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ScienceWeek
ASTROPHYSICS: ON GRAVITATIONAL WAVES
The following points are made by Peter S. Shawhan (American Scientist 2004 92:350):
1) To understand how gravitational radiation arises requires at least a rudimentary understanding of Einstein's general theory of relativity. This theory posits that time is a dimension similar to the three dimensions of space and that the combined four-dimensional "spacetime" can be treated using the language of geometry.
2) The complete history of an object's position as a function of time is described by a "world line", which threads through the four-dimensional coordinate system, from past to present to future. If no force acts on the object, it will move with a constant velocity, and its world line will be a straight line at some fixed angle relative to the coordinate axes.
3) An object near a large mass feels the force of gravity accelerate it, so that its world line follows a curved path relative to the coordinate system. For example, if a ball is thrown straight up into the air, a graph of its height versus time traces out a parabola. At least, that is the conventional view, dating back to Isacce Newton (1642-1727). Albert Einstein (1879-1955) took the bold step of casting that notion aside and postulating that a massive body curves the coordinate system itself. Rather than following a curved path in a Cartesian coordinate system, the ball actually follows a "straight" path (a geodesic) in a curved coordinate system, returning to the thrower's hand at a later time because the geodesic leads it there. Gravity, therefore, is not really a force but is a manifestation of curvature in the geometry of spacetime.
4) The difference between these two points of view may sound like a matter of definition, but Einstein's theory made a few specific predictions that have since been experimentally verified. For example, the British astrophysicist Sir Arthur Eddington (1882-1944) took advantage of a 1919 solar eclipse to measure the deflection of starlight passing near the Sun, finding it to be in agreement with theory. His result was trumpeted on the front pages of newspapers around the world, instantly establishing Einstein's popular reputation.
5) General relativity says that the geometrical curvature induced by a massive object does not arise everywhere instantaneously. Rather, it travels outward from its source at the speed of light. Thus, if a massive object alters its shape or orientation, or if a collection of objects changes its spatial arrangement, the gravitational effect -- the curvature of spacetime -- propagates away as a gravitational wave.
6) A gravitational wave may be described as a time-varying distortion of the geometry of space, temporarily altering the effective distance between any given pair of points. If the causative shift in mass is abrupt, the wave will take the form of a short pulse, much like the ripple produced after dropping a rock into a still pond. In the case of a periodic change, the wave will be sustained, much like the carrier wave for a broadcast radio signal. In either case, the amplitude of the wave will be inversely proportional to the distance from the source. Unlike ordinary gravitational acceleration, which always points toward the source, a gravitational wave acts perpendicularly to the direction in which it is traveling, and thus is called a transverse wave. In this sense it is like light, rather than like sound, which propagates as longitudinal waves.(1-5)
References (abridged):
1. Barish, B. C., and R. Weiss. 1999. LIGO and the detection of gravitational waves. Physics Today 52(10):44-50
2. Lyne, A. G., M. Burgay, M. Kramer, A. Possenti, R. N. Manchester, F. Camilo, M. A. McLaughlin, D. R. Lorimer, N. D'Amico, B. C. Joshi, J. Reynolds and P. C. C. Freire. 2004. A double-pulsar system: A rare laboratory for relativistic gravity and plasma physics. Science 303:1153-1157
3. Saulson, P. R. 1994. Fundamentals of Interferometric Gravitational Wave Detectors. Singapore: World Scientific. Schutz, B. S. 2003. Gravity from the Ground Up. Cambridge, U.K.: Cambridge University Press
4. Taylor, J. H., and J. M. Weisberg. 1982. A new test of general relativity: Gravitational radiation and the binary pulsar PSR 1913+16. Astrophysical Journal 253:908-920
5. Will, C. M. 1993. Was Einstein Right? Putting General Relativity to the Test. New York: Basic Books
American Scientist http://www.americanscientist.org
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Related Material:
ON GRAVITATIONAL WAVES
The following points are made by B.C. Barish and R. Weiss (Physics Today October 1999):
1) The idea of gravitational waves was already implicit in the 1905 special theory of relativity, with its finite limiting speed for information transfer. The explicit formulation for gravitational waves in general relativity was put forward by Einstein in 1916 and 1918. He showed that the acceleration of masses generates time-dependent gravitational fields that propagate away from their source at the speed of light as warpages of spacetime. Such a propagating warpage is called a "gravitational wave".
2) The best empirical evidence we have of the existence of gravitational radiation is indirect. It comes from the 1974 discovery and beautiful observations, by Russell Hulse and Joseph Taylor, of the first binary pulsar ever found. Exploiting the clockwork pulsar signal from the neutron star, they were able to monitor the orbital period of the binary star system with exquisite precision and confirm that it was indeed gradually speeding up at just the rate predicted for the general-relativistic emission of gravitational waves.
3) The direct detection of gravitational waves will mark the opening of a new window on the near and far reaches of the Cosmos. For physics, its most important promise is the direct observation of gravitation in highly relativistic settings, so that one can test general relativity in the strong-field limit, where it is not merely a small correction to Newtonian gravity. In that limit, the strong curvature of the spacetime geometry should show us fundamentally new physics.
Physics Today http://www.physicstoday.org
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Related Material:
A GRAVITATIONAL DIFFUSION MODEL WITHOUT DARK MATTER
The following points are made by R.J. Britten (Proc. Natl. Acad. Sci. 1998 95:3351):
1) The author presents a model that without dark matter quantitatively describes the flat rotation curves of galaxies and the mass-to-light ratios of clusters of galaxies. The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of about 5 kiloparsecs. As a result, the force between moderately distant masses separated by more than the mean free path diminishes as the inverse first power of the distance, following diffusion equations, and describes the flat rotation curves of galaxies.
2) According to the model, the force between masses separated by less than 1 kiloparsec diminishes as the inverse square of the distance. The excess gravitational force (ratio of 1/r:1/r^2) increases with the scale of structures from galaxies to clusters of galaxies, but there is reduced force at great distances because of the approximately 12 billion years available for diffusion to occur.
3) This model with a mean free path of about 5 kiloparsecs predicts a maximum excess force of a few hundredfold for galactic clusters with dimensions of a few megaparsecs. With only a single free parameter, the predicted curve for excess gravitational force vs. size of structures fits reasonable well with observations from those of dwarf galaxies through galactic clusters.
4) Under this diffusion model, no matter is proposed in addition to the observed baryons plus radiation, and thus the proposed density of the Universe is only a few percent of that required for closure.
5) The author suggests that although the model does not follow from present calculations based on the general theory of relativity, it is not necessarily inconsistent with the general theory because the diffusing gravitational elements might be interpreted as spatial curvatures (e.g., distortions of the metric inducing distortions in adjacent regions).
6) The author further suggests there is much at stake because of the scale of the intellectual investment and the subtle arguments in cosmology that make use of the general theory of relativity, and that the challenge of a theory of intrinsic "beauty" may not be met at this time because "beauty" is a subtle concept.
Proc. Nat. Acad. Sci. http://www.pnas.org
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