 The third test of Einstein's relativity theory, proposed by Einstein himself, involved the shifting of light wavelengths to the red in the curved space of a gravitational field. To see how this works, we'll take a minute to review just what redshift is. Most people have had the experience of hearing a pitch of a car horn, train whistle or ambulance siren drop off as the source moves past. As the sound source moves towards the observer, the sound waves are compressed, making the pitch of the sound higher. As the sound source moves away from the observer, the sound waves are stretched out, making the pitch of the sound lower. The same effect works for light. Here we have the visible spectrum from a star. Hydrogen in the star's atmosphere creates absorption lines with a unique pattern. Here's the pattern for a star at rest with respect to the observer. Light from an approaching star has its wavelengths shortened. We see that the lines shift to the blue. They are said to be blue-shifted. And light from a receiving star has its wavelengths lengthened. We see the lines shift to the red. They are said to be red-shifted. The key to measuring the Doppler effect is to measure the change in position of the spectral lines. The further the shift, the faster the radial velocity. When the shift to the red is caused by gravity instead of receding velocity, the phenomenon is called gravitational redshift. Einstein developed the concept for this using the elevator thought experiment. Consider the elevator at rest with a light emitter fixed to the floor and a receiver fixed directly above it on the ceiling at a known distance. The emitter sends photons with a controlled wavelength to the receiver where the arriving wavelength is measured. Here the measured wavelength of the light will be the same as the wavelength of the light emitted. Now put the elevator into a constant acceleration. Note that the receiver, at the time the light is observed, is further away from the point where the light was transmitted than it was in the static case. In other words, the receiver has acquired a velocity with respect to the light. And like the train whistle moving away, its wavelength is increased, shifted to the red. By the equivalence principle, the same result must hold in a gravitational field. But to calculate the effect as light moves away from a massive object, we need to take into account that the acceleration due to gravity is not constant. It decreases with distance as the light travels through the curved space around the object. The Schwarzschild metric that we used in the first two tests on Mercury's orbit and light bending around the Sun gives us the equation. We see that the amount of gravitational redshift for light from the surface of a massive object reaching a distant observer is proportional to the object's mass divided by its radius. Here's the gravitational redshift for the Earth and the Sun with triple the Earth's mass to radius ratio. These are very small, hard-to-measure shifts on the order of a tenth of a nanometer. Churning matter on the Sun's surface can have up to a thousand times the radial velocity equivalent to this redshift, making it impossible to measure gravitational redshift. Astronomers concluded that in order to measure this effect, they need a star with a calmer surface and larger mass to radius ratio. That would be a white dwarf. For that reason, they focused on the nearby Sirius binary star system with its giant star Sirius A and its orbiting white dwarf star Sirius B to test Einstein's theory. This binary system's orbital period is 50 years. In the 1920s, when the first measurements of Sirius B's gravitational redshift were made, the two stars were close together on the sky and the results were said to be contaminated by light from Sirius A. It wasn't until the 1960s that they were far enough apart to significantly reduce this contamination. At that time, astronomer Jesse Greenstein, working out of the Mount Wilson Observatory, measured the gravitational redshift effect to be 81 kilometers per second. Not far from the theoretical 81.3 kilometers per second. But the number of variables remained too large and difficulties separating out shift due to actual receding velocity made the results less than conclusive for testing Einstein's theory. But two physicists in the lab did prove Einstein correct. We'll cover their experiment in the next segment.