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Flip Tanedo | USLHC | USA

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My research [Part 2] — effective theories

We now return to Part 2 of the 3-part series, “my research.” We left off at Act 3: Particle Physics, where we introduced high energy physics as the study of the smallest scales in nature and hailed the Standard Model as the current gold-standard for understanding our observations of those scales.

Intermission: Effective Theories

Before we go any further, we should take a brief intermission to discuss one of the overarching themes in theoretical physics: effective theories. This is just a fancy name for something you already understand intuitively: “physics at different scales decouple.”

Bumpiness by scale.

Okay, that still sounds like fancy-talk. An example is in order. When you drive in your car, you prefer flat roads and watch out for potholes and rocks that might make your ride bumpier. On a much smaller scale, however, we can zoom into the asphalt and see that it’s actually made of little bits of sand and gravel that are actually very bumpy. Because this bumpiness is so small, however, we don’t feel it. Similarly, one can zoom out and note that we’re actually driving on very bumpy geological features on a big rock (the Earth). We don’t feel this bumpiness either, because we’re so much smaller than it.

This is what we mean by “physics at different scales decouple.” This isn’t exact, of course, but it’s a general principle whose utility in particle physics will be made clear in a moment.

Scales and Sciece

Let’s first start by really placing physics in context; think of this as a summary of Part I. I think here a picture is worth a thousand words:

scalesscience

The point to take from this is that science is made up of a series of “effective theories” at different scales. For example, chemistry can describe all of the complicated behavior within a cell; but to describe the physiology of cows or elephants one needs a different kind of understanding of nature, biology.

You could similarly say that “chemistry is just applied physics,” but this really obscures the richness of chemistry that cannot be clearly described by physics alone. In the same way that driving in a car we don’t need to think about the bumpiness of the sand in the asphalt, chemists don’t need to worry about the subatomic phenomena underlying their work: all of this physics is packaged into “effective rules” about chemical reactions.

I think one of my professors said it best when he expressed that

… a chef does not need to know gauge theory.

This means that even though what is actually happening when you bake a cake is a series of very complicated organic/chemical reactions, which are themselves based on subatomic physics, the chef only needs to know a set of rules (a recipe) to bake a cake. The art of being able to make a good cake is not easily understood from the ‘fundamental’ chemical or physical theory underlying the recipe, but can easily be explained by Alton Brown on television.

Effective theories in physics

Let’s get back to physics. A useful analogy to start with is Newtonian mechanics.

We know that Newtonian mechanics is not a complete theory of all physics. At the very least we know that general relativity becomes effective at large scales and quantum mechanics takes over at small scales. Why, then, do generations of high school students have to learn “lies” like F=ma? Isn’t Newton wrong?

No! If you want to calculate the trajectory of a baseball (or even a NASA satellite), you would use Newtonian mechanics. Sure, there would be incredibly small corrections from quantum effects and from the curvature of space… but these are usually much smaller than the precision you care about for the baseball. Newtonian mechanics isn’t wrong — it works just fine. It’s just that it only works within a domain of validity, i.e. within a specific scale.

In this sense it is not a “complete” theory, but nobody ever promised it was.

The unreasonable success of the Standard Model

In very much the same way the Standard Model is incomplete. This doesn’t make it “wrong” any more than F=ma is wrong; it just means that we expect more if we keep digging. There are many good reasons to believe this. The Standard Model does not explain “known unknowns” like gravity, dark matter, the origin of neutrino masses; it has little to say about tantalizing theoretical ideas like supersymmetry or grand unification; and it seems to suffer from a fine-tuning problem in the Higgs sector.

Why then, did I claim that the Standard Model has passed all experimental tests?

That’s because the Standard Model is an effective theory that agrees with all observations of nature at the scale in which it is effective. The “experimental tests” which I refer to are primarily the so-called “precision electroweak” measurements at the LEP I and II detectors in CERN and at the Stanford Linear Collider at SLAC in the 1990s and the flavor experiments whose current state-of-the-art are the B factories at BABAR (SLAC) and BELLE (KEK).

[ In fact, we can turn this question upside down: how can we know that the Standard Model has passed any tests if we haven’t even measured the properties of the Higgs boson? The answer is that we’re not actually probing the Standard Model (so I lied a little)… we’re probing an effective theory of the Standard Model without the Higgs. ]

At the LHC we hope to find hints to some of the outstanding questions of the Standard Model as we begin to probe scales that have heretofore been inaccessible. Hopefully we’ll find hints of “new physics,” but I’ll get to that in Part III.

Further Reading/Watching

One post isn’t enough to really express the elegance of the idea of effective theories. In particle physics the transition between different effective theories is one of the key ideas of the past 50 years, it goes under the rather lofty name of the “renormalization group.”

Perhaps the most visual tours of the scales of science (which I based my figure on) is the video Powers of Ten by Charles and Ray Eames. One of the great popular articles on the scales of physics was written in 1972 by Nobel laureate Philip Anderson, “More is different” (Science, New Series, Vol. 177, No. 4047. (Aug. 4, 1972), pp. 393-396). For students of particle physics who are just learning renormalization, I recommend starting with Paul Stevenson’s review “Dimensional Analysis in Field Theory.”

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