Thursday, September 06, 2007

Fertile patch of the heterotic landscape

Another posting about the landscape topic.

First, Maor, Krauss, and Starkman discuss anthropics and myopics. It is a general critique of the anthropic reasoning. While I don't think that they have discovered something new that hasn't been said or written on blogs many times, I agree with the essence of what they're writing.

They say that the prediction of the value of the cosmological constant only makes sense if we specify who is "us" and the detailed predictions thus depend on details of the definition of "us" that we adopt. I find some of their definitions of "us" extremely awkward but this fact only shows how diverse the opinions about "us" can be.

Why do I find their definitions awkward? For example, they say that life can only be "us-like" if the gauge group coincides with the Standard Model. I don't buy it. I think that everything you need for life based on the same DNA and proteins as ours is chemistry and one could probably emulate the whole life as we know it with QCD replaced by a different theory of the atomic nuclei.

A fair struggle against typicality

But let me return to the correct points. They say that the correlation between known quantities and the value of the cosmological constant can only be achieved with a certain definition of "us" and this fact effectively means that the agreement only shows that our life is compatible with the observed value of the cosmological constant which shouldn't be surprising.

But this correlation doesn't imply causation. In fact, the cosmological constant could be somewhat "atypical" because living beings don't have to be "typical" and they might be somewhat "lucky" to be created in the first place. That means that the cosmological constant could be on the "tail" of the interval preferred by anthropic reasoning. And finally, there could exist completely different forms of life even if they are hard to imagine.




Finally, they correctly declare another point, one that has been hinted by Hartle and Srednicki: any kind of anthropic reasoning is always a method to use some features of the observed data and pretend that they play more important a role than other features that are being suppressed or ignored.

What do I mean? When we define "intelligent life", we have some freedom to decide what it means. There are two extreme choices that are not terribly interesting for the proponents of the anthropic reasoning - they will be described below - so the proponents of the anthropic reasoning always need to find a "middle route". But there is clearly no canonical "middle route" definition of the intelligent life.

What are the two extreme definitions of intelligent life? One of them implies that basic structures such as black holes are already dealing with information - even with representations of the monster group :-) - and they can emit each other, collapse into larger black holes, and they are thus a primitive form of intelligent life. With this definition, any vacuum of string theory is allowed.

The other extreme choice is, of course, that only life that looks almost exactly like ours is intelligent because the beings in all other vacua are dumb. With this choice, only our vacuum is anthropically allowed. As we have said, neither of these two extreme choices enables the anthropic reasoning to work, so the anthropic people always must choose some aspects of our intelligent life that they find important and discard the rest. There is no objective way to preserve some known facts about the Universe while discarding the rest. Any choice is just a convention.

Moreover, this Universe arguably existed long before homo sapiens evolved. Whether someone studied it using mathematics clearly shouldn't influence scientific predictions as long as they are rational. I happen to think that the same physical laws apply both to string theorists as well as to those who don't satisfy my strict defining criteria of "intelligent life". ;-)

It is actually OK to adopt both of the extreme anthropic selection criteria above. If we say that every vacuum is fine, it clearly means that the anthropic reasoning tells us nothing whatsoever and we can move on. If we say that only our vacuum is fine, we are clearly going in the right direction - which means to find the full theory of all fundamental forces and matter around us. The only detail that remains to be answered is Which of the vacua is ours. :-)

If you ask how Weinberg's argument about the cosmological constant can be extended, the answer is obvious. Instead of looking at one number only (the cosmological constant), look at all observed facts about the Universe and just use them to find the right theory. This is how physics used to work before we realized that our Universe is one of the vacua in string theory and it is how physics should work now, too.

