In the paper, I show that every use of the anthropic principle claimed in physics and cosmology is either an example of this fallacy or is so vague that one can get any conclusion one wants, and match any observation, by manipulating the assumptions made.
I then go on to explain what a multiverse theory would have to do to yield genuine falsifiable predictions that actually depend on the existence of the multiverse. I give conditions for this to work. I then show that there exist real theories that satisfy these conditions, one of them being my old natural selection idea.
Therefore, the anthropic principle cannot help us to do science. But there are ways to do science if we are faced with a multiverse.
Lee
July 29, 2004: Susskind paper on Smolin’s theory of cosmic natural selection: Cosmic Natural Selection
hep-th/0407266
L. Susskind
Department of Physics
Stanford University
Stanford, CA 94305-4060
Abstract:
I make a number of comments about Smolin’s theory of Cosmic Natural Selection.
In an unpublished note [the “Answer to Smolin” email] I criticized Smolin’s theory of cosmological natural selection [1] which argues that we live in the fittest of all possible universes. By fitness, Smolin means the ability to reproduce. In my criticism I used the example of eternal inflation which is an extremely efficient reproduction mechanism. If Smolin’s logic is applied to that example it would lead to the prediction that we live in the universe with the maximum cosmological constant. This is clearly not so.
Smolin proposes that the true mechanism for reproduction is a bouncing black hole singularity that leads to a new universe behind the horizon of every black hole. Thus Smolin suggests that the laws of nature are determined by maximizing the number of black holes in a universe.
Smolin also argues that it is not obviously wrong that our physical parameters, including the smallness of the cosmological constant, maximize the black hole formation. To make sense of this idea, one must assume that there is a very dense discretuum of possibilities, in other words a rich landscape of the kind that string theory suggests [4][5][6][7].
The detailed astrophysics that goes into Smolin’s estimates is extremely complicated—too complicated for me—but the basic theoretical assumptions that go into the theory can be evaluated, especially in light of what string theory has taught us about the landscape and about black holes.
As I said, there are two mechanisms, eternal inflation and black hole production that can contribute to reproduction, and it is important for Smolin’s scenario that black holes dominate. Considering the low density of black holes in our universe and the incredible efficiency of exponential inflation, it seems very hard to believe that black holes win unless eternal inflation is not possible for some reason.
Smolin argues that we know almost nothing about eternal inflation but we know a great deal about black holes including the fact that they really exist. This is a bit disingenuous. Despite a great deal of serious effort [8][9], the thing we understand least is the resolution of black hole and cosmic singularities. By contrast, eternal inflation in a false vacuum is based only on classical gravity and semiclassical Coleman–De Luccia bubble nucleation [2][3].
The issue here is not whether the usual phenomenological inflation was of the eternal kind although that is relevant. Eternal inflation taking place in any false vacuum minimum on the landscape would favor [in Smolin’s sense] the maximum cosmological constant. But for the sake of argument I will agree to ignore eternal inflation as a reproduction mechanism.
The question of how many black holes are formed is somewhat ambiguous. What if two black holes coalesce to form a single one? Does that count as one black hole or two? Strictly speaking, given that black holes are defined by the global geometry, it is only one black hole. What happens if all the stars in the galaxy eventually fall into the central black hole? That severely diminishes the counting. So we better assume that the bigger the black hole, the more babies it will have. Perhaps one huge black hole spawns more offspring that 1022 stellar black holes.
That raises the question of what exactly is a black hole? One of the deepest lessons we have learned over the past decade is that there is no fundamental difference between elementary particles and black holes. As repeatedly emphasized by ’t Hooft [10][11][12], black holes are the natural extension of the elementary particle spectrum. This is especially clear in string theory where black holes are simply highly excited string states. Does that mean that we should count every particle as a black hole?
