Albert N. Schellekens wrote a popular 87-page preprint,

The emperor's last clothes?It is clearly a popular text but yes, indeed, it is way more technical than some books that are considered by their authors to be more-than-popular. ;-)

*Wordle...*

Schellekens, together with Dieter Lüst and Wolfgang Lerche, wrote a paper or two in the 1980s that argued that the number of vacua in string theory was huge, comparable to 10^{1500}. So if this insight is a discovery or a "paradigm shift", they should surely be included among the fathers of this idea. Well, I am not among those who would think that these "fathers" should be excessively proud about something or even fight for priority! :-) They just wrote a high number (an upper bound) whose derivation was not quite correct and whose philosophical consequences seem irrational to me (and at any rate, they were proposed centuries ago).

At the beginning, Schellekens criticizes the people who now say that they always knew that the number was huge but they didn't find it important enough to talk about it. ;-) Well, I think that his criticism is legitimate and I am not among the people criticized by Schellekens because I never thought that the number was that huge - even though now I think it is probably true - and I do think that this question is somewhat important: those who "knew" it shouldn't have been silent. But I also think that the large number of the vacua itself doesn't imply the anthropic reasoning.

So while there is a sense in which the anthropic principle is a very old story and no contemporary scientist should sell it as his discovery, it is also true that only the stringy flux compactifications that were found in this decade have made the possible anthropic picture of physics "complete". Even though string theory doesn't really imply that the anthropic reasoning is correct, it is also the only framework we know where the numerous vacua may be classified and co-exist in a huge multiverse. String theory offers the only satisfactory incarnation of the anthropic reasoning. As many other important keys, string theory is able to open the gates to the Heaven as well as the Hell.

**Is uniqueness the same thing as anthropocentrism?**

But as you can guess, I disagree with Schellekens' main theses. The anthropic principle is neither something we should be happy about (Schellekens views it as a victory of string theory and related breakthroughs) nor something we should feel certain about. However, this debate is not just about one-sentence "opinions" and even in his popular text, he has written 87 pages of somewhat insightful arguments. I won't offer you 87 pages but we will look at many of them, anyway.

First, there exist two full propaganda machines justifying the anthropic principle or, on the contrary, the possibility to find the full, unique, and complete laws governing the Universe (monovacuism, if you wish). Schellekens also dedicates a few pages to this propaganda - and various funny and subtle kinds of criticism invented by the physicists in both groups.

The anthropic people including Schellekens and Susskind claim that the "landscape revolution" is analogous to the Copernican revolution and other revolutions in science: stupid people used to think that they were terribly important (they believed in anthropocentrism) but brave scientists have shown that the humans were not so special, after all. The Earth is not a center of the Universe, and neither is our Sun or the Milky Way. The human DNA is not qualitatively different from the DNA of other animals. And perhaps, our Universe is just one among zillions of universes in the multiverse. The properties of elementary particles can't possibly be unique, can they? The Universe is a mess and it has always been one. :-)

Well, that's one story. But I also see a completely different story involving more recent breakthroughs in theoretical physics that are arguably more relevant for the question of predictability of the particle masses than Copernicus' adventures. During the last century or so, we have seen an incredible unification of concepts and observations that eventually allowed us to describe all of chemistry, engineering, and biology (thousands of materials, objects, and their diverse interactions) in terms of a single theory (QED) with one dimensionless parameter, the fine structure constant (and perhaps the proton-electron mass ratio), and even if you're interested in the other physical effects that are pretty much irrelevant for life (such as nuclear physics), we can describe everything by a similar theory with 28 parameters (the Standard Model; plus add General Relativity in a sloppy way to separately describe the gravitational phenomena). It is natural to expect that the missing step to complete the picture is analogous e.g. to the electroweak unification and it will make the remaining parameters calculable, much like the spectral frequencies of all atoms became calculable 80 years ago, and we seem to be damn close to completing this step. The Universe is elegant and it has been elegant even before the first moment when people noticed. ;-)

