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*:=
(*λ*_{2}–*λ*_{1})/*λ*_{1} = *ω*_{1}/*ω*_{2 }– 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].

@ __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–*β*^{2})^{1/2} *T* .

* __Transversal__: The period changes
according to *T '* = *γ* *T*.

* __In general__: The period and wavelength change according to

*T '* = (1+*β*cos*θ*)/(1–*β*^{2})
*T* , *λ* =
[(1+*β*cos*θ*)/(1–*β*^{2})^{1/2}] *λ*_{0} .

@ __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];
> 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].

@ __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.

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