Smolin’s theory requires not only that black hole singularities bounce but that the parameters such as the cosmological constant suffer only very small changes at the bounce. This I find not credible for a number of reasons. The discretuum of string theory does indeed allow a very dense spectrum of cosmological constants but neighboring vacua on the landscape do not generally have close values of the vacuum energy. A valley is typically surrounded by high mountains, and neighboring valleys are not expected to have similar energies.
Next—the energy density at the bounce is presumably Planckian. Supposing that a bounce makes sense, the new universe starts with Planckian energy density. On the other hand Smolin wants the final value of the vacuum energy density to be very close to the original. It sounds to me like rolling a bowling ball up to the top of a very high mountain and expecting it to roll down, not to the original valley, but to one out of 10120 with almost identical energy. I find that unlikely.
Finally, we have learned some things about black holes over the last decade that even Stephen Hawking agrees with [13]. Black holes do not lose information. The implication [14]is that if there is any kind of universe creation in the interior of the black hole, the quantum state of the offspring is completely unique and can have no memory of the initial state. That would preclude the kind of slow mutation rate envisioned by Smolin.
Smolin seems to think that there is significant evidence that singularity resolution [by bounce] is imminent. Loop quantum gravity, according to him, is on the threshold of accomplishing this. Perhaps it will. But either it will be consistent with information conservation in which case the baby can have no memory of the parent, or it will not. If not, it probably means that loop gravity is inconsistent.
A. Guth and L. Susskind, To be published.
References:
[1] Lee Smolin, Scientific alternatives to the anthropic principle, hep-th/0407213.
[2] S. R. Coleman and F. De Luccia, Phys. Rev. D 21, 3305 [1980].
[3] S. K. Blau, E. I. Guendelman. and A. H. Guth, “The Dynamics Of False Vacuum Bubbles,” Phys. Rev. D 35, 1747 [1987].
[4] Raphael Bousso, Joseph Polchinski, Quantization of four-form fluxes and dynamical neutralization of the cosmological constant, hep-th/0004134, JHEP 0006 [2000] 006.
[5] Shamit Kachru, Renata Kallosh, Andrei Linde, Sandip P. Trivedi, De Sitter vacua in string theory, hep-th/0301240.
[6] Leonard Susskind, The anthropic landscape of string theory, hep-th/0302219.
[7] Michael R. Douglas, The statistics of string/M vacua, hep-th/0303194, JHEP 0305 [2003] 046; Sujay Ashok, Michael R. Douglas, Counting flux vacua, hep-th/0307049; Michael R. Douglas, Bernard Shiffman, Steve Zelditch, Critical points and super-symmetric vacua math. CV/0402326.
[8] G. T. Horowitz and J. Polchinski, Phys. Rev. D 66, 103512 [2002] [arXiv:hep-th/0206228].
[9] L. Fidkowski, V. Hubeny, M. Kleban, and S. Shenker, The black hole singularity in AdS/CFT, JHEP 0402, 014 [2004] [arXiv:hep-th/0306170].
[10] G. ’t Hooft, “The unification of black holes with ordinary matter.” Prepared for Les Houches Summer School on Gravitation and Quantizations, Session 57, Les Houches, France, 5 Jul - 1 Aug 1992.
[11] L. Susskind, Some speculations about black hole entropy in string theory, arXiv:hep-th/9309145.
[12] G. T. Horowitz and J. Polchinski, “A correspondence principle for black holes and strings,” Phys
. Rev. D 55, 6189 [1997] [arXiv:hep-th/9612146].
[13] New York Times 7/22/04.
[14] G. T. Horowitz and J. Maldacena, The black hole final state, JHEP 0402, 008 [2004] [arXiv:hep-th/0310281].
July 29, 2004, Smolin’s email response to Susskind’s criticisms:
Dear Lenny and colleagues,
I am grateful to Lenny for taking the time to respond to my paper. I will be as brief as I can in replying, especially as the key points are already presented in detail in my paper hep-th/0407213 [“Scientific alternatives to the anthropic principle”] or in my book, The Life of the Cosmos, or previous papers on the subject.
