Consequences of General Relativity

General relativity has a number of physical consequences. Some follow directly from the theory’s axioms, whereas others have become clear only in the course of the ninety years of research that followed Einstein’s initial publication.

Gravitational time dilationSchematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body

Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly clocks run. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.

This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times. The effects detected in such experiments are extremely small, with differences being measured in nanoseconds.

Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference. In general relativity, it is considered to be difference in the passage of proper time at different positions as described by a metric tensor of spacetime. The existence of gravitational time dilation was first confirmed directly by the Pound-Rebka experiment.

Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System (GPS) needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect.

Gravitational time dilation has also been confirmed by the Pound-Rebka experiment, observations of the spectra of the white dwarf Sirius B and experiments with time signals sent to and from Viking 1 Mars lander.

  • According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.
  • The speed of light in a locale is always equal to c according to the observer who is there. The stationary observer’s perspective corresponds to the local proper time. Every infinitesimal region of space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they are made of the same essence (as shown in many tests involving the famous equation E=mc2). Such regions are significant whether or not they are occupied by an observer. A time delay is measured for signals that bend near the sun, headed towards Venus, and bounce back to earth along more or less a similar path. There is no violation of the speed of light in this sense, as long as an observer is forced to observe only the photons which intercept the observing faculties and not the ones that go passing by in the depths of more (or even less) gravitational time dilation.

If a distant observer is able to track the light in a remote, distant locale which intercepts a time dilated observer nearer to a more massive body, he sees that both the distant light and that distant time dilated observer have a slower proper time clock than other light which is coming nearby him, which intercept him, at c, like all other light he really can observe. When the other, distant light intercepts the distant observer, it will come at c from the distant observer’s perspective.

Light deflection and gravitational time delay

General relativity predicts that the path of light is bent in a gravitational field; light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.

This and related predictions follow from the fact that light follows what is called a light-like or null geodesic—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity. As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion), several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity.

Closely related to light deflection is the gravitational time delay (or Shapiro effect), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction. In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.

Gravitational waves

Gravitational waves, a direct consequence of Einstein’s theory are ripples in space-time, distortions of geometry which propagate at the speed of light. (They should not be confused with the gravity waves of fluid dynamics, which are a different concept.)Two stars of similar mass are in highly elliptical orbits about their center of mass.

Indirectly, the effect of gravitational waves has been detected in observations of specific binary stars. Such pairs of stars orbit each other and, as they do so, gradually lose energy by emitting gravitational waves. For ordinary stars like our sun, this energy loss would be too small to be detectable. However, in 1974, this energy loss was observed in a binary pulsar called PSR1913+16. In such a system, one of the orbiting stars is a pulsar. This has two consequences: a pulsar is an extremely dense object known as neutron star, for which gravitational wave emission is much stronger than for ordinary stars. Also, a pulsar emits a narrow beam of electromagnetic radiation from its magnetic poles. As the pulsar rotates, its beam sweeps over the Earth, where it is seen as a regular series of radio pulses, just as a ship at sea observes regular flashes of light from the rotating light in a lighthouse. This regular pattern of radio pulses functions as a highly accurate “clock”. It can be used to time the double star’s orbital period, and it reacts sensitively to distortions of space-time in its immediate neighborhood.

The discoverers of PSR1913+16, Russell Hulse and Joseph Taylor, were awarded the Nobel prize in physics in 1993. Since then, several other binary pulsars have been found. The most useful are those in which both stars are pulsars, since they provide the most accurate tests of general relativity.

Currently, one major goal of research in relativity is the direct detection of gravitational waves. To this end, a number of land-based gravitational wave detectors are in operation, and a mission to launch a space-based detector, LISA, is currently under development, with a precursor mission (LISA Pathfinder) due for launch in late 2009. If gravitational waves are detected, they could be used to obtain information about compact objects such as neutron stars and black holes, and also to probe the state of the early universe fractions of a second after the Big Bang.

Most scientists describe gravitational waves as “ripples in space-time.” Just like a boat sailing through the ocean produces waves in the water, moving masses like stars or black holes produce gravitational waves in the fabric of space-time. A more massive moving object will produce more powerful waves, and objects that move very quickly will produce more waves over a certain time period.

Orbital effects and the relativity of direction

General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation (precession) of planetary orbits, as well as orbital decay caused by the emission of gravitational waves and effects related to the relativity of direction.

Precession of apsidesEinstein cross: four images of the same astronomical object, produced by a gravitational lens.

In general relativity, the apsides of any orbit (the point of the orbiting body’s closest approach to the system’s center of mass) will precess—the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle. For him, the fact that his theory gave a straightforward explanation of the anomalous perihelion shift of the planet Mercury, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.

The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass) or the much more general post-Newtonian formalism. It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body’s gravity (encoded in the nonlinearity of Einstein’s equations). Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus and the Earth), as well as in binary pulsar systems, where it is larger by five orders of magnitude.

Orbital decay

According to general relativity, a binary system will emit gravitational waves, thereby losing energy. Due to this loss, the distance between the two orbiting bodies decreases, and so does their orbital period. Within the solar system or for ordinary double stars, the effect is too small to be observable. Not so for a close binary pulsar, a system of two orbiting neutron stars, one of which is a pulsar: from the pulsar, observers on Earth receive a regular series of radio pulses that can serve as a highly accurate clock, which allows precise measurements of the orbital period. Since the neutron stars are very compact, significant amounts of energy are emitted in the form of gravitational radiation.

The first observation of a decrease in orbital period due to the emission of gravitational waves was made by Hulse and Taylor, using the binary pulsar PSR1913+16 they had discovered in 1974. This was the first detection of gravitational waves, albeit indirect, for which they were awarded the 1993 Nobel Prize in physics. Since then, several other binary pulsars have been found, in particular the double pulsar PSR J0737-3039, in which both stars are pulsars.

Geodetic precession and frame-draggingDeflection of light (sent out from the location shown in blue) near a compact body (shown in gray).

Several relativistic effects are directly related to the relativity of direction. One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant stars—even though such a gyroscope represents the way of keeping a direction as stable as possible (“parallel transport”). For the Moon-Earth-system, this effect has been measured with the help of lunar laser ranging. More recently, it has been measured for test masses aboard the satellite Gravity Probe B to a precision of better than 1 percent.

Near a rotating mass, there are so-called gravitomagnetic or frame-dragging effects. A distant observer will determine that objects close to the mass get “dragged around”. This is most extreme for rotating black holes where, for any object entering a zone known as the ergosphere, rotation is inevitable. Such effects can again be tested through their influence on the orientation of gyroscopes in free fall. Somewhat controversial tests have been performed using the LAGEOS satellites, confirming the relativistic prediction. A precision measurement is the main aim of the Gravity Probe B mission, with the results expected in September 2008.

At the End

Albert Einstein’s general theory of relativity fundamentally changed the way we understand gravity and the Universe in general. So far, it has passed all experimental tests. This, however, does not mean that Newton’s law of gravity is wrong. Newton’s law is an approximation of general relativity; that is, in the approximation of small gravitational fields, general relativity reduces to Newton’s law of gravity. General relativity, too, is only an approximate description of certain aspects of Nature: this is known because general relativity does not agree with the predictions of quantum mechanics (the other great organizing idea of modern physics) in describing extremely small phenomena. Quantum mechanics, similarly, makes erroneous predictions at the cosmic scale. Physicists are striving to discover an even more general or unified theory that will yield both general relativity and quantum mechanics as special cases.

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