By Sean Carroll | November 25, 2010 11:10 am

This year we give thanks for an idea that is absolutely crucial to how our understanding of nature progresses: effective field theory. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, and conservation of momentum.)

“Effective field theory” is a technical term within quantum field theory, but it is associated with a more informal notion of extremely wide applicability. Namely: if we imagine dividing the world into “what happens at very short, microscopic distances” and “what happens at longer, macroscopic distances,” then it is possible to consistently describe the macroscopic world without referring to (or even understanding) the microscopic world. This is not always true, of course — our macroscopic descriptions have very specific domains of applicability, past which the microscopic details begin to matter — but it’s true very often, for a wide variety of situations with direct physical relevance.

The most basic examples are thermodynamics and fluid mechanics. You can talk about gasses and liquids very well without having any idea that they are made of atoms and molecules. Once you get deep into the details, we start talking about effects for which the atomic granularity really matters; but there is a very definite and useful regime in which it is simply irrelevant that air and water are “really” made of discrete units rather than being continuous fluids. Fluid mechanics is the “effective field theory of molecules” in the macroscopic domain.

How awesome is that? If it weren’t for the idea of effective field theory, it’s hard to imagine how we would ever make progress in physics. You wouldn’t be able to talk about atmospheric science without knowing all the details of microscopic physics (known in the trade as the ultraviolet completion), all the way down to the Planck scale! Fortunately, the universe is much more kind to us.

In particle physics, this idea is absolutely central. Protons, neutrons, and pions constitute an effective field theory that describes how quarks and gluons behave over sufficiently large distances. Another great example comes from Enrico Fermi’s theory of the weak interactions. Back in the 1930’s, Fermi proposed a theory that made use of the new “neutrino” particle. It involved processes that looked like this interaction of a proton plus electron converting into a neutron plus neutrino.

Fermi interaction

Nowadays we know better. What’s really going on is that the proton is made of two up quarks and a down quark, while the neutron is made of two downs and an up. The electron exchanges a W boson with one of the quarks, converting into an electron neutrino in the process.

Electroweak interaction

But the miracle is: it doesn’t matter. Knowing that the weak interactions are “really” carried by W bosons is completely irrelevant, as long as we are concerned only with large distances. In quantum mechanics, large distances correspond to low energies. (Remember that the energy of a wave decreases as its wavelength increases; quantum mechanics is all about waves.) So for low-energy processes, the effective field theory provided by Fermi is all you need to know about the weak interactions.

The universe is kind, but that kindness comes at a price. Sometimes you want to care about the microscopic realm — for example, if you’re a physicist trying to figure out what is going on down there. When we look at spacetime on length scales of 10-33 centimeters, do we see vibrating strings, or noncommuting matrices, or spin networks, or what? Hard to tell, because it makes no difference at all to the large-distance/low-energy physics we can actually observe.

That’s okay. A world described by a succession of effective field theories of ever-higher resolution helps us make sense of the world, while leaving physicists plenty of puzzles to think about. Very deserving of our thanksgiving.

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  • James B

    I think it’s worth distinguishing effective field theory from a more general class of emergent phenomena in science, wouldn’t you agree?

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  • Brian Too

    “Effective field theory”.

    Cool. I learned this today, from you. Thank you!

  • spyder

    I was pleasantly surprised by my reading through the December issue of Harper’s that on page 29 there was an advertisement for a lecture series on the Universe. I suspect that even much of the above is presented; and sadly and gladly, for a considerable discount it seems. Thanks Sean for availing yourself to the Teaching Company microphones and cameras; it is one series i look forward to experiencing.

  • Vladimir Kalitvianski

    What a song to the “effective theory” idea!

    Even if a theory does not work at all, you still say “it works” but it is an “effective theory”.

    Tell me how to call a theory that fails to predict the most probable events? Effective or ineffective?

    Look at QED. Take the first Born approximation results: Mott, Klein-Nishina, and Bhabha elastic cross sections. They are different from zero and presented as a success of the theory whereas all exact elastic cross sections are identically equal to zero. And the most probable events – soft radiation – is missing in those results. Then perturbative theory tries to correct these mis-predictions but it diverges and one can obtain the right results only after summation of all divergent results. That means the first Born approximation results are quite different from the exact ones. That means a quite bad start for the perturbation theory? That means the physicists do not understand how to obtain the most probable results immediately, not after 500 pages of a textbook.

    I do not mention renormalizations – the clear self-fooling about short distance physics and about how one has to perform calculations.

    The SM is even worse in this respect.

    Ineffective theories of ineffective but smug theorists. What a shame!

  • AI

    Sean: “it is possible to consistently describe the macroscopic world without referring to (or even understanding) the microscopic world.”

    OK, but is that really surprising? I would say that a much more powerful statement is true:
    It is possible to consistently describe any part of the real world.

    Why? Because 1. a description is always possible – we can simply invent new terms if the old ones prove inadequate so this approach cannot fail, and 2. if something correctly describes the real world it is consistent by definition (unless you believe the real world can be inconsistent).

