Thursday, June 09, 2005

A Constructive Critique of the Three Standard Systems

by F. Wilczek. Preprint in the physics archive.
It has become conventional to say that our knowledge of fundamental physical law is summarized in a Standard Model. But this convention lumps together two quite different conceptual structures, and leaves out another. I think it is more accurate and informative to say that our current, working description of fundamental physics is based on three standard conceptual systems. These systems are very different; so different, that it is not inappropriate to call them the Good, the Bad, and the Ugly. They concern, respectively, the coupling of vector gauge particles, gravitons, and Higgs particles. It is quite a remarkable fact, in itself, that every nonlinear interaction we need to summarize our present knowledge of the basic (i.e., irreducible) laws of physics involves one or another of these particles.

More critical remarks on the Standard Model:
Looking critically at the structure of a single standard model family, as displayed in Figure 3, one has no trouble picking out flaws.
The gauge symmetry contains three separate pieces, and the fermion representation contains five separate pieces. While this is an amazingly tight structure, considering the wealth of phenomena described, it clearly fails to achieve the ultimate in simplicity and irreducibility. Let me remind you, in this context, that electroweak “unification” is something of a misnomer. There are still two separate symmetries, and two separate coupling constants, in the electroweak sector of the standard model. It is much more accurate to speak of electroweak “mixing”.
Worst of all, the abelian U(1) symmetry is powerless to quantize its corresponding charges. The hypercharge assignments – indicated in Figure 3 by the numerical subscripts – must be chosen on purely phenomenological grounds. On the face of it, they appear in a rather peculiar pattern. If we are counting continuous parameters, the freedom to choose their values takes us from three to seven (and more, if we restore the families). The electrical neutrality of atoms is a striking and fundamental fact, which has been checked to extraordinary precision, and which is central to our understanding of Nature. In the standard model this fact appears, at a classical level, to require finely tuned hand-adjustment.

What makes this very tight, predictive, and elegant theory of quantum gravity “bad” is not that there is any experiment that contradicts it. There isn’t. Nor, I think, is the main problem that this theory cannot supply predictions for totally academic thought experiments about ultrahigh energy behavior. It can’t, but there are more pressing issues, that might have more promise of leading to contact between theory and empirical reality.
A great lesson of the standard model is that what we have been evolved to perceive as empty space is in fact a richly structured medium. It contains symmetry-breaking condensates associated with electroweak superconductivity and spontaneous chiral symmetry breaking in QCD, an effervescence of virtual particles, and probably much more. Since gravity is sensitive to all forms of energy it really ought to see this stuff, even if we don’t. A straightforward estimation suggests that empty space should weigh several orders of magnitude of orders of magnitude (no misprint here!) more than it does. It “should” be much denser than a neutron star, for example. The expected energy of empty space acts like dark energy, with negative pressure, but there’s much too much of it.
To me this discrepancy is the most mysterious fact in all of physical science, the fact with the greatest potential to rock the foundations. We’re obviously missing some major insight here. Given this situation, it’s hard to know what to make of the ridiculously small amount of dark energy that presently dominates the Universe!

The Flavor/Higgs Sector

We know of no deep principle, comparable to gauge symmetry or general covariance, which constrains the values of these couplings tightly. For that reason, it is in this sector where continuous parameters proliferate, into the dozens. Basically, we introduce each observed mass and weak mixing angle as an independent input, which must be determined empirically. The phenomenology is not entirely out of control: the general framework (local relativistic quantum field theory, gauge symmetry, and renormalizability) has significant consequences, and even this part of the standard model makes many non-trivial predictions and is highly over-constrained. ...
Neutrino masses and mixings can be accommodated along similar lines, if we expand the framework slightly. ... The flavor/Higgs sector of fundamental physics is its least satisfactory part. Whether measured by the large number of independent parameters or by the small number of powerful ideas it contains, our theoretical description of this sector does not attain the same level as we’ve reached in the other sectors. This part really does deserve to be called a “model” rather than a “theory”.

Another cute sarcastic remark (somewhat unfairly out of context):
Finally let me mention one redeeming virtue of the Higgs sector. (“Virtue” might be too strong; actually, what I’m about to do is more in the nature of advertising a bug as a feature.)

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