These are stories about two scientific "trends". These trends seem to have the opposite "signs". They are "derived" from our experience at different time scales. They are "derived" by selectively focusing on some stories while neglecting and humiliating others. I think that every rational person realizes that the answer to the question whether the anthropic explanation of the Standard Model or its unique derivation from a fundamental theory is the right approach doesn't necessarily have to mimic the answers to "similar" questions answered by Copernicus. It doesn't have to "reproduce" the uniqueness of QED, either. We are simply asking different questions than the previous generations and different questions sometimes have the same answers but they often have different answers. For example, the world has been increasing in size in Copernicus' and Hubble's time but so far it has never increased behind the boundaries where we can actually see anything. Many quantities - such as temperature - were shown to depend on the environment (distance from the Sun etc.) but it still seems that the particle masses and couplings we want to calculate are universal across those 14 billion light years of the visible Cosmos.

And the uniqueness has worked in fundamental physics but there are many stories close to fundamental physics where it didn't work and where we believe that historical coincidences played a critical role in determining some parameters.

I say that all sane people must be aware of the fact that we can't "derive" the answer to this completely new question by extrapolating the previous experience. But at the same moment, it seems that many people try to pretend that they believe that such an extrapolation is possible. Sorry but as long as you focus on rational arguments, such an extrapolation is impossible. There's no way to be sure. The "uniqueness" answer hasn't been proven; it is probably necessary to actually find the correct unique answer before we will know that the answer is unique. ;-) And the "anthropic principle" hasn't been proven, either. Whoever thinks that he has a simple philosophical proof of his attitude is sloppy. And whoever thinks that his answer must be correct because all other answers can be defined "not to be science" is an imbecile. And Nature doesn't give a damn how imbeciles define science: Not Even Woit.

When we discuss these anthropic questions, there exist various technical differences between field theory and string theory: string theory actually allows us to define the measure on moduli spaces, count the discrete vacua, and connect them to a unified cosmology via the eternal inflation and tunneling. Because the stringy realistic vacua are discrete, they are more specific and, in principle, completely localizable (even though one of the points of the anthropic approach is that you shouldn't even try to do it). Nevertheless, the deep essence of the anthropic argument seems to be identical in field theory and string theory. So we can ask:

**Can the Standard Model parameters be derived from a fundamental theory?**

We don't know the answer. Once people actually derive them, the answer will clearly be "Yes". The anthropic people say that the answer is almost certainly "No" and the rest of us says that their conclusion is premature.

Schellekens describes the reactions of the anthropic infidels as disgust (or even religion!) :-), denial, and derision but he also mentions that Burton Richter considers the anthropic people to be creationists. By the way, it is actually very subtle which group is closer to creationism: it depends on your optics.

Schellekens recalls some of the anthropic coincidences that seem to be necessary for life and offers us an anthropic checklist - four steps that help a careless reader to wash his brain and become an anthropic person, too. ;-) The checklist is rather clever, so let us look at it:

- The Standard Model may not be the unique mathematical solution of any fundamental theory.
- Not all alternative solutions allow observers.
- The total number of solutions should be sufficiently large to make the existence of a solution with observers plausible.
- We live in the most probable Universe which allows observers.

First, I tend to agree with (1). I find it unlikely that a fundamental theory - or even string theory with a selection mechanism - would make the rather messy Standard Model (with its parameters) a completely unique solution. After all, we know many other solutions to string theory and I am convinced that many (or most) of them will survive the test of time.

The statement (2) is almost clearly correct, too. For example, some stringy vacua with unbroken supersymmetry can be almost proven not to have any observers or intelligent observers. We don't have a full proof of it - because we can't really define observers and classify all conceivable "types of life" - but it is plausible that we could construct such an argument. One of Schellekens' powerful tools is to emphasize that we don't have to prove that "our island" in the parameter space is the only place that admits life (which seems extremely hard to argue because there can be discretely many "types of life"). It is enough to show that there are many generic places outside that almost certainly don't admit life.

Now, because I have accepted the points (1) and (2), Schellekens says that I have already adopted "some kind of anthropic reasoning" because there are places (different universes) where we don't live. Well, fair enough. It is "some kind" but I still haven't accepted (4), have I? :-) Just the fact that I don't live in the middle of ocean doesn't mean that I can't exactly calculate the the number of protons in the atoms dominating our atmosphere (nitrogen).

