Frank Wilczek has a new book out, it’s called Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm, and is published by World Scientific. It’s a great read by one of the best in the business for anyone interested in physics and should be accessible to people with a wide variety of backgrounds. The book consists of a collection of 43 short pieces, most of which have been published elsewhere (often as “Reference Frame” columns in Physics Today), broken into 11 sections, each with a short introduction. The writing is exceptionally well-informed, elegant, lucid, and thought-provoking.

There’s also a section of 6 original poems, which I’ll not comment on since I’m not a literary critic, as well as a final section of extracts from Wilczek’s wife Betsy Devine’s blog Funny Ha-Ha or Funny Peculiar?. The blog entries explain exactly what it’s like to be a family member of a Nobel prize winner, and contain lots of useful tips for you and your fellow family members should you ever win a Nobel prize and need to know exactly how to prepare for your trip to Stockholm. I hope I won’t be damaging sales of the book by noting that they’re available on-line.

Wilczek started out his career with a bang, discovering the asymptotic freedom of Yang-Mills theory in joint work with his advisor David Gross. He was thinking of this work in terms of perhaps showing that the SU(2) part of the new electro-weak gauge theory of Weinberg and Salam might not have the same problem that QED had (effective coupling growing at short distances, invalidating perturbation theory), but Gross was thinking more about the strong interactions and the short-distance scaling behavior recently observed at SLAC. If it could be shown that Yang-Mills theories also had effective couplings that grew at short distances like all other known QFTs, that would rule out QFT as a theory of the strong interactions. The discovery of asymptotic freedom made it clear that Yang-Mills theories might provide a successful strong interaction theory, and there was one obvious choice for the right theory: QCD.

Many of Wilczek’s pieces deal with QCD in one way or another, from explaining his original work with Gross, to more recent developments concerning high temperature (relevant to heavy-ion collider experiments) and high density versions of the theory. He also explains some of the beautiful data that has accumulated over the past more than thirty years since its discovery that give us impressive evidence for the validity of QCD. Wilczek puts QCD into a more general context, explaining how logarithmic running of coupling constants can explain the small size of the strong interaction scale when compared to the scale of a putative GUT or even the Planck scale. Besides QCD, he provides excellent discussions of the rest of the standard model, the electroweak theory.

In several different pieces about beyond the standard model physics, Wilczek emphasizes two pieces of evidence that we have for some sort of GUT scenario. One is the fact that if you take the 16 dimensional half-spinor representation of SO(10), under the SU(5) subgroup it decomposes as 1 + 5 + 10, giving all the standard model fields of one generation (including a right-handed neutrino), but in a single irreducible representation. The second is the calculation (that he did in 1981 with Dimopoulos and Raby) of the running coupling constants for the supersymmetric SU(5) GUT (see here, although I’m not sure I agree that this falsifies Popper), which show much closer unification of the three couplings at a single energy than in the non-supersymmetric case.

These two facts are definitely the strongest evidence around for the idea of a supersymmetric GUT, an idea which has dominated thinking about beyond the standard model physics for nearly 30 years, but they are far from convincing. Wilczek deals with the other main idea that has dominated the field, string theory, by essentially ignoring it. I only noticed one or two mentions of string theory in passing in the book. He’s not taking a position pro or con on the subject, just deciding that other things are more worth writing about.

The longer pieces in the book are among the best, including a piece on the Dirac equation, written for a book on the most beautiful equations, and pieces on fractional charge quantization and quantum field theory in general, which are a bit more technical than the others. Wilczek brings in interesting historical context to most of the things he writes about, often in an original way.

Perhaps my favorite piece is one entitled “What is Quantum Theory?”, which deals with one of my obsessions. Wilczek claims that perhaps we still don’t properly understand the significance of quantum theory, especially what it has to do with symmetries. He notes that Hermann Weyl, soon after the discovery of quantum mechanics, realized that the Heisenberg commutation relations are the relations of a Lie algebra (called the Heisenberg Lie algebra), and that this exponentiates to a symmetry group (the Heisenberg group to mathematicians, Weyl group to physicists). Wilczek goes on to speculate that:

*The next level in understanding may come when an overarching symmetry is found, melding the conventional symmetries and Weyl’s symmetry of quantum kinematics (made more specific, and possibly modified) into an organic whole.*

Wilczek is still at it; last week he had a new preprint with Brian Patt which I wish I had time to look at more carefully. In this month’s Physics Today, he has another Reference Frame article, now about the anthropic principle, and I’ll write about that soon and separately.

