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The anthropic lack of principles

Sean Carroll just wrote an essay on his blog (incidentally in the same domain as my blog), and Peter Woit has replied. Why don't we write a couple of words about it, too?

  • As an introduction, let me say that the "anthropic principle" is a philosophical paradigm designed to reduce our curiosity about the patterns in Nature. When we ask "How is it possible that a value of some parameter in Nature is XY, which (always) happens to be the right value necessary for life?", the anthropic principle answers "in all the other Universes (whose existence is an assumption of the anthropic thinking) where the value is different, there is (probably) no human being (no 'anthropos') to ask this question."
  • Consequently, this approach allows us to say "We don't need to look for any other explanations because if the things were different, we could not be here." Such an attitude makes further scientific research less meaningful, and therefore the attitude is anti-scientific

  • It seems to me that both guys mentioned above - Peter and Sean - write pretty reasonable things, but both of them also write things that are harder to agree with
  • I believe that Peter Woit has a very similar algorithm like me to decide whether a theory is predictive and interesting, but he really misunderstands some important aspects of string theory - and this partial ignorance invalidates his conclusions about string theory
  • Even though I am counted, much like Peter Woit, as an anti-anthropic extremist according to Sean's classification, as the title of my article indicates, I totally agree that it is a conceivable scenario that some parameters of this Universe will eventually be explained as environmental parameters without a deeper quantitative explanation
  • However, much like Peter, I will only believe that such a model of reality is better and more likely (and scientifically plausible) than others once it successfully predicts many new phenomena (more phenomena than competing or older theories) or relates the previously unrelated phenomena that have already been observed - more precisely, once it calculates a lot of verifiable new numbers that go beyond the input
Let me start the main text by telling you what's wrong with Peter's description. Peter systematically tries to create the impression that string theory cannot be predictive. In fact, the emergence of the anthropic reasoning has just the opposite reason. Why?

In the Standard Model, which is a non-gravitational theory, the sum of the vacuum diagrams does not really matter because the vacuum energy has no effects in a non-gravitational theory.

However, if you couple such a theory to gravity, the vacuum energy does matter, because it curves the space and time. However, in quantum field theory, you can always add a counter-term and adjust your vacuum energy to whatever you want. You need some fine-tuning, but you can always adjust such "constants" in quantum field theory. It's just a matter of naturalness, much like in the hierarchy problem (associated with the Higgs mass).

That's not the case of string theory. Here, you can really calculate the vacuum energy, and in the simplest models/vacua, you obtain a far too huge value of the cosmological constant - assuming that some serious bug about our understanding of SUSY breaking don't invalidate the whole conclusion.

In this sense, the cosmological constant problem in string theory is (or was) more serious than in quantum field theory because string theory is a very rigid theory that does not allow you to mess with the parameters. On the other hand, a part of the stringy calculation relied on quantum field theory and it is still plausible that a more complete, inherently stringy calculation of the cosmological constant leads to more realistic results.

Well, the anthropic industry in string theory is more or less meant to put the cosmological constant problem in string theory onto a comparable level with the cosmological constant problem in field theory. The freedom to continuously fine-tune the vacuum energy in field theory is replaced by the large number of vacua in string theory - and you can really see that some of them are more or less guaranteed to predict a qualitatively correct value of the cosmological constant "by chance". This anthropic thinking is annoying, but honestly speaking, its well-being is caused by the absence of a really convincing quantitative calculation of a small cosmological constant.

You know, I am among those who believe that we don't quite understand this counting, especially after SUSY breaking, properly, but the anthropic people will disagree. Shamit Kachru et al. will tell you how to calculate all possible contributions to the potential, and he will argue that nothing is neglected and all approximations they make are justified.

They will tell you that they have a full control over the class of the KKLT-like vacua (that was elaborated by Mike Douglas and his collaborators and others), and this full control allows them to state quite certainly that string theory does predict a large number of vacua - even those controllable ones form large classes.

Once again, Peter is absolutely wrong if he thinks that string theory's nature is its inability to predict. On the contrary, string theory in principle predicts everything - its character certainly makes it the most predictive theory we ever had (and that one can imagine). In fact, the appearance of the landscape in string theory may be viewed as a consequence of its strong predictive power - because some people just became convinced that a choice of one of a few "simple" and "natural" enough vacua is more or less guaranteed to predict an incorrect cosmological constant. This is why the people started to propose the convoluted vacua that can give you, more or less by chance, a realistic cosmological constant, too.

