Gravitational waves
some history
(based on D. Kennefick’s work)
Historical tidbits
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1776: Laplace suggests four mechanisms that could explain secular perturbations of Moon-Earth
orbit. One the explanations was a non-instantaneous propagation of gravity, affecting the binary
system (abandoned because its speed would be too large to be measurable to explain the effect).
1908: Poincare proposes emission of gravitational waves (similar to Maxwell’s EM waves) to explain
Mercury’s perihelion anomaly.
Max Abraham
Einstein to Szhwarzschild, Feb 1916: “Thus there are no gravitational waves analogous to light
waves. This probably is also related to the one-sidedness of the sign of the scalar T”.
Einstein’s paper, 1916: W eshall show that these guv [the small perturbative quatities] can be
calculated in a manner analogous to that of retarded potential in electrodynamics. From this it
follows that gravitational fields propagate with the speed of light. Subsequent to this general
solution we shall investigate gravitational waves and how they originate.”. He founds some
solutions (with longitudinal components) that do not transport energy (coordinate artifacts), and
one that does (transverse).
Einstein’s paper, 1918 “On Gravitational Waves”: corrects a actor of 2 mistake in 1916 paper, and
derives the “quadrupole” formula”.
Eddington rederived in 1922 Einstein’s radiation equations without assuming propagation at the
speed of light; he discovered that waves with longitudinal component had a coordinate-dependent
velocity: [LL and LT waves] “are merely sinuosities in the coordinate system, and the only speed of
propagation relevant to them is `the speed of thought’”. In the same paper, he rederived the
quadrupole formula, focusing on binary systems (and later rods), and correcting a factor of 2 in
Einstein’s paper.
Historical tidbits
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Einstein to Born, 1936: “Together with a young collaborator [Rosen], I arrived at an interesting
result that gravitational waves do not exist,..” (Probably because exact GR vacuum solutions with
plane waves required unphysical singularities).
A paper by Einstein and Rosen in 1936 on “Do Gravitational Waves exist?” [Answer: no] is sent to
Physical Review, later withdrawn (protesting the referee report and the refereeing process), and
later sent and revised to the Journal of the Franklin Institute, with a different answer. A key point is
whether an exact solution to the non-linear equations without a physical singularity (or one that
can be associate with a source) exists. “Einstein-Rosen” waves are an exact solution with cylindrical
waves and a singularity at the axis. [This solution had been published by others earlier].
1938: Einstein, Infeld and Hoffman develop “post-newtonian theory” (EIH method) to study the
problem of motion. [The binary system was of particular interest to many].
Using the EIH formalism Infeld and Scheidegger (1951) concluded that the most natural treatment
of the scheme, employing the standing wave boundary condition, led to a no-radiation-reaction
result. “Back reaction” (damping) terms could be transformed away by coordinate transformations.
Goldberg (1955) proved EIH (slow motion) approach was not appropriate to study back reaction
effects.
Historical tidbits
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Bern conference (1955) revitalizes the field, induces Bondi to work on the topic. “Energy is nonlocalizable and notl defined in a covariant way” is a key topic.
Chapel Hill conference (1957, attended by Feynman) also discussed gravitational waves, and
quantum gravity (and their relationship!). Feynman then presented an argument based on Pirani’s
earlier talk. Appealing to the equation of geodesic deviation, he argued that a particle lying beside a
stick would be rubbed back and forth against the stick by a passing wave, and the friction would
generate heat, so that energy would have been extracted from the wave. Furthermore, he felt that
any system which could be an absorber of waves, could also be an emitter. For these reasons, he
expected gravitational waves to exist.
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); rederived the quadrupole formula (to higher orders).
Burke and Thorne also derived the quadrupole formula for emission from binary systems (Burke
and Thorne 1970).
During the sixties, great progress had been made on many fronts in the description of wave
propagation and interaction with matter. Possible astrophysical sources, such as supernovae and
binary neutron stars, began to be suggested, inspired at first by Weber’s work (Dyson 1963).33
Some experts were of the opinion that the subject was maturing and furthermore the prospect of
some real astrophysical application for gravity waves, seemed to emerge with the discovery of the
quasi-stellar (“quasar”) radio sources. Then, to the great surprise of the theoreticians, Weber
announced in 1969 that he was detecting gravitational waves.