There’s also a podcast of an interview with Wilczek and his wife conducted at a party in Brooklyn held last month to celebrate the release of the book. If you listen closely maybe you can hear me and others chatting in the next room, despite being told to keep it down because of the recording session…

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Five years ago, Wilczek wrote in his Future summary:

“5.5. Produce the New Particles!

Of course, the ultimate test for low-energy supersymmetry will be to produce some of the predicted new R-odd particles. Even in the focus point scenario, there must be several accessible to the LHC.”

That is what I call a real prediction!

Perhaps my favorite piece is one entitled “What is Quantum Theory?”, which deals with one of my obsessions. Wilczek claims that perhaps we still don’t properly understand the significance of quantum theory, especially what it has to do with symmetries.Gauge symmetries are indeed poorly understood on the quantum level, in more that 2D. This has been noted by many people, e.g. in Haag’s book (p 325). One can of course check the Noether identities of the classical action, but quantically one would want to realize gauge transformations as well-defined operators acting on the (kinematical) Hilbert space. To me, it is more important to have such a well-defined realization on

someHilbert space, rather than demanding that the Hilbert space comes from QFT in the strict sense (which would be impossible, there are no-go theorems). The missing ingredient can be viewed as explicit observer dependence.My experience leads me to strongly support Thomas Larson´s remark about a deeper quantum understanding of what is behind gauge theory being still very precarious and tentative. In fact I may add some very specific partial (yet unpublished) results which underline this point.

The quantum physical origin of the gauge issue is the fact that family of zero mass finite helicity Wigner representations allow for a covariantization in terms of pointlike field strength, but not for pointlike potentials (a restriction which does not exist in the classical setting because there the positivity of Hilbert space is not an issue). In fact even before one argues about the necessity of potentials in formulating interactions, there is the kinematical observation that it is not possible to write the Wigner inner product in terms of an integral over a local density in terms of field strength, one needs potentials even on a kinematical level. In order to maintain the standard perturbative formalism in terms of pointlike potentials, one is forced to extend the Wigner representation by (Gupta-Bleuler, BRST ghosts), leaving the quantum physical Hilbert space. Although it is deeply relaxing to see that the cohomological aspects of BRST allow a physical descend after having done the computations, such a BRST catalyzer (which was not there in the beginning and left no trace after the physical descent), this situation should not serve as a soft pillow.

Indeed there is a completely different autonomous way (which unlike BRST does not take any hint from the classical selection principle via gauge theory): the best possible localization of potentials in the Wigner space is along semiinfinite spacelike “strings”, i.e. the potentials lead to stringlike objects which fluctuate in both the starting point x of the (linear) string and its direction described by a spacelike unit vector e. Since these “strings” have vacuum fluctuation in both x and the de Sitter point e (the space of directions), the fluctuations in x become much milder and are “renormalizable” in the sense of power counting independently of the value of the helicity (Mund-Schroer-Yngvason, math-ph/0511042). So the new problem is how to do perturbation involving such “strings” (since there is no Lagrangian for such objects: how to adjust the Epstein-Glaser method to the more complicated causal geometry of strings). This is a bigger project which I am involved in together with Jens Mund and Jakob Yngvason. But since the results for the metric potential of the (linearized Riemann tensor) field strength are already available, I asked Jens Mund to separate his short computation from the bulk of our joint project and post his short computation onto the server (it should be available within the next two weeks). As far as I know there has been no classical gauge suggestion for helicity larger than one.

Although in the present form these remarks are a bit remote from the main theme of Peters Webblog (to present a platform for alternative ideas to string theory), they may not be so in the future (if it turns out that with there new concepts one can really obtain a well-defined perturbation theory relevant for gravity).

After re-reading physics/0403115, I’d say that Wilczek conveniently ignores the context in which Popper’s ideas about the importance of falsification arose. He is essentially saying that he and his colleagues will pursue potential solutions to problems in theoretical physics in whatever way seems sensible to them under given circumstances and in light of prior experience. That’s fine, but it in no way undercuts the idea that the impossibility of testing an ostensibly empirical theory is of central importance, and that significant empirical confirmation really only amounts to survival of stringent tests.

To the extent that falsifiability is derided as irrelevant to the actual practice of science by some influential particle physicists one can understand how we have arrived at our current predicament. [Sorry if that remark strikes some as needlessly provocative.]