Traveling at the Speed of Thought by Kennefick Daniel

Author:Kennefick, Daniel.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2016-07-21T16:00:00+00:00

Figure 8.1. This photo of Richard Feynman (right) speaking with Paul Dirac (left) at the Warsaw conference on General Relativity and Gravitation (GR2) in 1962 made the cover of Physics Today, a sign of the increasing importance of the field. Presumably Dirac was not one of the 126 “idiots” Feynman encountered at the conference. (Courtesy AIP Emilio Segré Visual Archives, Physics Today Collection)

Throughout the 1960s, Chandrasekhar developed his own slow-motion formalism, dealing with extended fluid bodies (as opposed to point masses) at one post-Newtonian order after another (Chandrasekhar 1965). By the end of the decade he had advanced far enough in the expansion to describe reaction effects. His conclusion agreed with the quadrupole formula result (Chandrasekhar and Esposito 1970).

At about this time William Burke, a student of Kip Thorne’s at Caltech, introduced improvements to the slow-motion approach that removed much of the arbitrariness in imposing the boundary conditions. Burke selected the problem of radiation damping in binaries for himself, since Thorne had been convinced by Peres’s work that the problem was solved in the slow-motion case. Introduced to general relativity by Frank Estabrook of the Jet Propulsion Laboratory (later to become a pioneer of the use of Doppler tracking of deep-space probes such as the Voyager spacecraft to attempt to detect gravitational waves), Burke was greatly influenced by an applied mathematician at Caltech, Paco Lagerstrom (Thorne and Estabrook, pers. comms.). Lagerstrom and his group had developed the technique of matched asymptotic expansions (abbreviated MAX), which had finally set on a mathemematically secure foundation the brilliant insights of Ludwig Prandtl that inaugurated the modern field of fluid dynamics in the early twentieth century. Werner Heisenberg had said of Prandtl that he had “the ability to see the solution of equations without going through the calculations” (Narasimha 2004). Lagerstrom had provided a way to actually do the calculations. Burke saw that this revolutionary technique was the solution to the problem that plagued the radiation reaction problem in relativity. (Note that general relativity shares with fluid dynamics the challenge of nonlinearity in the equations.)

Matched asymptotic expansions is a method that permits one to compare two quite separate approximation schemes having different areas of validity by matching them term by term in an intermediate zone where they are both valid. Burke realized that doing so could allow one to compare a post-Newtonian expansion, valid for the source of the gravitational waves, with a linearized approximation, valid towards infinity, where the waves actually existed, by matching them in an intermediate zone far, but not too far, from the source. In this way boundary conditions, such as outgoing-wave-only, that could be stated unambiguously in the linearized approximation could be imposed in a consistent way on the near-zone solution that actually described the source, thus addressing the arbitrariness that had bedeviled the slow-motion approach up to this time (Burke 1969). With this novel approach, Burke and Thorne also derived the quadrupole formula for emission from binary systems (Burke and Thorne 1970). Burke also constructed a radiation-reaction potential that could describe the damping force exerted on the orbiting bodies.

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