## Tuesday, August 21, 2007 ... /////

### Aaron Bergman & multiverse

Aaron Bergman has fulfilled his threats ;-) and wrote two additional short texts about the multiverse.

A multiverse apologist
The lay of the landscape
While the first text is just an introduction, he uses mini-golf analogies in the second text to explain what it means for your theory to have many solutions. He doesn't say much and omits names - because the authors of the ideas really don't have anything to be proud about so far, as two of us think :-) - but it's kind of OK.

Once we accept that the most accurate theory we can have predicts very many valleys or environments (vacua) where life in principle can occur, we may choose different strategies to look for "our" valley in the landscape. Either to give up, or to map all of them and compare their shape with the measured shape (encoded in properties of elementary particles), or start to play with statistics of these valleys and fuzzy "predictions" resulting from it. The only two other choices are to hope and search for missing cosmological or selection rules or, more speculatively, searching for a completely different theory than string theory.

His comments are minimalistic and thus fair. There are a few questions underneath.

Is the set of minima finite?

Well, it is certainly infinite but countable if we include all of them: one infinite collection, for example the bulk dual of the SU(M) N=4 gauge theory, is enough to show it. But the number of vacua that qualitatively agree with our Universe and differ by 50% in each quantity, for example, is probably finite. That really means that the density of stabilized vacua per unit volume of the low-energy parameter space is probably finite. If we're able to map all vacua in "our" neighborhood in the low-energy parameter space, we would see that string theory gives very accurate predictions of all quantities.

Why are the many science fiction stories and novels about the multiverse different from what string theory tells us?

Because there still unfortunately exist actors and directors in Hollywoord who don't have a PhD in high-energy theoretical physics. And even those who have one often surrend to the temptation to create a fairy-tale that will be more catchy for the audiences without a physics PhD and sometimes even audiences with a physics PhD. ;-)

How well are actual analyses of data (WMAP etc) doing at defining WHICH universe we happen to inhabit?

WMAP tells us some numbers that string theorists wouldn't otherwise know - such as the cosmological constant and perhaps the spectral tilt relevant for cosmic inflation. However, in order to determine which vacuum in the landscape is the right one, we still extract much more data from particle physics experiments than from cosmology. The masses of elementary particles and the strength of their various interactions inform us about the shape of our valley.

Is BRST invariance true?

BRST invariance is not a hypothesis about Nature. BRST invariance is a part of one of the useful mathematical frameworks in which physical theories can be studied, especially physical theories with natural local symmetries. Within this framework, BRST invariance of states is not only true but it is an axiom. However, there exist physically equivalent ways to obtain the same predictions in these theories, ways that don't require any BRST operator.

The wave equation has infinitely many solutions. If you pluck a violin string, it could vibrate with the fundamental frequency, with the first overtone, or with the 4711th overtone. In fact, it is most likely that the frequency will be even higher, since there are infinitely many overtones above the 4711th but only finitely many below it. Hence the violin frequency will be a GHz or higher. ... This is bad news for orchestras.

Well, are there statistical distributions that would be dominated by infinite numbers? Actually, there are. Imagine that the probability of a positive integer being equal to N is equal to C/N^2 where C is a normalization constant. You can see that C is finite. But the expectation value of the integer is the sum of C/N which is logarithmically divergent. Nevertheless, even in this distribution, it is extremely likely that the integer will be less than 10. Moreover, I think that such distributions are unnatural. If there exists any cosmological rule that assigns probabilities to different vacua, I think that the vacua that are special in some sense - i.e. vacua analogous to small integers in my example - will be preferred according to this distribution. No well-defined and justifiable calculus to count the probabilities of different vacua exists at this moment.

An alternative explanation

A famous critic has written an alternative analysis of these ideas that is appropriate for the intelligence of the people who like to read him. Let me include it in its entirety here:

The Usual

Blah, blah, more anthropic pseudo-science on hep-th, blah, blah, blah, [... quote ...] blah, blah, blah, this pseudo-science is on hep-th because of blah, blah, blah.

Blah, blah, blah written for Templeton-funded conference, blah, blah, Science-Religion Interaction in the 21st Century. Usual blah, blah, turn science into religion, blah, blah Institute for Interdisciplinary Research in Science, Philosophy and Religion.

Apologies for the repetitive nature of some recent postings. I can’t even stand to write them any more, but still think someone should be documenting the descent of particle theory into pseudo-science and complaining about it.

As you can see, the text is filled with ingenious ideas even though most of these gems - for example the idea about blah blah the pseudo-science - have been repeated roughly 587 times. In the case that you don't find his newest essay sufficiently rich, deep, careful, charming, original, comprehensive, multi-dimensional, rational, and diverse, you may read other illuminating articles by this giant. ;-) The recent ones are called:
• The usual
• Message to our overlords
• Latest on K-theory journal situation
• More of the usual sorts of things
• Various stuff
• Another journal board resigns
• University grants program subpanel report
• Various news
• Less stuff than usual
• Too much good stuff
• Assorted news
• Random collection of stuff
• Even more stuff than usual
• This week's hype
• New blogs and other stuff
• All sorts of stuff
• Various events and other news
• Various stuff
• Not good