+Matt Strassler has an awesome series of posts on the strong force, part of a series called

*Quantum field theory, string theory and predictions.* It takes place at the intersection of two independently interesting questions in high energy physics: First, how to turn the abstract formulation of the strong force into actual predictions for particle experiments (the former is relatively simple to understand and state for any physicist, but the latter is extremely difficult and computer-intensive to obtain). Secondly, to what extent are the frameworks we use – QFT and its theorized extension, string theory – understood, well-defined and predictive?

*Matt has just completed Part 6 of the series. If you only want to read about the details of the strong force calculations, you might concentrate on parts 4 and 5. Of course, I highly recommend beginning at part 1 and reading the full exposition on quantum field theory, string theory and predictions:*http://profmattstrassler.com/2013/09/23/quantum-field-theory-string-theory-and-predictions/ , or

http://profmattstrassler.com/2013/10/07/quantum-field-theory-string-theory-and-predictions-part-4/[In the image, I included two of the graphs from Part 4 that are among the most important and interesting in strong force phenomenology. The first shows some experimental scattering data that currently

*cannot be predicted* by the theory of the strong force, quantum chromodynamics or QCD. It's the fraction of proton-proton collisions that are elastic – producing no new particles – as a function of collision energy. The second chart shows something that

*can* be calculated to great accuracy from theory: the masses of various hadrons. The horizontal lines are the measured values whereas the nearby colored dots correspond to different numerical implementations of the same simplified model, involving just the 3 lightest quarks and all 8 gluons. However, as described in the text, actually extracting these predictions from the theory is incredibly complicated and difficult.]

To get a proper sense of where we are today in our quest to understand nature, its just as important to understand the limits of our knowledge as it is to understand what we definitely know. If you only read about the incredible successes of the Standard Model – and they really are spectacular – you might be surprised by just how much of quantum field theory, and even the Standard Model in particular, remain shrouded in mystery. This doesn't tend to come through the pop-sci media prism nearly well enough. In particular, it has been most heavily confused by the people who want to dismiss string theory in the name of "science" and "skepticism" by denying that it predicts anything, while implicitly holding up modern quantum field theory as the pinnacle of predictivity. The problem with this caricature is that it distorts the truth in two different ways, it exaggerates the predictive challenges associated with string theory, and second it completely sweeps the analogous challenges in QFT under the rug. So it's quite refreshing to see a real scientist and expert on particle physics standing up, calling out the misleading rhetoric, and shedding light on the neglected facts.

One very direct parallel between the predictive challenges of QFT and string theory is the major role played by the standard approximation techniques, called perturbation theory. Most of what we know about both frameworks comes from this approximation method. At the same time, both frameworks have some really important aspects that are not captured by it, as well as some partial methods to go beyond it. The basic idea is straightforward enough; there is a quantity called the coupling constant that in a precise sense controls "how strongly interacting" the theory is. The theories are perfectly solvable at zero coupling, and as long as the coupling is small, the system can still be well-described in perturbation theory by including some of its infinite number of corrections. When the theory is weakly-coupled the corrections get progressively smaller in general, which is why the perturbative approximation works.

The value of the coupling constant also effectively depends on the distance scale. The electroweak forces are, as the name implies, weakly coupled. This is why the electroweak theory has had such incredible success making verified predictions using perturbation theory, culminating with the Higgs boson last July. It's also very important that the electroweak forces

*become more weak at longer distances.* So the breakdown of this perturbative description lies somewhere in the very high-energy / short-distance regime. But the strong force is a whole different animal, and in this case that perturbative success story I just told you is turned on its head. The strong force becomes more weakly coupled at

*short distances.* So we can make very precise predictions for very high-energy scattering experiments, but at longer distances and lower energies we loose control of it completely. This de-facto means that we can't really make meaningful predictions for a whole range of situations that actually matter in practice. In string theory we have the same basic challenge: the theory can be weakly or strongly coupled, and most of the direct knowledge comes from the weakly couple regimes.

There is another major aspect to the comparison with string theory that Matt touches on a little bit, but could use some elaboration. Namely there is a crucial difference between

*a framework* and

*a model.* A framework is the broad mathematical structure that describes the real world, but is also general enough to describe other worlds

*like* ours, with the the same basic principles, but different precise properties. In order to make any predictions, we need a framework but we also need a model, which amounts to making some choices, and then at this point we get to actually making predictions. Overall, the whole backlash against string theory you see these days is based on comparing string theory to the standard model. But thats the wrong comparison; the correct comparison is between string theory and quantum field theory. Both of these frameworks accommodate such a wide range of phenomena that its difficult to come up with any

*completely general* prediction. But thats only if you refuse to specify a model. When the Standard Model was written down, a specific kind of guess was made about what kinds of matter exists, and how it interacts. This model comes from a framework that could be branded "not even wrong" by today's commentators, since there are an infinite number of quantum field theories, and in complete generality they predict essentially nothing. But in neither case is that any barrier to making predictions. (This is the main message of Part 2.)

This confusion between models and frameworks actually stems from the uniqueness of string theory, but this uniqueness isn't a negative if your goal is to learn something about nature. Just like quantum field theory needs a specific model to make any predictions, the same is true for string theory. But unlike QFT, there is only one string theory, so your choice of model is in reality

*a choice of configuration,* (or 'vacua', or 'regions of moduli space'). Some configurations are difficult to analyze, just like some regions of QFT, but a great many are very well-understood and can and do make many predictions for particle physics. This framework / model distinction is also crucial for framing the very problem string theory exists to solve. Namely that the short-distance breakdown of quantum general relativity is the main problem today that

*cannot* be solved within the framework of quantum field theory. This is fundamentally different from the many shortcomings of the SM that are expected to be solved by new models, without the need for a whole new framework, like for example neutrino masses, dark matter, or the cosmological matter/antimatter asymmetry. But generalizing to a whole new framework is a totally different matter. The scale of these problems is wildly different, and so are the associated challenges. It's no wonder people get bent out of shape about theoretical physics if they haven't understood this difference. That is also, in a nutshell, the reason for the interest in string theory: its the framework that can produce realistic models

*and* is powerful enough to fully overcome this main hurdle.

For more in-depth discussion about the framework / model distinction in light of history and string theory, I highly recommend this great writeup by

+Urs Schreiber:

http://ncatlab.org/nlab/show/string+theory+FAQOverall, these kinds of issues have come up before in science. There is no doubt that the challenges are daunting, but thats just life. Nobody ever claimed solving these problems was supposed to be easy. If its hard to make a prediction, thats a reason to work harder, not run around yelling about a "crisis in physics". And moreover many of these challenges are directly related to why these frameworks are so interesting and so effective. Much of the beauty of QFT lies in how diverse its actual implementations are, even just in the ones Nature actually uses! By the same token, most of the criticism of string theory has to do with this same richness and variety, but it is still a completely rigid framework that can be very predictive in practice. Overall you can't help but get the impression that people want something that is simpler and easier to understand, but the frameworks that are robust enough to describe Nature tend to be a bit more complex and a bit more interesting. As Matt expertly demonstrates, that certainly holds true for quantum field theory.

#sciencesunday