John Wheeler, relativity, and quantum information Charles W. Misner, Kip S. Thorne, and Wojciech H. Zurek From the mid-1950s on, John Wheeler’s “radical conservative-ism” allowed him to explore without fear crazy-sounding ideas that often led to profound physical insights. Charles Misner is professor of physics, emeritus, at the University of Maryland. Kip Thorne is Feynman Professor of Theoretical Physics at the California Institute of Technology. Wojciech Zurek is a laboratory fellow at Los Alamos National Laboratory. Two were John Wheeler’s PhD students, Misner in 1954–57 and Thorne in 1962–65; Zurek was his student in 1976–79 and his postdoc in 1979–81. Misner and Thorne coauthored the 1973 textbook Gravitation with Wheeler; Zurek coedited the 1983 Quantum Theory and Measurement with him. In spring 1952, as John Wheeler neared the end of design realized, the conditions for creating a geon almost certainly work for the first thermonuclear explosion, he plotted a rad- do not exist in our universe except possibly in its earliest ical change of research direction: from particles and atomic moments. And once a geon was created, not only would its nuclei to general relativity. waves leak out slowly but a collective instability would de- With only one quantitative observational contact (the stroy it in a short time. Nevertheless, for Wheeler the geon perihelion shift of Mercury) and two qualitative ones (the was crucial: It hinted at a richness that might reside, as yet expansion of the universe and gravitational light deflection) unexplored, in Albert Einstein’s general theory of relativity; general relativity in the early 1950s had become a backwater it gave him the courage to enlist students and postdocs in his of physics. It was more a branch of mathematics than of quest for that richness; and it gave him the idea that funda- physics, and a not very interesting one. Among the world’s mental particles might actually be built, in some manner, leading physicists at the time, only Wheeler envisioned a from curved spacetime—quantum mechanical variants of future in which curved spacetime would be fundamental to a geon. the nature of matter and the astrophysical universe. Because, Charge without charge might also exist: Resurrecting a in his words, “relativity is too important to leave to the math- 1924 idea of Hermann Weyl, Wheeler imagined electric field ematicians,” Wheeler set out to discover its roles. Through lines threading topological handles in the structure of space that quest, over the subsequent two decades, he, his students, (for which he coined the word “wormhole”). One mouth of and their intellectual descendants would revitalize general the wormhole would have electric fields entering it and thus relativity and make it an exciting field for other researchers. exhibit negative charge, and the fields emerging from the “If you would learn, teach!” was one of Wheeler’s fa- other mouth would make it positively charged. Could an vorite aphorisms (figure 1). So as the first step in his quest, electron’s or proton’s charge be some quantum variant of that he taught a course in relativity at Princeton University—the scenario? first such course since 1941. In his 1952–53 course, he began By 1955, when Wheeler published his first geon paper2 to develop his own physical and geometric viewpoint on the (including remarks about charge without charge and worm- subject, a viewpoint that would later be enshrined in his text- holes), he was bubbling over with ideas for general-relativity book Gravitation.1 research projects and was starting to feed them to his first set of relativity students. He was also developing an approach “Everything is fields” to physics that he called radical conservative-ism: Insist on ad- While teaching his first relativity course, Wheeler realized hering to well-established physical laws (be conservative), there could exist, at least in principle, a spherical or toroidal but follow those laws into their most extreme domains (be object made up of electromagnetic waves that hold them- radical), where unexpected insights into nature might be selves together gravitationally, with the waves’ gravitational found. He attributed that philosophy to his own revered binding produced by their energy. He called such an object a mentor, Niels Bohr. geon (gravitational–electromagnetic entity), and he explored In that spirit, in the mid- and late 1950s Wheeler and his its properties in depth as a classical model for an elementary entourage explored geons of all conceivable types, cylindrical particle.2 (For “geon” and other terms coined by Wheeler, see gravitational waves, the interaction of neutrinos with curved box 1.) More interesting, he realized a bit later, was a purely spacetime, the interface between general relativity and quan- gravitational geon: a bundle of gravitational waves held to- tum theory, the physical interpretation of quantum mechan- gether gravitationally. Such a geon would pull on its sur- ics, and a closed universe made from a large number of roundings, thereby exhibiting mass, but it would not contain wormhole mouths with collective