Relativistic Doppler effect

The change in observed frequency or wavelength caused by relative motion at speeds where special relativity matters. It combines classical Doppler shifting with time dilation and the relativity of simultaneity.

Lorentz transformation: The equations relating space and time coordinates measured in inertial frames moving at constant relative velocity. Transforming the wave’s phase between frames yields the relativistic frequency shift.
Special relativity: The theory of space, time, and motion in inertial frames, with invariant light speed and Lorentz symmetry. The effect is a direct consequence of special relativity applied to light and moving clocks.
Relativistic jet: A narrow outflow of plasma launched from an active galactic nucleus, microquasar, or other energetic source at relativistic speed. Doppler shifting makes radiation from a jet pointed toward Earth appear unusually bright and energetic.
Classical Doppler effect: The frequency change predicted by classical wave physics for relative motion between source and observer. It approximates the relativistic result at speeds much smaller than the speed of light.
Time dilation: The relativistic slowing of elapsed time measured by a moving clock relative to a clock at rest in another inertial frame. The moving source’s emission rate changes in the observer’s frame, contributing to the shift.
Doppler effect: The change in observed wave frequency caused by relative motion between a source and an observer. The relativistic effect extends this general phenomenon to speeds where classical formulas fail.
Cosmic microwave background dipole: The large-scale temperature anisotropy in the cosmic microwave background caused mainly by the Solar System’s motion relative to it. Its hotter and colder directions are a measurable Doppler signature of our motion.
Transverse Doppler effect: The frequency shift for relative motion perpendicular to the line of sight, arising in relativity from time dilation. It isolates a shift with no classical counterpart for light when source and observer are at closest approach.
Relativistic beaming: The concentration of radiation into a narrow forward direction for a source moving at relativistic speed. At nonzero viewing angles, aberration changes the shift beyond the purely longitudinal formula.
Proper time: The time interval measured by a clock traveling along a particular path through spacetime. A moving source emits cycles according to its own proper time, not the observer’s coordinate time.

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