November 2010

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.

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.

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.

There was some excitement last week about a Maxwell’s-Demon-type experiment conducted by Shoichi Toyabe and collaborators in Japan. (Costly Nature Physics article here; free arxiv version here.) It’s a great result, worth making a fuss about. But some commentators spun it as “converting information into energy.” That’s not quite right — it’s more like “using information to extract energy from a heat bath.”

Say you have a box of gas with a certain temperature at maximum entropy — thermodynamic equilibrium. That is, the gas is smoothly spread throughout the box. (We can safely ignore gravity.) There’s certainly energy in there, but it’s not very useful. Indeed, one way of thinking about entropy is as a measure of how useless a certain amount of energy is. If we have a low-entropy configuration, we can extract useful work from the energy inside, such as pushing a piston. If we have a high-entropy configuration, the energy is useless; there’s nothing we can do to consistently extract it.

Here’s an example from my book. Consider two pistons with the same number of gas particles inside, with the same total energy. But the top container is in a low-entropy state with all the gas on one side of the piston; the bottom container is in a high-entropy state with the gas equally spread out.

You see the difference — from the top configuration we can extract useful work by simply allowing the piston to expand. In the process, the total energy of the gas goes down (it cools off). But in the bottom piston, nothing’s going to happen. There’s just as much energy inside there, but we can’t get it out because it’s in a high-entropy state.

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Using Information to Extract EnergyRead More »

That’s the name of a new paper by Akihisa Shioi, Takahiko Ban, and Youichi Morimune. Abstract:

The design of autonomously moving objects that resemble living matter is an excellent research topic that may develop into various applications of functional motion. Autonomous motion can demonstrate numerous significant characteristics such as transduction of chemical potential into work without heat, chemosensitive motion, chemotactic and phototactic motions, and pulse-like motion with periodicities responding to the chemical environment. Sustainable motion can be realized with an open system that exchanges heat and matter across its interface. Hence the autonomously moving object has a colloidal scale with a large specific area. This article reviews several examples of systems with such characteristics that have been studied, focusing on chemical systems containing amphiphilic molecules.

The journal is called Entropy, which I love. The paper discusses a variety of different systems that can travel, wiggle around, and respond to stimuli in ways that resemble living organisms. Not exactly building life in a test tube, but the boundary grows increasingly blurry.

Have any friends or colleagues who don’t believe in dark matter? Showing them this should help.

That ghostly haze is dark matter — or at least, an impression of the gravitational field created by the dark matter. This is galaxy cluster Abell 1689, in the constellation Virgo. (We feel compelled to add that information, in case you’re going to go looking for it in the night sky tonight or something.) It’s easy to see that the images of many of the galaxies have been noticeably warped by passing through the gravitational field of the cluster, a phenomenon known as strong gravitational lensing. This cluster has been studied for a while using strong lensing. The idea is that the detailed distribution of dark matter affects the specific ways in which different background images are distorted (similar to what was used to analyze the Bullet Cluster). Astronomers use up massive amounts of computer time constructing different models and determining where the dark matter has to be to distort the galaxies in just the right way. Now Dan Coe and collaborators have made an unprecedentedly high-precision map of where the dark matter is (paper here).

This isn’t all about the pretty pictures. We have theoretical predictions about how dark matter should act, and it’s good to compare them to data. Interestingly, the fit to our favorite models is not perfect; this cluster, and a few others like it, are more dense in a central core region than simple theories predict. This is an opportunity to learn something — perhaps clusters started to form earlier in the history of the universe than we thought, or perhaps there’s something new in the physics of dark matter that we have to start taking into account.

But the pretty pictures are certainly a reward in their own right.