It's wrong to think that string theory - even with the anthropic accent - is less predictive than field theory. Even if you imagined that string theory could give you virtually any field theory at low energies, it is still morepredictive because it is a UV complete theory containing quantum gravity - something impossible in quantum field theory - and each of its vacua tells you the cross section of gravitons at any energies etc. Its low energy physics may have many types, and in this sense the "Landscape" of stringy vacua is analogous to the "Landscape" of quantum field theories - with the difference that the landscape of QFTs has continuous parameters, while string theory only has discrete ones (although there can be many of them).

Unfortunately, string theory is not only the best predictive theory (in principle), but it is also the only known semi-scientific incarnation of the anthropic reasoning. In order to deal with the anthropic reasoning semi-scientifically (the word "scientifically" would seem too ambitious), you must have a theory with a large number of possible Universes and a dynamical mechanism that allows you to go from one to another.

Moreover, to invent a well-defined measure, it's easiest to have a discrete set of vacua - then you can say that each vacuum is "equally likely". (I believe that this is a non-scientific and unjustified assumption, but I also agree that the game based on this assumption is well-defined.) There is no other theory like that (with a large discrete number of dynamically connected vacua) known, except for string theory.

Sean Carroll's "non-partisan" objections against us, the extremists

Let me now look at Sean's criticism of his anti-anthropic colleagues. He thinks that the anti-anthropic physicists have two basic types of arguments:
  • we say that it is not scientific to "give up" a scientific explanation of a universal number in Nature and to demand some "random unexplainable" or even "divine" justification of such a number
  • we say that the other Universes required by the anthropic reasoning are unobservable in principle, and therefore they should not count as a part of a truly scientific description of the world
Yes, it seems fair, and I count both points as parts of my basic objections against the anthropic principle, but let me clarify some details.

The first objection is the "defeatism" of the anthropic reasoning. Yes, I think that it is a very wrong approach to science. One might have stopped the progress in science at virtually any moment in the past by claiming that some not-quite-understood features of reality are consequences of unexplainable dynamics involving zillions of Universes (or choices for the laws of Nature), and the only reason why reality behaves the way it does is that if it behaved otherwise, we would not be here. Examples of possible past applications of the anthropic reasoning will be discussed at the end of this article.

In fact, it is not just about "might have stopped". Such a thing has happened many times in the history of our civilization. The medieval anthropic biology has stopped the research of the relations between different organisms, and the research of the reasons why the animals and plants had the observed properties, for several centuries. The official answer was that the plants and animals were created by God. They had to be created exactly in this way because God, who is perfect, simply did so before he created us (at the end of the week). If you imagine any modification, you would obtain a Universe with a less perfect god that would not be capable to create us, and moreover, you should be burned at the stake.

Darwin's theory replaced this picture by something else, and even though it has not become as quantitative a science as we desire, the progress is clear and many previously mysterious properties of the animals could have been explained. Darwin's theory also agrees with other newer developments, including the discovery of genetics and DNA.

You may say - and some people actually say - that the anthropic reasoning is not similar to religion, but instead, it is analogous to Darwin's theory because the Universe "compete" much like the animals, and there is no explicit God there. Well, it is as analogous as much as the evolutionary theory itself is analogous to creationism, but not more. Darwin's theory has pretty well-defined rules and mechanisms. The animals are doing all these familiar things and they live together - and compete - according to some schemes that are deeply rooted in biology, chemistry, and physics - and that we can predict.

On the other hand, the arena of very many Universes that "compete" has no testable rules like that, and therefore it mimicks religion. (Of course, if someone could derive really exact rules that govern the Universes in the multiverse, the situation would change.)

This brings me to the second point why most of the forms of the anthropic reasoning are not quite scientific: the conjectured properties, role, and existence of the other Universes are not subject to science, especially not the experiments.

First of all, if someone were thinking in terms of an ensemble of the Universes that even do not belong to a single theory, that would be a completely anti-scientific approach simply because he would be combining things without any physical connections between them into a single whole. Such versions of the anthropic approach would be a realization of the idea "anything goes" and their value for science is certainly zero or less. An average person 10,000 years ago, with no experience and no experiments, could have conjectured this sort of crap. I think that many did, but it has led to no progress in science.

