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Let’s examine the travel (in slow motion) of the light emitted in S with wavelength as it travels from S (a planet or star) to S’ (a platform orbiting S). As the light travels from S it will increase in speed as it goes from the surface clock rate to the faster clock rates as it gains distance from the S. There is no reason that the change in speed would change the actual frequency, so the wavelength must increase. As the light approaches an observer O’ in S’, it will start encountering a slowing of the clock rate, and thus its speed and wavelength will decrease. When it reaches S’, O’ will measure the wavelength as , which will be longer than since the clock rate in S’ is greater than in S. O’ will also calculate the energy for the light as being less than would be expected for light emitted from the same atom and energy level in S’ (provided the clock rate difference in the two locations is ignored). This is the ‘gravitational red shift’.
The following illustration shows the wavelength change as a photon leaves a large body such as the sun and travels to a smaller body such as the earth. The concentric circles represent the time gradient fields around each body. As the photon leaves the sun it increases in speed and the wavelength gets longer. It then travels through space with a wavelength consistent with the clock rate in that space. When it reaches the earth, it again slows down and the wavelength decreases, with the decrease being much less than the increase as it left the sun.
Illustration 1
