Editing Special relativity (section)

=== Relativistic Doppler effect ===
{{main|Relativistic Doppler effect}}

==== Relativistic longitudinal Doppler effect====
The classical Doppler effect depends on whether the source, receiver, or both are in motion with respect to the medium. The relativistic Doppler effect is independent of any medium. Nevertheless, relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, can be derived as if it were the classical phenomenon, but modified by the addition of a [[time dilation]] term, and that is the treatment described here.<ref>{{cite journal |last1=Sher |first1=D. |title=The Relativistic Doppler Effect |journal=Journal of the Royal Astronomical Society of Canada |date=1968 |volume=62 |pages=105–111 |bibcode=1968JRASC..62..105S |url=http://adsbit.harvard.edu//full/1968JRASC..62..105S/0000105.000.html |access-date=11 October 2018}}</ref><ref name="Gill">{{cite book |last1=Gill |first1=T. P. |title=The Doppler Effect |date=1965 |publisher=Logos Press Limited |location=London |pages=6–9 |ol=5947329M }}</ref>

Assume the receiver and the source are moving ''away'' from each other with a relative speed <math>v</math> as measured by an observer on the receiver or the source (The sign convention adopted here is that <math>v</math> is ''negative'' if the receiver and the source are moving ''towards'' each other). Assume that the source is stationary in the medium. Then
<math display="block">f_{r} = \left(1 - \frac v {c_s} \right) f_s</math>
where <math>c_s</math> is the speed of sound.

For light, and with the receiver moving at relativistic speeds, clocks on the receiver are [[time dilation|time dilated]] relative to clocks at the source. The receiver will measure the received frequency to be
<math display="block">f_r = \gamma\left(1 - \beta\right) f_s = \sqrt{\frac{1 - \beta}{1 + \beta}}\,f_s.</math>
where
* <math>\beta = v/c </math>&nbsp; and
* <math>\gamma = \frac{1}{\sqrt{1 - \beta^2}}</math> is the [[Lorentz factor]].

An identical expression for relativistic Doppler shift is obtained when performing the analysis in the reference frame of the ''receiver'' with a moving source.<ref name=Feynman1977>{{cite book| title=The Feynman Lectures on Physics: Volume 1 | publisher=[[Addison-Wesley]] | location=Reading, Massachusetts |date=February 1977 | last1=Feynman | first1=Richard P. | author-link1=Richard Feynman | last2=Leighton | first2=Robert B. | author-link2=Robert B. Leighton | last3=Sands | first3=Matthew | author-link3=Matthew Sands | lccn=2010938208 | isbn=9780201021165 | pages=34–7 f |chapter-url=https://feynmanlectures.caltech.edu/I_34.html |chapter=Relativistic Effects in Radiation}}</ref><ref name=Morin2007/>

==== Transverse Doppler effect ====
[[File:Transverse Doppler effect scenarios 5.svg|thumb|300px|Figure 5–3. Transverse Doppler effect for two scenarios: (a) receiver moving in a circle around the source; (b) source moving in a circle around the receiver.]]

The transverse [[Doppler effect]] is one of the main novel predictions of the special theory of relativity.

Classically, one might expect that if source and receiver are moving transversely with respect to each other with no longitudinal component to their relative motions, that there should be no Doppler shift in the light arriving at the receiver.

Special relativity predicts otherwise. Fig.&nbsp;5-3 illustrates two common variants of this scenario. Both variants can be analyzed using simple time dilation arguments.<ref name=Morin2007/> In Fig.&nbsp;5-3a, the receiver observes light from the source as being blueshifted by a factor of {{tmath|1= \gamma }}. In Fig.&nbsp;5-3b, the light is redshifted by the same factor.