Let's not waste time with this nonsense, and let's look at something more scientific: the anthropic principle with an ensemble of different "vacua" that are connected into a single dynamical theory. Of course, we can't require that the actual people can move in between the Universes because "our life" is only possible here - and perhaps, it does not have to be necessarily possible to physically create a bubble of another Universe within your Universe (these issues have been discussed by Tom Banks). Nevertheless, it seems essential to require that all these Universe belong to a single theory - well, string theory is the only known reliable framework for this kind of game.

I still find it obvious that the "other" Universes or vacua of string theory - which the humans will never be able to observe - can only have the following scientific consequences:
  • they are often useful toy models (well, they can be rather convoluted toy models) to study physical phenomena that will also be useful for the investigation of our real Universe, or phenomena that are exciting mathematically even without direct links to observable physics
  • these other vacua can also be relevant if they occur in the early history (or prehistory) of our Universe, and if we find the right mechanism that allows us to study the transmutation of one Universes to another from a well-defined starting point
Otherwise, if we don't have any measure on the space of vacua and no cosmological mechanism to generate this measure (which would essentially mean that such a mechanism could really predict something), then the existence of other, unobservable vacua is totally irrelevant for our investigation of this specific Universe. It is irrelevant for two related reasons:
  • from a pragmatic viewpoint, we can only observe effects in this Universe, and the other Universes are uninteresting
  • even if we found the other Universes interesting, the statements about them are not directly testable
In this sense, I agree with Peter Woit that having a large number of possible Universes that can imply anything is equally bad as having no explanation whatsoever. At the end, we can show that string theory is correct - by hundreds of new and nontrivial quantitative predictions - and this final form of string theory may imply the existence of other Universes, and Peter will have to believe it, too. But I sympathize with his opinion that he should not be asked to believe in the other Universes before the theory is proved correct. Extraordinary claims require extraordinary evidence, and the necessity for 10^{500} of Universes like ours seems to be an extraordinary claim.

Where should science go?

I think that at the very end, all of us would agree that all these possibilities are conceivable, at least in principle. Peter Woit and me would almost certainly agree that it may happen that some much more perfect science in the 25th century will consider some parameters of Nature to be environmental parameters which either can't be calculated at all, or they can be calculated once a finite amount of information (about the discrete vacua) is determined. On the other hand, I am pretty sure that Sean Carroll would agree with us that it is possible that a very scientific, canonical, and quantitative calculation of the Standard Model parameters will be found and the anthropic proposals will become irrelevant.

But these questions are not just "yes/no" questions: they are about the probability of various things and our methods to estimate the probability and judge whether a direction of research is promising or not. Therefore, let me return to the analysis of how damaging for science would it have been if the people decided that something were not explainable, but they were rather a consequence of a divine choice or perhaps necessary conditions for us to exist (even though no one can actually prove the necessity).

I've already said that the whole evolutionary biology would be blocked (and genetics and DNA research would be blocked, too) because the whole motivation of Darwin's theory and genetics is to explain some previously mysterious properties of plants and animals, and the relations between them (and between the properties of the parents and their offsprings). All of these things could have been treated as environmental coincidences that don't admit an explanation, and science would be stuck.

Physics has even much more impressive examples what could have happened if people gave up and accepted the anthropic "answers" in the past. The properties (density, permitivity, freezing point etc.) of all elements and perhaps all compounds could have been treated as a conglomerate of environmental parameters whose choice would be believed to be necessary to explain our existence.
  • Well, today we can in principle calculate all these things, even from simple non-relativistic quantum mechanics with roughly two parameters. As Einstein said, "The most incomprehensible thing about the Universe is that it is comprehensible." The anthropic principle offers no explanation how is it possible that we've been able to understand so many things already.
People could have said that the properties of the nuclei - that also often seem necessary for our lives - only have an anthropic explanation. A carbon nucleus must be stable together with some other nuclei, and all these conditions constrain the allowed properties of nuclear physics. All these things look like a wonderful application of the anthropic reasoning. Nevertheless, today we know that the anthropic reasoning is just wrong: all properties of hadrons follow from a single nice theory (QCD) that has no dimensionless parameters whatsoever. (Well, the small bare fermion masses are sometimes necessary, and they add small corrections.)

