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].

**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 a1610 [redshift shifts as probes of local inhomogeneities].

**Related Topics** > see gravitational redshift.

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oct 2016