Shapiro delay

The Shapiro delay, named after Irwin I. Shapiro, allows the propagation of light in the vicinity of a large crowd for a distant observer appear slower than the speed of light. This is consistent with the general theory of relativity.

The gravitational lens effect in which light is deflected by gravity can be explained with the Shapiro delay. Here, the deflection results similar to the refraction of light of lenses made ​​of glass, of a local change of the propagation speed.

Effect

For weak, time-independent gravitational fields is obtained as an approximation for the metric in spherical coordinates

The approximation can be as good to use on the surface of a star, but on the surface of a much denser neutron star it is not so easy to apply and there are measurable deviations. When applied to a star is the gravitational potential, where m is the mass of the star, G is the Newtonian gravitational constant and c is the speed of light.

With this approximation can be vividly the deflection of light by gravity interpreted as a refraction effect. Therefore one must consider what is the real time on a space-time point. We define for an infinitesimal time interval:

Than that of an observer at space-time point x measured real time or proper time. You also have to take into account the length contraction and x define the length close to the ground as

If one now considers a light beam as is its real speed, the speed of light, and its speed is measured. They stand by the above definition of the proper time in the following context

If one considers that an attractive gravitational potential, that is negative, it can be seen that the measured speed of the light beam is smaller than the speed of light. One can therefore interpret the gravitational field in this analysis as a medium with location-dependent refractive index. Since light propagates along geodesics, this can therefore be formulated as that near a mass geodesics are curved in space. In addition to the light curve, this also leads to delay light, called after its discoverer as Shapiro delay.

At the edge of the sun is resulting in a refractive index. The effect is thus very small compared to ordinary optical refraction. Accordingly, small is also the angle of light deflection in the gravitational field.

Experiment status

The light delay was predicted theoretically by Irwin I. Shapiro in 1964 and measured in 1968 and 1971. Here, the time shift was measured by means of reflected on the Venus radar signals, while this was from the Earth behind the Sun, so that the radar waves had to happen at the solar limb near. The measurement uncertainty amounted initially to several percent. In case of repeated measurements, and later by measurements using space probes ( Mariner, Viking) instead of Venus, the measurement accuracy could be increased to 0.1%.

The most precise measurement of the effect led 2002 with the conjunction of the Cassini spacecraft with the sun. Frequency measurements in the Ka-band enabled the determination of the Shapiro delay with an accuracy of 0.001%.