Gravitational redshift

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In physics and general relativity, gravitational redshift (known as Einstein shift in older literature)^[1][2] is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known more generally as a redshift. The opposite effect, in which photons gain energy when travelling into a gravitational well, is known as a gravitational blueshift (a type of blueshift). The effect was first described by Einstein in 1907,^[3][4] eight years before his publication of the full theory of relativity.

Gravitational redshift can be interpreted as a consequence of the equivalence principle (that gravity and acceleration are equivalent and the redshift is caused by the Doppler effect)^[5] or as a consequence of the mass–energy equivalence and conservation of energy ('falling' photons gain energy),^[6][7] though there are numerous subtleties that complicate a rigorous derivation.^[5][8] A gravitational redshift can also equivalently be interpreted as gravitational time dilation at the source of the radiation:^[8][2] if two oscillators (attached to transmitters producing electromagnetic radiation) are operating at different gravitational potentials, the oscillator at the higher gravitational potential (farther from the attracting body) will tick faster; that is, when observed from the same location, it will have a higher measured frequency than the oscillator at the lower gravitational potential (closer to the attracting body).

To first approximation, gravitational redshift is proportional to the difference in gravitational potential divided by the speed of light squared, ${\displaystyle z=\Delta U/c^{2}}$, thus resulting in a very small effect. Light escaping from the surface of the Sun was predicted by Einstein in 1911 to be redshifted by roughly 2 ppm or 2 × 10⁻⁶.^[9] Navigational signals from GPS satellites orbiting at 20000 km altitude are perceived blueshifted by approximately 0.5 ppb or 5 × 10⁻¹⁰,^[10] corresponding to a (negligible) increase of less than 1 Hz in the frequency of a 1.5 GHz GPS radio signal (however, the accompanying gravitational time dilation affecting the atomic clock in the satellite is crucially important for accurate navigation^[11]). On the surface of the Earth the gravitational potential is proportional to height, ${\displaystyle \Delta U=g\Delta h}$, and the corresponding redshift is roughly 10⁻¹⁶ (0.1 parts per quadrillion) per meter of change in elevation and/or altitude.

In astronomy, the magnitude of a gravitational redshift is often expressed as the velocity that would create an equivalent shift through the relativistic Doppler effect. In such units, the 2 ppm sunlight redshift corresponds to a 633 m/s receding velocity, roughly of the same magnitude as convective motions in the Sun, thus complicating the measurement.^[9] The GPS satellite gravitational blueshift velocity equivalent is less than 0.2 m/s, which is negligible compared to the actual Doppler shift resulting from its orbital velocity. In astronomical objects with strong gravitational fields the redshift can be much greater; for example, light from the surface of a white dwarf is gravitationally redshifted on average by around (50 km/s)/c (around 170 ppm).^[12]

Observing the gravitational redshift in the Solar System is one of the classical tests of general relativity.^[13] Measuring the gravitational redshift to high precision with atomic clocks can serve as a test of Lorentz symmetry and guide searches for dark matter.