I kind of agree with the binary content of the point (3), too, but the precise explanation why I agree could be highly disappointing for Schellekens. If we make an estimate of the probability (or plausibility) that life is born somewhere in the multiverse allowed by the fundamental theory, the probability shouldn't be much smaller than one. The life shouldn't be a completely unexpected accident according to science.

However, one must be very careful how this probability of having life somewhere is calculated. Schellekens is now slowly trying to convert the readers to the irrational anthropic reasoning, in order for them to accept (4), too. Why? Because he wants you to believe that the probability that the life exists somewhere - among N universes - is essentially equal to N times P where P is the probability that the life is created in one "typical" universe (the formula gets corrected if N times P would be close to one or greater than one).

This could be a good order-of-magnitude estimate in an "egalitarian" multiverse where all universes have the same chance to host observers. But I think that this "egalitarianism" is simply incorrect and it is very important for this whole anthropic debate that this principle is incorrect. In fact, I can make the accurate calculation of the probability that a correct fundamental theory allows for observers somewhere on its landscape: the probability is not N times P but rather 100%. It's that simple.

We know that life exists, so if the theory is correct, it must predict life inside one of its solutions. The only problem could occur if no fundamental theory existed at all, but I choose to discard this possibility. If we only want to know whether it predicts life or not, it doesn't matter how many classical solutions it has and what is the distribution of the probabilities that each of them allows intelligent observers. What matters is that it contains at least one universe - ours - that admits life.

This "N times P" calculation is sloppy, ideological, and this ideology - the egalitarianism between vacua that are clearly different, non-equal, and hierarchical in many respects - is the essence of the anthropic fallacy. In my calculation, I didn't even have to multiply two numbers: you might think that it makes my calculation less mathematical. However, my result is actually exact, unlike the results of Schellekens' implicit formula.

It is interesting to look at Schellekens' calculation of the probability in (3) from one more viewpoint. He seems to require that the density of the stringy vacua in the vicinity of our region of the Standard Model parameter space should be huge, otherwise it is awkward to believe that any vacuum of string theory matches reality. I fundamentally disagree with this proposition. Here is my checklist to see why this proposition is irrational:

- The density of the stringy vacua near our locus in the SM parameter space is not infinite because the number of semirealistic stringy vacua is finite: so Schellekens can never be "completely satisfied".
- When you try to find out a "natural lower bound" for the density, you won't find an acceptable answer. For example, you might require that the small region that describes our Standard Model with the error margins of parameters as extracted from the 2008 measurements should contain at least one stringy vacuum, if calculated by the densities. But this "falsification" would clearly be irrational because such major decisions about the validity of a theory cannot depend on the number "2008" or some random coincidences about our present world.
- Moreover (and the following argument is related to the previous one), sometimes in the future, the measurements of the SM parameters will be more accurate, the error margins (and therefore the relevant region) will be smaller, and the number of vacua calculated in the "ball" around our point through the densities could drop well below one. In the future, the "test of sufficient density" is likely to fail even if it passes today. Sometimes in the future, this "density" test will fail. If you know so, shouldn't you agree that the test is failing already today?

- Once you agree that there exists no "sensible" lower bound on the density of stringy vacua near our locus, you will realize that it should have been completely expected that this criterion was nonsensical from the very beginning. When the density of stringy vacua near our point is (much) lower, it simply means that string theory will be (much) more predictive when it comes to the Standard Model parameters. There is nothing wrong with a theory that is more predictive. We have always believed that we were looking for predictive theories and if the supposed "paradigm shift" is that we must require the theories to be unpredictive, I simply disagree. Schellekens seems to believe otherwise: he thinks that every theory that is predictive is excluded and only theories that can be adjusted in any way to match the observations by chance are allowed. I beg to differ.
- To summarize, the only sensible "phenomenological" way to falsify string theory (or another hypothetical theory with many vacua) is to show that the number of vacua in the vicinity of our locus in the SM parameter space, plus minus the known error margins, is strictly equal zero. Any other "falsification" claiming that the density seems "too low" is a fallacy based on the (ludicrous) assumption that theories are never allowed to predict anything.