Even though we may find the anthropic principle in this case (nuclear masses and stability) pretty plausible because the masses seem essential for life to exist - perhaps more plausible than in the explanation of the top quark mass - it is not the correct explanation.

And the anthropic reasoning is suspicious because of the opposite reason, too. We know that it is incomplete. As John Donoghue noted, the anthropic reasoning will never be sufficient to explain - even with the limited ambitions of an "explanation" according to anthropic "science" - some facts about the Nature. Namely the QCD theta angle could be much bigger, without affecting our lives too much, but nevertheless it is small. The explanation of this fact will have to be a scientific one, and there is no reason why similar explanations won't explain the rest.

I find it obvious that we should never be satisfied with our explanations until all numbers are explained, or until we have a more or less rigorous proof that they can't be explained; such a proof must be justified by clear evidence that leads to many other, highly nontrivial predictions. The Standard Model with neutrino masses has roughly 30 parameters, and a few more parameters such as the QCD theta angle, the cosmological constant etc. must be added. It may happen that new physics will be found, and we will need more parameters.

But let me now assume that it won't be the case. Then I don't think that a theory constitutes progress compared to the Standard Model if it needs an equal number of parameters (or even more). String theory, if it works, is definitely progress, maybe even the final one, because it contains no continuous adjustable non-dynamical parameters.

But string theory in the form as understood today still has many discrete parameters. A discrete parameter carries much less information than a continuous parameter, but it can still be counted as a parameter. Even in the realm of discrete parameters, the usual scientific requirements for a theory to lead to new predictions must be respected. If we need to specify 500 bits of discrete information (about the vacuum and its fluxes), it's a price that we should only pay if a larger number of nontrivial features of the Universe is explained.

The idea that we should prefer the vacua that have many possible types - i.e. the less predictive vacua - in our quest for the right theory of the Universe is an anti-scientific idea. I've been talking about similar issues already in the article Parameters of Nature.

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reader Anonymous said...

Nice essay, I agree. I don't know why people make so much about this, it really strikes me as rather self evident. Even if I were a layman (which im not).

Unfortunately, this whole spiel really doesn't help the segment of string theorists who need the most help right now. Eg the phenomenologists. Currently they have an astronomical amount of *nearly* completely disjoint, nontrivial working models which they have to consider. Each of those broad classes of theories of course has some nonzero probability of containing the real physics of our universe.

Telling them that they can just pick whichever parameters and model that gives the correct parameters for life, is rather like preaching to the choir. They have been trying to do that for over 20 years. In fact, im sure they would love to be able to find a single consistent model that reproduces such a thing.

But there is no brownie points for close second place. Unfortunately there is no such thing at this time. If you ask the phenomenologists, they can almost get the SM, but there are always little problems here and there (like getting the correct CKM matrix with the presence of neutrinos) that mucks things up. Or too many flavor changing neutral currents, bad proton decay bounds, etc etc

So either there is identically zero such models (a horrendous nogo theorem that is still possible in principle). Or we could have the situation *but that has yet to be shown rigorously* that we end up with a potentially worse situation.. Everything. That is Peters argument roughly.

Of course, those are not the only possibilities (or else he would be correct). There is still hope that there is identically one such solution, and I would say thats what people in the field are working for. I don't see why everyone has to lambast a theory if its not even completely worked through yet, by our admittedly small minds. In that sense Brian Greene is right.

There might be some as yet to be discovered governing principle hiding in the background. Something analagous perhaps to say Einsteins principle of equivalance. Anthropic reasoning in that sense is just the eternal lazy *I give up* principle, b/c finding such a thing is hard, and people need some way to put their kids through college.

reader Anonymous said...

I'd also like to add the rather obvious subpoint. Even with the anthropic argument, it is blatantly obvious that it doesn't even suffice. There are several parameters (even in the standard model), that could in principle be quite different without spoiling too much life giving physics. For instance, would things really be bad if we had identically zero mass neutrinos (wait I hear the cries of the leptogenesis cosmologists). There are other such things floating around as well.

So the rather more constraining anthropic argument degenerates rather quickly into the usual initial condition spiel. Which is a logical fallacy, it begs the question.

reader Lumo said...

Very relevant comments! Sorry, the modem is not the best tool to post long answers.