For clarity, I had in section 5.1.6 identified two arguments in Weinberg’s papers. The first is the one I criticized in the summary. Susskind reponds, reasonably, by agreeing, and then raising the second argument. This argument is also criticized in detail in my paper, and it was perhaps a mistake not to include this in the summary I sent to Susskind.
This second argument is based on a version of the AP called the principle of mediocrity by Garriga and Vilenkin, who have done the most to develop it. Their version states that “. . . our civilization is typical in the ensemble of all civilizations in the universe.”
This argument is discussed in full in sections 5.1.5 and 5.1.6. There I argue that the mediocrity principle cannot yield falsifiable predictions because it depends on the definition of the ensemble within which our civilization is taken to be typical, as well as on assumptions about the probability distribution. I establish this by general argument as well as by reference to specific examples, including Weinberg’s use of it.
Can this be right if, as Susskind claims, Weinberg’s prediction was found to hold? In fact, Weinberg’s prediction did not work all that well. In the form that he made it, it led to an expectation of a cosmological constant larger than the observed value. Depending on the ensemble chosen and the assumptions made about the probability distribution, the probability that Lambda be as small as observed ranges between about 10 percent and a few parts in ten thousand. In fact, the less probable values are the more reasonable, as they come from an ensemble where Q, the scale of the density fluctuations, is allowed to vary. While I am not an expert here, it appears from a reading of the literature [references in the paper] that to make the probability for the present value as large as 10 percent one has to assume that Q is frozen and fixed by fundamental theory. It is hard to imagine a theory where the parameters vary but Q does not, as it depends on parameters in the inflaton potential.
But, because there is so much flexibility—and an absence of strict, up or down, falsifiable predictions—anyone who wants to continue to use the AP in this context is free to modify the assumptions about the prior probability distribution to raise the probability for the observed value of the vacuum energy from 10-4 to order unity. No one can prove they are wrong to do so—and this is precisely the problem.
I do believe it is important to insist on falsifiability, because it alone prevents we theorists from keeping theories alive indefinitely, by freely adjusting them to match data.
It was worry about the possibility that string theory would lead to the present situation, which Susskind has so ably described in his recent papers, that led me to invent the Cosmological Natural Selection [CNS] idea and to write my first book. My motive, then as now, is to prevent a split in the community of theoretical physicists in which different groups of smart people believe different things, with no recourse to come to consensus by rational argument from the evidence.
The CNS idea was invented, not for itself, but to give an existence proof that shows that the anthropic principle can be replaced by a falsifiable theory, that explains everything the AP claims to. The reason I chose the term “landscape” of string theories, is to anticipate the transition to “fitness landscapes,” a term that comes from mathematical models that explain why the mechanism of natural selection is falsifiable.
As the theory of CNS is falsifiable, it is vulnerable to criticisms of the kind Susskind makes. Let me briefly address them.
The last first. Susskind claims that life is exceptional in the ensemble of universes. This is not true in CNS. The whole point of cosmological natural selection is that it follows the logical schema described in section 5.1.4 and 5.2. There, and in more detail in the book and papers, I show that falsifiable predictions can be gotten from a multiverse theory if the distribution of universes is very different from random. CNS results in a distribution peaked around small regions of the parameter space—so that a typical universe in this distribution is very untypical in any randomly chosen ensemble. I show in detail why falsifiability follows from this. I also show why reproduction through black holes leads to a multiverse in which the conditions for life are common—essentially because some of the conditions life requires, such as plentiful carbon, also boost the formation of stars massive enough to become black holes.
Next, there is a big difference between the explanatory power of the reproduction mechanisms of eternal inflation and black holes bouncing. This stems from the fact that any selection mechanism can only operate to tune parameters that strongly affect the rate of reproduction. Given that standard inflation acts on grand unified scales, the differential reproduction rate due to eternal inflation is only sensitive to the parameters that govern GUT [Grand Unified Theory]–scale physics plus the vacuum energy. Thus, eternal inflation cannot explain the values of any of the low-energy parameters, such as the masses of the light quarks and leptons. This means it cannot explain why there are long-lived stars or many stable nuclear bound states leading to a complex chemistry.