Let me say one more comment. The anthropic selection could be "partially correct" etc. but even if it is so, the interesting observations are the aspects in which the anthropic reasoning is incorrect. This is where the new patterns and new scientific insights are located. So it would be highly counterproductive to assume that the anthropic assumptions of genericity are "nearly universal".

And one more observation about the point (3). I calculated the probability that a viable universe is somewhere in the landscape of the fundamental theory. That was equal to 100%. But if I give you a Hartle-Hawking-like cosmological selection criterion, it secretly assumes that only one universe gets materialized, not all of them simultaneously, and the formula can produce a different probability for the realization of a (any) universe - and a different formula for the probability that life emerges. The result could be much smaller than 100%. That's true. But what is not true is the implicit assumption of the anthropic people that if I require the probability to be calculated in this way and if I want the result to be close to 100%, I must allow (almost) all vacua on the landscape to contribute. The final section of this essay describes a very dramatic scenario how the probability could be high even if the vast majority of the landscape had a highly suppressed weight in the probabilistic measure. But even if you find the scenario unlikely, there exist less dramatic possibilities where only a tiny fraction of the landscape contributes.

So the answers are

- Yes.
- Yes.
- Yes, but the answer is trivial and the very question tries to make you accept a wrong formula.
- No.

In order to show how political, vague, and socially dependent the anthropic methods are, let me consider the following gedanken experiment. Imagine that you establish a new country and you invite 100 million settlers. Now, the question is: What is the expected number of Fields medal winners? The anthropic people would divide the population by the world population, multiply it by the total number of the Fields medal winners who are alive, and they would get something like 1 Fields medal winner.

But what if I tell you that 99 million settlers are female? Now, it will be an inconvenient question for the left-wing anthropic people. Some of them will say that the probability hasn't changed at all because the sex doesn't matter. The more reasonable ones will make a new calculation and their estimate will decrease by a factor of 100 because there are no female Fields medal winners which is why only the male ones contribute to the expectation value: their total expected number of Fields medal winners will be smaller than one, essentially zero.

Eventually, someone manages to look at the people and among the 1 million of the male settlers, they find Witten, Tao, and Connes. So the correct answer is 3, after all. But the previous estimates turn out to be useless.

The procedures to quantify the phenomenological viability of the multiverse and its subsets are completely analogous. The more we know, the more irrelevant the initial estimates become. And they often turn out to be completely wrong. The anthropic people usually assume that certain quantities, densities, and probabilities are constant for all members of vast sets. But it matters how finely you divide the set into subsets: will you allow your grad students to count the F-theoretical flux vacua and heterotic vacua (or males and females) separately? If you want to get the accurate result, you should divide it to the individual members and do the exact calculation.

Let me mention another, more physical example explaining why we often need to know the exact (or almost exact) answers. The fusion in the Sun is important for our lives but it can only work well if the mass of the helium nucleus is slightly lower than the mass of two protons and two neutrons in the two deuterium nuclei (apologies for oversimplifications, this example is easy to talk about). But you might think that these nuclei are generic states of QCD and by dimensional analysis, the difference of their masses is comparable to the QCD scale. That would generate too high temperatures and maybe other problems. However, the argument is wrong. The energy generated by fusion is comparable to 1% of E=mc^2 only.

And I don't need to assume life to find the 1% figure: a better calculation rooted in QCD or nuclear physics is enough. Some "deeper" patterns that go beyond order-of-magnitude estimates are often damn important for figuring out whether a physical system allows life, among other things. Assuming that all vacua in the landscape have the same probability to host life is analogous to the assumption above that all energy differences in nuclear physics are comparable to the QCD scale. They're not and in many cases, there is a very good scientific reason (not just chance or the requirement of life) why some of them are much smaller.

