In praise of theorists who build bridges

Abstract

For Physics Today’s August 2006 issue I wrote a news story about the observation of the Berezinskii-Kosterlitz-Thouless topological phase transition in flattened clouds of ultracold rubidium atoms. As conceived in the early 1970s by Vadim Berezinskii, J. Michael Kosterlitz, and David Thouless, the BKT transition occurs in a two-dimensional lattice model known as XY. When I wrote the story, the transition had already been observed in superfluid films of helium-4 and superconducting films of mercury–xenon alloy.The 2006 experiment was conducted at the École Normale Supérieure (ENS) in Paris by Zoran Hadzibabic, Peter Krüger, Marc Cheneau, Baptiste Battelier, and Jean Dalibard. In summarizing its significance, I wrote, “Their experiment not only confirms BKT theory in a new system, but also reveals for the first time the transition’s microscopic instigators: local topological defects or vortices.”Then as now, the editors who write for Physics Today’s Search and Discovery department choose papers to cover based primarily on the advice of experts. We don’t learn a paper’s backstory until we interview its authors. When I phoned Hadzibabic to ask about his experiment, I found out something unexpected and interesting. To connect the predictions of BKT to the measurements made in the lab, he and his collaborators relied on a method devised by an independent trio of theorists, Anatoli Polkovnikov, Ehud Altman, and Eugene Demler.11. A. Polkovnikov, E. Altman, E. Demler, Proc. Natl. Acad. Sci. USA 103, 6125 (2006). https://doi.org/10.1073/pnas.0510276103 As in the plot of a B movie, a preprint from the three theorists arrived at ENS just as the experimenters were wondering how to interpret their data. “Within a minute, we wrote back to say we have the same equation on the board!” Hadzibabic told me.Polkovnikov, Altman, and Demler took up the challenge after reading a previous paper by the ENS group. The correlations that embody the BKT transition are manifest when two pancakes of ultracold atoms are released from their traps and allowed to interfere with each other. Those correlations, Polkovnikov, Altman, and Demler realized, depend on system size in an experimentally accessible way that can be tied directly to BKT physics.One of my favorite examples of theorists building bridges between experiment and theory comes from solar physics. Our star’s photosphere is so dense that a photon emitted at the core takes 170 000 years of repeated scattering off electrons and ions before it escapes. Some of the sunlight that fell on your face today was born when Neanderthals hunted and gathered in Europe! If astronomers relied only on solar photons, they’d have little to test their theories of the Sun’s composition and structure. Fortunately, prompt, direct information from the Sun’s interior reaches us in two other forms: acoustic oscillations, which I discuss here, and solar neutrinos.The Sun is a self-gravitating, differentially rotating ball of plasma that quivers in myriad acoustic modes, some of which entrain matter deep in the solar interior. Those helioseismic signals are manifest as Doppler shifts of certain spectral lines at localized patches in the photosphere. Remarkably, those seemingly limited data are sufficient to constrain models of the Sun—provided someone goes to the trouble of collating, among other things, all the nuclear reactions of all the chemical elements at all levels of the Sun and then creating models that predict what can be detected.The effort of helioseismologists is prodigious. To give one example, in a 1991 paper, Jørgen Christensen-Dalsgaard, Douglas Gough, and Michael Thompson derived the depth of the Sun’s convection zone.22. J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991). https://doi.org/10.1086/170441 To get to their answer of 0.287 ± 0.003 solar radii, they started with the Schwarzschild criterion, which specifies when convention ensues. Over the course of 25 pages, the three theorists described how they built two models of the Sun and then computed the sound speed, which can be inferred from helioseismic observations.I mention the work of those bridge-building theorists not just to praise them and their kind. When I look back at my own physics education, I don’t recall being taught what might be called applied theory. Polkovnikov has recognized the same gap. When I sought his comments about this editorial, he told me that he, Marcos Rigol, and Pieter Claeys are writing a new quantum mechanics textbook that will include realistic, nonideal examples. “When the formalism is too abstract and is related to very particular experiments,” he wrote, “it creates a gap in intuition and a gap in connecting theory and experiment.”ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. A. Polkovnikov, E. Altman, E. Demler, Proc. Natl. Acad. Sci. USA 103, 6125 (2006). https://doi.org/10.1073/pnas.0510276103, Google ScholarCrossref2. J. Christensen-Dalsgaard, D. O. Gough, M. J. Thompson, Astrophys. J. 378, 413 (1991). https://doi.org/10.1086/170441, Google ScholarCrossref© 2020 American Institute of Physics.