Is there something illegal about using observational data in order to find the right vacuum? Well, I don't think so. ;-) It would be illegal if someone promised to find the right vacuum by pure thought. In that case, he would be cheating if he used the known gauge group or the number of generations, among many other facts. However, he would be cheating anyway because the fact that the world is described by quantum mechanics or string theory has been found after centuries in which pure thought was contaminated by experiments anyway. ;-)

When I am saying that we are allowed to use all information about the Universe to find the right vacuum, I am afraid that this assertion is indeed considered to be a heresy by the advocates of the anthropic reasoning, especially by those who want to study the landscape "statistically". The whole purpose of the statistical approach is to include zillions of vacua that definitely don't describe the Universe around us into your phenomenological toolbox i.e. to ignore some known facts about the Universe around us.

How should we search for the right vacuum while taking the known data into account? Well, we will probably not be sure about the right single vacuum instantly. So we must find some groups into which the right vacuum belongs, using all known data. That really means to look for classes of vacua that have some desired phenomenological properties. By refining our reasoning and taking ever more detailed data into account, we can finally pinpoint the right vacuum. This statement sounds obvious except that it is controversial according to the proponents of the anthropic reasoning.

Mini-landscape search

That's why I think that the approach of string phenomenologists like Lebedev et al. is the right one. One just identifies classes of vacua that are much more likely to describe reality. In their case, they look into a "fertile patch" of the heterotic landscape that is based on a Z6-II orbifold with SO(10) and E_6 local structures. Similar models have always been the most promising ones and not much has changed about it. Read the paper to see how closely they reproduce the correct particle physics. Three generations become a part of their prior but they still find hundreds of models whose qualitative features seem to be entirely correct.

Why do the anthropic people think that this classical way of looking for the right vacuum - analogous to the pre-stringy searches for the right theories - is no longer correct? Well, they unfortunately think that despite the presence of good features, the promising heterotic vacua are not more likely than some other classes - such as IIB flux compactifications - simply because there are so many IIB flux compactifications that their number beats any advantage of the heterotic vacua by brute force.

This reasoning is based on a rationally unjustifiable assumption that each single vacuum in the landscape is a priori equally likely regardless of the group where it belongs. This assumption - nothing else than a comparison of apples and oranges - is not a scientific principle that has been demonstrated by any arguments whatsoever. It is actually a scientific reflection of the egalitarian philosophy: it is therefore complete rubbish.

In reality, the fact that a group of vacua contains many elements doesn't make it more likely. From the viewpoint of explanatory power or Bayesian inference, if you wish, the groups with many elements can be "fudged" by the discrete tuning to agree with reality. That's why they should be viewed as less likely than if you forgot about the tuning discount.

If you think that there is some democracy between different theories and vacua, the democracy should be between different classes of vacua rather than the individual elements. The heterotic string vacua form 2/6 of the uncompactified superstring/M-theory vacua and they should be given 1/3 of the attention or so regardless of the number of type IIB flux compactifications. Paying attention to an exponentially larger number of elements of the IIB flux class is as irrational as saying that this planet is controlled by insect because most of the animals who live here belong to this class. Perhaps, all biologists and sociologists should study insect, too. Sorry if it sounds as extreme racist, undemocratic bigotry but I just don't think that this planet belongs to insect. ;-)

Are you worried that a moderate number of heterotic vacua inevitably predicts a wrong cosmological constant? Don't be too worried. There might either be a mechanism that violates the expectations of naturalness about the magnitude of the cosmological constant (naturalness is not a proven theorem, especially not in the case of the cosmological constant), or the perturbative heterotic string could be just a part of the full story. There could also exist some non-perturbative physics that gives a heterotic model a huge degeneracy - something needed if you believe that all flux vacua have heterotic duals - but the perturbative part would still be essential and perhaps sufficient to obtain most of the correct particle physics out of the model.

So I think that the standard string phenomenology should resume. The classes of vacua or models that have some desired properties should be preferred over others. It may sound paradoxical but physicists should look for their keys under the lamppost (near the models with mostly attractive features) because in reality, the light from that lamppost determines the probability distribution that the keys are there.

And that's the memo.

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