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The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of general relativity
Tests of general relativity

At its introduction in 1915, the general relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Isaac Newton's law of universal gravitation with special relativity....
. Radar
Radar

Radar is a system that uses electromagnetic radiation waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain....
 signals passing near a massive object take slightly longer to travel to a target and longer to return (as measured by the observer) than it would if the mass of the object were not present.

History
The time delay effect was first noticed in 1964, by Irwin I. Shapiro
Irwin I. Shapiro

Irwin I. Shapiro is an American astrophysicist. Since 1982, he has been a professor at Harvard University. Shapiro was director of the Harvard-Smithsonian Center for Astrophysics from 1982 to 2004....
.






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Encyclopedia


The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of general relativity
Tests of general relativity

At its introduction in 1915, the general relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Isaac Newton's law of universal gravitation with special relativity....
. Radar
Radar

Radar is a system that uses electromagnetic radiation waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain....
 signals passing near a massive object take slightly longer to travel to a target and longer to return (as measured by the observer) than it would if the mass of the object were not present.

History


The time delay effect was first noticed in 1964, by Irwin I. Shapiro
Irwin I. Shapiro

Irwin I. Shapiro is an American astrophysicist. Since 1982, he has been a professor at Harvard University. Shapiro was director of the Harvard-Smithsonian Center for Astrophysics from 1982 to 2004....
. Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury, and measure the round trip travel time. When the Earth, Sun, and Venus are most favorably aligned, Shapiro showed that the expected time delay, due to the presence of the Sun, of a radar signal traveling from the Earth to Venus and back, would be about 200 microseconds, well within the limitations of 1960s era technology.

The first test, using the MIT
Massachusetts Institute of Technology

The Massachusetts Institute of Technology is a private university research university located in Cambridge, Massachusetts, Massachusetts, United States....
 Haystack radar antenna, was successful, matching the predicted amount of time delay. The experiments have been repeated many times since, with increasing accuracy.

Calculating time delay


The speed of light in meters per given interval of "proper time" is a constant, however the travel time of any electromagnetic wave, or signal, moving at 299,792,458 meters per "second" is affected by the gravitational time dilation
Gravitational time dilation

Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the higher the local distortion of spacetime due to gravity, the more slowly time passes....
 in regions of spacetime through which it travels. This is because the coordinate time
Coordinate time

In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. An event is specified by one time coordinate and three spatial coordinates....
 and proper time
Proper time

In theory of relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events....
 diverge as the gravitational field strength increases.

Time delay due to light travelling around a single mass


For a signal going around a massive object, the time delay can be computed as the following:

Here is the unit vector pointing from the observer to the source, and

is the unit vector pointing from the observer to the gravitating mass M.

See Dot product
Dot product

In mathematics, the dot product, also known as the scalar product, is an operation which takes two vector over the real numbers R and returns a real-valued scalar quantity....
.

The above formula can be rearranged like this:

which is the extra distance the light has to travel, where is the Schwarzchild radius.

This is the same as:

Special cases


Shapiro delay and interplanetary probes

Shapiro delay must be considered along with ranging data when trying to accurately determine the distance to interplanetary probes such as the Voyager and Pioneer spacecraft (see the Voyager program
Voyager program

The Voyager program is a series of U.S. unmanned space missions that consists of a pair of unmanned scientific Space probes, Voyager 1 and Voyager 2....
, the Pioneer program
Pioneer program

The Pioneer program is a series of United States unmanned space missions that was designed for planetary exploration. There were a number of such missions in the program, but the most notable were Pioneer 10 and Pioneer 11, which explored the outer planets and left the solar system....
, and the Pioneer anomaly
Pioneer anomaly

The Pioneer anomaly or Pioneer effect is the observed deviation from predicted trajectory and velocity of various unmanned spacecraft visiting the outer solar system, most notably Pioneer 10 and Pioneer 11....
).

Quote by Einstein


"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." - Albert Einstein (The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity)

Shapiro delay of neutrinos and gravitational waves


From the near-simultaneous observations of neutrinos and photons from SN 1987A, we know that the Shapiro delay for neutrinos is same as that for photons to within 10 %. Since gravitational waves have not been directly detected, we don't have any data on the Shapiro delay for gravitational waves. In general relativity and other metric theories of gravity, the Shapiro delay for gravitational waves is expected to be same as that for light (and neutrinos). However in theories such as Teves
Tensor-vector-scalar gravity

Tensor-Vector-Scalar gravity is a proposed relativistic theory which purports to explain galactic rotation curves without invoking dark matter....
 and other modified GR theories which reproduce Milgrom's law and avoid the need for dark matter, the Shapiro delay for gravitational waves is much smaller than that for neutrinos or photons.

See also

  • Tests of general relativity
    Tests of general relativity

    At its introduction in 1915, the general relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Isaac Newton's law of universal gravitation with special relativity....
  • Gravitational redshift
    Gravitational redshift

    In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field....
     and Blueshift
  • Gravitational time dilation
    Gravitational time dilation

    Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the higher the local distortion of spacetime due to gravity, the more slowly time passes....
  • Proper time
    Proper time

    In theory of relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events....