    So I would say that the way you formulated it this more informal notion of “effective field theories” is vacuous. There is nothing remarkable about the fact that we can describe physical systems without knowing their microscopic details – it would be remarkable if for some reason we couldn’t do that.

    What I think you meant to say was that there exist universal laws, which hold (to a very good approximation) even though they ignore the microscopic details of the matter they deal with.

    To use the fluid example, it means that just a few parameters like density, viscosity, or compressibility are enough to in many instances correctly predict fluid behavior on a macroscopic scale even though said fluid may actually be a mixture of very complex molecules each one with an intricate electronic structure.

    Formulated this way it is certainly a valid observation though I still don’t think it is all that remarkable, it’s just a consequence of statistical averaging, and it only works in situations in which such averaging takes place.

  • Jimbo

    Effective field theories are certainly a buzz word in HEP that’s hard to get a handle on. Sean has helped with the analogies above. For those interested in how EFTs might be applicable to quantum gravity, here is a beautiful & relatively easy primer from 15 yrs ago, that helped me:

  • Vladimir Kalitvianski

    Any practical theory is phenomenological. It has its limits of applications. But there are some theories that are self-inconsistent. The first one is the Classical Electrodynamics. It has a self-action that spoils physical behavior. QED inherits this self-action and one has to repair the theory on the go to get some meaningful results. But there are unrepairable theories like QG. Instead of recognizing the failure in theory constructing, they say “it makes sense as an effective theory”. It means one cannot go farther than the tree level. As I mentioned in the previous post, even QED is not correct on the tree level. So effective theories are ineffective in reality.

    The problem is not in unknown physics at short distances. The problem is in admitting self-action and in not taking into account permanent coupling between charges and their quantized boson fields in a natural way, in my opinion.

  • Vladimir Kalitvianski

    Compare formulas (52) and (64) from with my example (6) in “On probing small distances in quantum world.pdf (see also page 4 in “Atom as a ‘Dressed’ Nucleus”).

  • Peter Coles

    It’s a bit off the point, but do you have a recommendation for a nice package for drawing Feynman diagrams?

  • Sean

    Don’t have any special packages. I just use Adobe Illustrator, in which I spent a couple of hours lovingly crafting some wavy lines, which I can now copy and paste at any time.

  • Moshe

    One good way to draw Feynman diagrams:

  • Yeah

    For the record–

    An effective theory can go beyond tree level, as Weinberg showed us many many years ago…

  • Vladimir Kalitvianski

    I have his “Living with infinities” of 2009. He says: “All of these theories (GR and SM) lose their predictive power at a sufficiently high energy.” (

    But high “virtual” energy is not the same as high transferred energy. Going higher in the transferred energy, we may obtain excited states that are otherwise the ground state. This is an unknown region.

    Loop divergences have nothing to do with our knowledge of high-energy physics. It is a non-physical self-action effect which is removed with non-physical renormalizations (subtractions, discarding the corresponding “contributions”).

    We must learn to live without those infinities. For that we have to better formulate our theories. Currently we have immediately failures and no chorus of self-flattery can repair this fact.

  • Mark P

    It is pretty cool. I suspect that if it were not true, physics would have had a much, much harder time arriving at any conclusions at any level. It’s almost like the universe provides a simple first course in physics.

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  • Yeah

    Vladimir– glad to see you have changed your mind and now agree that effective theories make sense beyond tree level.

    Most practitioners would agree that loop divergences are probably an artifact of some kind of the way calculations are done, not a sign of underlying sickness. And they go way beyond self-interactions, although they include those too.

    QED is a very effective description of nature (at some scales), although one whose interpretation is quite subtle.

  • Vladimir Kalitvianski

    Dear Yeah,

    I would like to discuss QED with you in some details, if you don’t mind. Not in this blog but in mine or by e-mail:

    I would like to ask some simple questions about perception of QED.

  • Vladimir Kalitvianski

    > QED is a very effective description of nature (at some scales), although one whose interpretation is quite subtle.

    Your phrase shows how unexpected were divergences and success of renormalizations. Any interpretation is based on the original construction entities. Generally, QED and QFT is a banal set of equations dealing with the occupation numbers of entities at a given total energy (kind of balance equations). No other interpretation is necessary.

    Divergences in calculations originate from unphysical assumptions admitted in the theory (self-action and “decoupling” charges from fields). Renormalizations, as mathematically illegitimate prescription, discards contributions of unphysical terms and thus “repairs” the theory on the go. The theory is not correct if it needs immediately repairing. The repaired theory is quite different from the original one. I think this is the only plausible explanation of “subtleties”.

  • Rhys

    Vladimir, this schtick is growing tiresome very quickly. Apart from anything else, comments on blogs are not the place to try to convince us all that you have successfully overturned the last 40 years of understanding of QFT (roughly the age of the renormalisation group).

  • Vladimir Kalitvianski

    Rhys, are you sure that you’ve reached full understanding?

  • Vladimir Kalitvianski

    A typical unknown physics of short distances is given, for example, here:

    Nobody knows it.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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