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Relativity

artificial satellites, classical theories, elementary calculus, General relativity theory, world line

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>  Classical Physics

>  Special Theory of Relativity

>  Confirmation and Modification

As in the cases mentioned above, classical and relativistic predictions are generally virtually identical, but relativistic mathematics is more complex. The famous apocryphal statement that only ten people in the world understood Einstein's theory referred to the complex tensor algebra and Riemannian geometry of general relativity; by comparison, special relativity can be understood by any college student who has studied elementary calculus.

General relativity theory has been confirmed in a number of ways since it was introduced. For example, it predicts that the world line of a ray of light will be curved in the immediate vicinity of a massive object such as the sun. To verify this prediction, scientists first chose to observe a star appearing very close to the edge of the sun. Such observations cannot normally be made, because the brightness of the sun obscures a nearby star. During a total eclipse, however, stars can be observed and their positions accurately measured even when they appear quite close to the edge of the sun. Expeditions were sent out to observe the eclipses of 1919 and 1922 and made such observations. The apparent positions of the stars were then compared with their apparent positions some months later, when they appeared at night far from the sun. Einstein predicted an apparent shift in position of 1.745 seconds of arc for a star at the very edge of the sun, with progressively smaller shifts for more distant stars. The expeditions that were sent to study the eclipses verified these predictions. In recent years, comparable tests were made of radio-wave deflections from distant quasars, using radio-telescope interferometers (see Radio Astronomy). The tests yielded results that agreed, to within 1 percent, with the values predicted by general relativity.

Another confirmation of general relativity involves the perihelion of the planet Mercury. For many years it had been known that the perihelion (the point at which Mercury passes closest to the sun) revolves about the sun at the rate of once in 3 million years, and that part of this perihelion motion is completely inexplicable by classical theories. The theory of relativity, however, does predict this part of the motion, and recent radar measurements of Mercury's orbit have confirmed this agreement to within about 0.5 percent.

Yet another phenomenon predicted by general relativity is the time-delay effect, in which signals sent past the sun to a planet or spacecraft on the far side of the sun experience a small delay, when relayed back, compared to the time of return as indicated by classical theory. Although the time intervals involved are very small, various tests made by means of planetary probes have provided values quite close to those predicted by general relativity (see Radar Astronomy). Numerous other tests of the theory could also be described, and thus far they have served to confirm it.

The general theory of relativity predicts that a massive rotating body will drag space and time around with it as it moves. This effect, called frame dragging, is more noticeable if the object is very massive and very dense. In 1997 a group of Italian astronomers announced that they had detected frame dragging around very dense, rapidly spinning astronomical objects called neutron stars. The astronomers found evidence of frame dragging by examining radiation emitted when the gravitational pull of a dense neutron star sucks matter onto its surface. This radiation showed slight differences from the radiation that was predicted by classical physics.

In 1998 another group of astronomers from the United States and Europe announced that the orbits of some artificial satellites around the earth showed the effects of frame dragging. The earth is much lighter and less dense than a neutron star, so the effects of the earthís frame dragging are much more subtle than those of the neutron starís frame dragging. The astronomers found that the orbits of two Italian satellites seem to shift about 2 m (about 7 ft) in the direction of the earthís rotation every year. The launch of the U.S. spacecraft Gravity Probe B in 2000 should provide even more evidence of frame dragging around the earth and other bodies.

General Theory of Relativity

Any simple sound, such as a musical note, may be completely described by specifying three perceptual characteristics: pitch, loudness (or intensity), and quality (or timbre). These characteristics correspond exactly to three physical characteristics: frequency, amplitude, and harmonic constitution, or waveform, respectively. Noise is a complex sound, a mixture of many different frequencies or notes not harmonically related.

Later Observations

The amplitude of a sound wave is the degree of motion of air molecules within the wave, which corresponds to the changes in air pressure that accompany the wave. The greater the amplitude of the wave, the harder the molecules strike the eardrum and the louder the sound that is perceived. The amplitude of a sound wave can be expressed in terms of absolute units by measuring the actual distance of displacement of the air molecules, the changes in pressure as the wave passes, or the energy contained in the wave. Ordinary speech, for example, produces sound energy at the rate of about one hundred-thousandth of a watt. All of these measurements are extremely difficult to make, however, and the intensity of sounds is generally expressed by comparing them to a standard sound, measured in decibels.



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