gravitational pulls suffi- any material mass. Mass without mass, he called it. cient to bend the universe’s space up into a topological The geon in one sense was a dead end. As Wheeler soon 3-sphere. In a tour de force, Wheeler and his group of nine 40 April 2009 Physics Today © 2009 American Institute of Physics, S-0031-9228-0904-030-7 Figure 1. John Wheeler lecturing at a conference in Cambridge, UK, in 1971. Wheeler’s style was to cover the blackboard with inspirational colored-chalk diagrams and phrases before the lecture, then work his way through them, one by one. KIP THORNE students, postdocs, and visitors presented papers on all those technique to solve Einstein’s vacuum field equations. That issues at the First International Conference on General Rela- technique, in the hands of Richard Isaacson, a student under tivity and Gravitation—held in Chapel Hill, North Carolina, one of us (Misner), morphed into the rigorous description of in January 1957—and wrote them up,3 mostly as eight papers gravitational-wave energy that forms the buttress of today’s in the July 1957 issue of Reviews of Modern Physics. gravitational-wave searches. As with Wheeler’s geon paper, some of those papers are While working on thermonuclear weapons in the now historical curiosities, but four laid crucial foundations early 1950s, Wheeler had learned the power of numerical for major developments. Joseph Weber used his paper with simulations, so he encouraged his students to begin laying Wheeler on cylindrical gravitational waves as a springboard foundations for numerical relativity. He envisioned an era, for launching his pioneering research on gravitational-wave which has now arrived, when numerical simulations would experiments—research that underpins today’s gravitational- reveal the nonlinear dynamics of curved spacetime— wave observatories. A paper, discussed below, by Tullio geometro dynamics under the most extreme circumstances. Regge and Wheeler became the foundation for future studies Seminal papers by Richard Arnowitt, Stanley Deser, and of black hole pulsations. Hugh Everett laid out in his paper Misner expressed geometrodynamics in the mathematical what has come to be called the many-worlds interpretation form that would become for decades the preferred starting of quantum mechanics, and in an accompanying paper point for computational work.6 Papers on binaries made from Wheeler explained Everett’s ideas in different language. wormholes attracting each other, written in the late 1950s and Despite his own misgivings about “many worlds,” which he early 1960s by Wheeler’s students Brill, Misner, and Richard more modestly called the relative-state formulation of quan- Lindquist, are still used today, a half century later, to provide tum mechanics, Wheeler recognized the importance of initial data7 for some simulations of binary black holes. And Everett’s ideas: He encouraged Everett and helped dissemi- an elegant, analytical solution of the constraint equation, sug- nate those ideas, and even returned to them in 2001 in one of gested by Wheeler and carried through by Brill, is used today his last published papers.4 as the starting point for simulations of highly distorted black The gravitational geon and the model universe con- holes that vibrate wildly, emitting copious gravitational structed from wormholes were entities made solely from waves, before settling down into a quiescent state. Fifty years spacetime curvature—entities whose geometries must evolve ago Wheeler could only dream of the 21st-century simulations as time passes. Wheeler realized they were examples of that are now teaching us wonderful things about nonlinear geometrodynamics—a term he coined by analogy with elec- geometro dynamics. trodynamics to denote the structure and dynamics of curved In 1953 or 1954, while pondering geons in the quantum spacetime. He chose Geometrodynamics as the title of his first domain, Wheeler identified the characteristic length scale long treatise on relativity, mostly a collection of his early rel- (~10−33 cm) and time scale (~10−43 s) on which general relativity ativity publications. In his students’ hands, those early ideas must break down and be replaced by new laws of quantum have had a huge impact:5 In 1960 Wheeler’s postdoc Dieter gravity. The lengths and times had been introduced into Brill and undergraduate James Hartle fleshed out the gravi- physics a half century earlier by Max Planck, so Wheeler gave tational geon by developing a two- length-scale expansion them the names “Planck length” and “Planck time.” (In www.physicstoday.org April 2009 Physics Today 41 the probability distribution for tiny fluctuations away from Box 1. Wheeler coinages general relativity’s classical spacetime geometry. Through John Wheeler believed that the names given to concepts or discussions with Misner, Bryce DeWitt (then at the University to descriptions of an idea strongly influence how we think of North Carolina), and others, Wheeler came to understand about concepts and ideas, even how we work on them and the arena for that wavefunction: It is defined on the space of build on them.