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The transverse Doppler effect (TDE) may refer to (a) the nominal blueshift predicted by special relativity that occurs when the emitter and receiver are at their points of closest approach; or (b) the nominal redshift predicted by special relativity when the receiver sees the emitter as being at its closest approach. [6]
Special relativity therefore predicts that the center of gravity of Doppler-shifted emission lines emitted by a source moving towards an observer and its reflected image moving away from the observer will be offset from unshifted emission lines by an amount equal to the transverse Doppler effect. [11] [12]
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
Only a single jet is visible in M87. Two jets are visible in 3C 31.. In physics, relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light.
Both special and general relativity require that the receiver should observe no Doppler shift. Surprisingly, this obvious result has been disputed, with some claiming that emitter and absorber may be considered to be in uniform relative motion, and that a special relativity requires a transverse Doppler shift to be observed.
The effects of special relativity can phenomenologically be derived from the following three fundamental experiments: [8] Michelson–Morley experiment, by which the dependence of the speed of light on the direction of the measuring device can be tested. It establishes the relation between longitudinal and transverse lengths of moving bodies.
The link between f_o and f_s in the section "Transverse Doppler effect" (eq. 2 of that section) states exactly this. So eq. 2 of transverse doppler section should reduce to eq. 4 from top if you take theta = pi/2. But it does not, as eq.3 of transverse doppler section states f_0 = f_s / gamma, not *times* gamma.
This is the equation for doppler shift in the case where the velocity between the emitter and observer is along the x-axis. The second special case is that where the relative velocity is perpendicular to the x-axis, and thus θ = π/2, and cos θ = 0, which gives: ′ =