Chapter IV of my dissertation was a joint project that I undertook in 1978 with my advisor, Professor Kip Thorne. Kip wanted to help jump-start gravitational-wave (GW) astronomy — the study of the universe through direct observation of gravitational radiation. Since it's expensive and difficult to build GW detectors, any estimates of how much (or how little) a signal to expect is an aid. Kip proposed to examine common "Cherished Beliefs" about the cosmos, and to derive limits from those beliefs on what waves might be detected at various frequencies. I helped him compute and explore those implications. The original questions we addressed were posed by experimentalists Ronald Drever and Rainer Weiss.
The astrophysical cherished beliefs we assumed are quite straightforward and relatively uncontroversial:
- the cosmological principle that we don't live in a special time or place in the universe;
- the conservative assumption that there is no significant amount of "relict" primordial gravitational radiation bathing the Earth;
- the local power limit that within our Galaxy no single, coherently radiating object has mass more than 100 million solar masses (a generous upper bound);
- the isotropy hypothesis that the dominant sources of GW in the universe have no significant beaming of their radiation; and
- the random-parameter notion that narrow-band emitters of gravitational waves (e.g. binary stars, or spinning neutron stars) are scattered over a wide range of frequencies.
In addition to these astronomical postulates, we relied on some simple and plausible cherished beliefs about the correct theory of gravitational waves:
- that a source can't radiate coherently at wavelengths much shorter than the light-travel time across the source;
- that the brightness of a source is limited by something like the standard quadrupole radiation formula;
- that the total energy radiated by a source is restricted by Einstein's mass times the speed of light squared;
- that waves arriving at the Earth have an amplitude governed by the usual frequency-energy relationships of General Relativity, within an order of magnitude or so;
- that energy is conserved (you can't get something for nothing!); and
- that weak gravitational waves propagate at roughly the speed of light.
The final paper that explored all this was titled "The Gravitational Waves That Bathe the Earth: Upper Limits Based on Theorists' Cherished Beliefs". It was dedicated to Abraham H. Taub, on the occasion of his retirement from the University of California at Berkeley, and appeared in a festschrift in honor of him published in 1980. Taub is a towering figure in relativity theory, whose work on ideal models of the universe (e.g., "Taub-NUT Space") is reputed to provide a counterexample to just about every common prejudice about cosmology. Kip knew Abe Taub personally as a colleague; I didn't have the privilege, though we met once or twice at seminars.
Our essay provided bounds on how strong gravitational waves might be at various frequencies for extragalactic and galactic sources, and for discrete objects — bursters, transient sources, and continuous-wave monochromatic emitters — as well as for an unresolved stochastic background. Thus far, no gravitational waves have been seen in confirmed experiments (though likely side-effects of waves are apparent in such systems as the Taylor-Hulse binary pulsar). Detectors are now becoming sensitive enough to get below our "cherished belief" limits. Perhaps some day soon!
Wednesday, April 19, 2000 at 06:11:35 (EDT) = 2000-04-19