The very program of the anthropic approach is to forget and deny all deeper patterns and all more accurate and more detailed calculations, to replace our sharp picture of the world by a permanent colorless uniform fog of ignorance. The very goal of this ideology is to convince physicists not to improve their understanding of Nature and to replace exact calculations by low-brow order-of-magnitude estimates. The anthropic reasoning hasn't worked in previous scientific revolutions because more specific explanations were always found and the idea that it is exactly around 2008 when the sharp answers disappear and the anthropic fog becomes relevant for all open questions is a form of fine-tuning. There is no reason for the number 2008 to play such a special role in the scheme of the Universe. ;-)

The assumption that all vacua in the landscape have the same probabilities etc. and we must live in a vacuum in the class that dominates the "total number", whatever the artificial boundaries of the class should be, seems obviously false to me. There exist all kinds of hierarchies, including hierarchies that have neither an anthropic explanation nor a universally acceptable scientific explanation (such as the QCD theta-angle), that show that our vacuum is not completely generic. We kind of know that we have three generations (or the Euler character of a Calabi-Yau) and with further high-energy experiments, it is plausible that we will be able to "measure" other invariants describing the correct compactification, its topology, the numerical values of fluxes, the number of branes, and the shape of the throats. The idea that there can't ever be progress in science is also ludicrous and it's been falsified zillions of times. The only question is how fast the progress will be. We're not guaranteed anything.

The idea that we must live in the "gray" zone of the "most generic" and "uninteresting" vacua could be a great theory for insect in China because it may be the most numerous group of living objects, classified by their country and their class in the Linnaean taxonomy. But this theory simply doesn't look good enough for certain mammals in the Czech Republic.

Schellekens and other anthropic people say that they would be worried if some feature of our world were not "generic" in the stringy vacua - a point analogous to their requirement of a "high density" near our locus. I would not be worried because there exists no law that we would have to be generic. After all, the exact properties of our life and our nationality require the exact vacuum we live in, despite the low density of vacua around (or despite the low population of the nation). But even if someone convinced me that our vacuum should be generic (in "most aspects"), I don't think that anyone knows what the right measure to determine the genericity should be: the "each vacuum has the same vote" measure is surely not good enough because of many reasons, for example because the total number of all vacua (including the AdS5 x S5 vacua) is infinite and the uniform probability measure can't be normalized. It is even wrong to use the counting based on volumes of the Standard Model parameter space because the Standard Model is clearly neither the first nor the last effective field theory that can be written down: it only corresponds to the state of our experimental knowledge of particle physics as of 1973-2008. The QED used to have a smaller parameter space and the MSSM or other future effective theories will require different, possibly larger parameter spaces.

Because the anthropic people rely on so many concepts that are only relevant in 2008, what they're doing is a statistical interpretation of the history of physics, with a focus on the present era, not physics itself. Note that I am in no way saying the "same thing" as Peter Woit. I am actually finding particular material flaws in various arguments while the obnoxious repetitive crackpot only says (731 times) that none of these things is science and he doesn't even have to think about any of the arguments - which is just an arrogant propagandistic nonsense and surely not a contribution to the scientific debate.

We may not be the most special creatures (and universe) in the multiverse (even though Leibniz used to say that our world/life is the best possible world/life) but we are not the most generic (or messy) ones, either. Both of these assumptions are irrational philosophical prejudices and unjustified extrapolations from cases where they happened to work. Now, we can pretty much sit at a reasonably generic point of a statistical distribution but you can't ever be sure how close to the central or most likely values you are. For different quantities, the distance from the "genericity" may be very different. There is clearly no universal answer.

Sometimes you are very generic, and then the insight about your genericity is not too interesting because it carries low information. Sometimes you are special. The information clarifying why you are so special is higher (if a theory predicts a very special feature, it is very predictive) but such cases are less likely. There is a trade-off going on here and whoever thinks that the very anthropic assumptions can lead to a high-information conclusion that is nevertheless very likely to be true, without finding non-anthropic arguments and mechanisms, is clearly making a logical error.

