soon. 2b) The universe runs for a while longer, then gets reset to a low entropy state and starts over. This happens in an endless cycle. 2c) The universe never ends, and life become ever more complex and intelligent. 2d) No true cosmological constant, but we get heat death and endless Poincare recurrences for some other reason. 2e) The universe never ends, but the total number of observers is a relatively small finite number. I think these exhaust all of the possibilities. A huge problem with SIA is that 1, 2b, 2c, and 2d all imply an infinite number of observers, which makes SIA impossible to use. But for sake of argument let's say these universes do eventually end, and they all have the same (very large) number of observers. Applying just DA (Doomsday argument) favors 2a, 2b and 2e. Applying both SIA and DA favors 2b. So I guess you're right, whether or not you apply the SIA does not affect the the paper's conclusion that a shift away from 1 is warranted. This makes me realize that SIA doesn't perfectly counteract the Doomsday argument. DA makes you shift to 2a, 2b, and 2e. SIA then makes you shift to 2b, whereas what we really want is to shift back to the original distribution so we don't have to rule out 2c.
