Analogies and metaphors

I’ll be the ticket if you’re my collector

I’ve got the fare if you’re my inspector

I’ll be the luggage if you’ll be the porter

I’ll be the parcel if you’ll be the sorter

—"Love Song ” by Dave Vanian, Captain Sensible, Rat Scabies, and Algy Ward

“Love Song” is the opening track of the Damned’s album Machine Gun Etiquette, which I bought in 1979 when it was first released as a vinyl LP. The punk band’s deft use of metaphor in the opening verse has always reminded me that analogy, metaphor, and other tropes are not just for poets and orators. Indeed, physicists and the people who write about physics deploy them freely.

Perhaps the most straightforward use of metaphor in physics is for descriptive labels. In 1937 John Slater approximated the atomic potentials in a crystal as a lattice of nonoverlapping wells. By 1961—at least according to the earliest reference I could find—Slater’s approximation had acquired the apt, delightful, and easy-to-recall name “muffin tin.”

In 1997 observations made by the SOHO spacecraft cleared up a mystery having to do with the inactive, “quiet” regions of the Sun’s corona. Thanks to its then-unprecedented resolution and sensitivity, the SOHO‘s Michaelson Doppler Imager revealed that the quiet corona’s magnetic field arises not from plasma that diffuses from active regions, but from the magnetic activity of the quiet corona itself. To Alan Title the newly discovered field lines that sprout from the quiet corona resembled the looped tufts of a carpet—hence the name he devised, “magnetic carpet.”

Some concepts in physics can be hard to convey, especially to nonphysicists. As an explanatory tool, my fellow science writers and I sometimes use analogy and metaphor to relate an unfamiliar concept to a familiar one.

For example, in a 2004 news story for Physics Today I compared molecular dynamics (MD) simulations, which seek to track the motion of every particle, with a new variant of the Monte Carlo algorithm that Nicholas Metropolis and his collaborators devised in 1953:

However, sometimes analogies and metaphors are not used for literary effect, but for literal comparison. Earlier this year my colleague Richard Fitzgerald wrote about a tabletop experiment that sought to mimic the radiation that leaks out of a black hole via a mechanism proposed in 1974 by Steven Hawking.

Remarkably—at least at first glance—the experiment involved water flowing at high speed over and around obstacles. Because of the similarity of the equations that underlie both Hawking radiation and the waves shed by the obstacles, the two systems are analogous to each other. But whereas one system, the waves, is easily observed in the lab, the other, Hawking radiation, isn’t.

Whether studying one member of an analogous pair brings true physical insight into the behavior of the other member is not obvious. To justify evoking the analogy, you have to be sure that both systems are governed by the same mathematics. Yet to make that justification, you have to understand both systems well—which would seem to vitiate the need to evoke the analogy in the first place.

That said, knowing the equations that govern a system isn’t the same as understanding its behavior. Superconductivity, ferromagnetism, and other electronic phenomena could emerge from quite simple Hamiltonians, but the long-range many-body interactions embodied in the Hamiltonians are too complex to calculate or even to simulate.

But in principle, a cold-atom analogue of an electronic system could be engineered to test whether, say, the Hubbard model is sufficient to capture the onset of superconductivity in a high-T_c cuprate. Indeed, several research groups around the world are working toward that end—which, if achieved, would be a literal, not metaphorical, triumph.

Thanks to Maire Evans for suggesting the topic of analogies.