There is no rational reason to think that individual vacua should carry the same "weight" in the anthropic distribution. And if you use the very existence of life to deduce something about the low-energy parameters, you won't get too much interesting information because we know much more than the fact that life exists in our Universe. We also know the values of all low-energy parameters that make this life (and many other things) possible. Anything that can be derived about our compactification from the existence of life can clearly be derived from the known values of the parameters, too (because the life itself can be derived from them). Physicists should finally appreciate that it is legal for them to use all the known experimental data (including those found in the near future) in their search for the correct theory (and its vacuum). It used to be legal in the past, too. ;-)

Why would you ever use the incomplete information about the existence of life only rather than the full information you can have? It looks like a children's game where a kid has to determine something without looking somewhere. But scientists are allowed to look, aren't they? Note that it is still the same complaint against the "selection fallacy" that I have already raised many times. When the anthropic people calculated a probability as "N times P" (Schellekens in his point (3)), they were also using an incomplete information, representing every vacuum by a "generic representative" for some class even though more accurate calculations are clearly possible as long as people keep on improving and sharpening their knowledge about particular vacua and abilities to deal with them.

**Laws that maximize life naturally**

Finally, I want to say that the ultimate laws governing the vacuum selection can be "naturally" compatible with the existence of life in the preferred Universes.

A universe that admits life has to satisfy all kinds of features and many of them have a quantitative character: various parameters and ratios have to be small. You have to have a lot of hierarchies of scales (a small cosmological constant, an electroweak-Planck gap, fermionic mass hierarchies), a lot of different long-lived states (nuclei, molecules) in the spectrum that have sufficiently different geometries, and so on. Imagine that you create a similar "index of life magic" I_{LM} as a function of various "healthy gaps" in such a way that the vacua with a higher value of the index can reasonably be expected to admit life "more easily" than the vacua with a low value of the index.

This index is an artificial human invention but it is completely plausible that there exists a natural formula - e.g. one derivable from a generalization of a Hartle-Hawking wave function - that has similar consequences and that naturally makes it more likely for life to appear in the universe that is also predicted to be more likely by a cosmological HH-like selection formula.

Do you think that such a hypothesis is a form of a conspiracy theory? Feel free to believe it is. But the objects that make life extremely unlikely in certain environments are just continuous numbers: discrete conditions only reduce the number of viable vacua by a factor comparable to one (such as two). And continuous numbers often like to enter formulae. When you have a Hartle-Hawking formula dictating the probability of different vacua (or low-energy parameters) after an early era of cosmology, it usually depends on these numbers: recall the dependence on the cosmological constant (with the problematic sign). The dependence can be strong, it is almost guaranteed that there is a bias, and the probability that the bias is in the direction that favors the "viable" vacua is significant, maybe even higher than 50% (a priori). When you actually fill in the details of this theory, you will be able to say that the probability is 100%. ;-)

If this picture is correct, there can exist an old-fashioned scientific, non-anthropic explanation why we live in a universe where life looks a priori easy. I find this picture speculative but from the viewpoint of eternity, it is very plausible. Viability can be imprinted to our world through the basic laws of early cosmology. Every "theorem" that tried to prove that similar calculations must be impossible has been circular so far: all of them had to assume that our Universe belongs to the gray zone and it has no theoretical or phenomenological "fingerprints" or special features that could identify it - and they proudly proved that one can't ever identify such a vacuum by its fingerprints in a polynomial time (sorry, Frederik and Michael, but that's what you're doing).

I wouldn't make a bet that someone will actually find such a non-anthropic explanation of the viability of our Universe in a few years but many key events in the history of science have been unexpected. Moreover, the belief that the anthropic fog won't be falsified in a near future (a belief I share) is something different than a belief that it is the correct answer (which I don't share). People naturally focus on research directions where they can make progress, so I am certainly not afraid that every talented physicist is going to work on a hopeless project. But even if some project loses man-hours, it doesn't mean that there can't ever be a new breakthrough in this project. But even if you don't believe that such new insights about the vacuum selection problem will be found in the future, it is probably more fruitful for the physicists to focus on attempts to find new patterns and laws rather than self-fulfilling attempts to prove that science is over. ;-)

Because the arguments that our Universe must be generic (and there is no extra information we can ever learn about it) seem to be circular and seem to contradict the whole history of science which has always seen some additional progress, I think it is reasonable for a physicist to expect that every "generic" description of a system we don't understand is a temporary state of affairs. The more we will know, the more the fuzzy anthropic fog is going to be replaced by a sharper picture full of fascinating insights, important patterns, illuminating relationships, exact numbers, and specific links to previous theories as well as observations, insights that are similar to hundreds of those that have already been found.

And that's the memo.

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