Reproduction through black holes explains all the puzzles and coincidences of low-energy physics because carbon chemistry, long-lived stars, etc., are essential for the mechanisms that lead to the formation of massive stars—those that become black holes. There is a long list of observed facts this turns out to explain, and a few genuine predictions. These are summarized in the paper and discussed at length in the book.
With regard to cosmological natural selection and the cosmological constant: If both mechanisms of reproduction exist, there is a competition between them that determines Lambda. Eternal inflation favors a larger cosmological constant, as Lenny says. But by Weinberg’s first argument, if Lambda is too big, there are no galaxies, hence many fewer black holes. To my knowledge, nobody has attempted to do a detailed analysis including both mechanisms. Vilenkin has pointed out that too-small Lambda can hurt black-hole production in a single universe by making mergers of spirals more common. This is briefly discussed in section 6.2, where I propose that the observed value may maximize the production of black holes—but this has not been analyzed in any detail.
Certainly, if the only mechanism of reproduction is eternal inflation, cosmological natural selection is wrong. But we know that there are black holes, and we have reasonable theoretical evidence that black-hole singularities bounce. I expect that in the next year we may have reliable quantum gravity calculations that will settle the issue, building on the methods Bojowald and collaborators have used to study cosmological bounces. So the consequences of reproduction through black holes seem reasonable to explore. Not only that, we are on firm ground when we do so, because star and black-hole formation are observed and controlled by known physics and chemistry.
We know much less about eternal inflation. We cannot observe whether it takes place or not, and there is little near-term chance to check the theories that lead to it independently, as there are alternative early universe theories—inflationary and not—that agree with all the cosmological data and do not yield reproduction through eternal inflation.
I do not know if CNS is the only way to get a falsifiable multiverse theory; it is just the only way I’ve been able to think of. As I have been saying for more than ten years, if CNS can be proved wrong, and if people are stimulated to invent more falsifiable theories to explain the observed parameters, this would be all to the good. So far CNS has not been fals
ified, but I read astro-ph every day looking for the discovery of a very massive neutron star that will disprove it.
I am very glad that Susskind has been able to give these issues much more visibility. But it would be very unfortunate if string theorists finally accept that there is an issue with predictability, only to fall for the easy temptation of adopting a strategy towards it that cannot yield falsifiable theories. The problem with nonfalsifiable theories is nothing other than that they cannot be proven wrong. If a large body of our colleagues feels comfortable believing a theory that cannot be proved wrong, then the progress of science could get stuck, leading to a situation in which false but unfalsifiable theories dominate the attention of our field.
Thanks,
Lee
Leonard Susskind’s “Final Letter”
When I was asked if I would be willing to continue a debate with Lee Smolin on the Edge website, my initial reaction was to say no. The problem is that the easiest ideas to explain, which sound convincing to a general audience, are not always the best ideas. The unwary layman says to himself, “Yeah, I understand that. Why is this other guy making it so complicated?” Well, the answer is that those simple ideas, that sound like you understand them, often have deep technical flaws, and the correct ideas can be very difficult to explain. All a person like myself can do is to say, “Trust me. I know what I’m doing, and he doesn’t. And besides, so-and-so agrees with me.” That doesn’t make a good impression. It can be a no-win situation.
Why did I agree to do it? Partly because I love explaining physics. Mostly—I don’t know why. But here goes nothing as they say.
In a nutshell, here is the view of physics and cosmology that Smolin is attacking:
(1.) In the remote past, the universe inflated to an enormous size, many orders of magnitude bigger than the observed portion that we can see. Most of the universe is behind the cosmic horizon and cannot be directly detected.
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