Doppler Effect and Other Causes of Frequency Shift

Doppler Effect / Shift in General > s.a. sound; wave phenomena; Doppler Lensing.
* Idea: The change in frequency of a wave when the source is moving with respect to the observer.
* Redshift: Can be used as a quantitative measure of frequency/wavelength shift; It is defined as the quantity z:= (λ2λ1) / λ1 = ω1 / ω2 − 1.
@ General references: Seddon & Bearpark Sci(03)nov [inverse effect]; Barreiro et al PRL(06)qp [rotational, from light angular momentum]; Drake & Purvis AJP(14)jan [from the postulates of relativity]; Lewis AusP-a1605 [unified view]; Nolte PT(20)mar [history].
@ Experiments: Bernal & Bilbao AJP(07)mar [optical, using rotating mirrors]; Friedman a0912 [test, accelerated source]; Giuliani EJP(13), EJP(14) [in rotating systems].
> Online resources: see Wikipedia page.

Relativistic Doppler Shift
* Longitudinal: For source and observer moving at speed v with respect to each other,

T ' = (1−β2)1/2 T .

* Transversal: The period changes according to T ' = γ T.
* In general: The period and wavelength change according to

T ' = (1+βcosθ) / (1−β2) T ,    λ = [(1+βcosθ) / (1−β2)1/2] λ0 .

@ General references: Bertotti GRG(98), MPLA(98) [moving medium]; Mashhoon PLA(02)gq [helicity-rotation effect]; Ruggiero et al IJMPD(06)gq [and light bending in general relativity]; Giuliani EJP(15)-a1502 [for photons, theory and experiment].
@ Special cases and applications: Carrera & Giulini CQG(06)gq [spacecraft tracking, in FLRW spacetime]; Radosz et al PLA(09)-a0901 [Schwarzschild spacetime, factorization into relativistic, kinematical and gravitational contributions]; Bunney & Gradoni a1912 [in curved spacetime, coupling with gravitational redshift]; > s.a. Mössbauer Rotor Experiment.

Cosmological Redhift > s.a. cosmological expansion and acceleration, gravity tests [redshift surveys] and models [interpretation].
* Idea: Due to the expansion of the universe; For z = 1 the fractional lookback time is about 65%; 2009, The highest cosmological redshift for a single object is z = 8.26 ± 0.08 for a gamma-ray burst detected by the Swift orbiter; The cosmic microwave background has z ≈ 1100.
@ General references: Oliveira & Hartnett FPL(06) [and time]; Kaiser MNRAS(13)-a1303 [effects for galaxies in clusters]; Hasse & Perlick a1904 [in Finsler spacetimes].
@ Interpretation: Bedran AJP(02)apr [vs Doppler shift]; Braeck & Elgarøy GRG(12)-a1206; Li CQG(14) [as Doppler shift].
@ For specific metrics: Nwankwo et al JCAP(11) [Szekeres inhomogeneous cosmological models]; > s.a. acceleration of the cosmological expansion.
@ Measurement: Messenger et al PRX(14) [from gravitational-wave signatures of merging neutron stars]; Ferreras & Trujillo ApJ(16)-a1605 [bounds on wavelength dependence of the redshift]; Calcino & Davis JCAP(17)-a1610 [redshift shifts as probes of local inhomogeneities].

Related Topics > see gravitational redshift; Thought Experiments.

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