Editing Relativistic Doppler effect (section)

==Doppler effect on intensity==
{{further|Black-body radiation#Doppler effect}}

The Doppler effect (with arbitrary direction) also modifies the perceived source intensity: this can be expressed concisely by the fact that source strength divided by the cube of the frequency is a Lorentz invariant<ref group="p">{{Cite journal| volume = 79| issue = 4| pages = 1340| last1 = Johnson| first1 = Montgomery H.| last2 = Teller| first2 = Edward| title = Intensity changes in the Doppler effect| journal = Proc. Natl. Acad. Sci. USA | date = February 1982|doi=10.1073/pnas.79.4.1340 | pmid = 16593162|bibcode = 1982PNAS...79.1340J | pmc=345964| doi-access = free}}</ref><ref group=note>Here, "source strength" refers to [[spectral intensity]] in ''frequency'', i.e., power per unit solid angle and per unit frequency, expressed in watts per steradian per hertz; for spectral intensity in ''wavelength'', the cube should be replaced by a fifth power.</ref>  This implies that the total radiant intensity (summing over all frequencies) is multiplied by the fourth power of the Doppler factor for frequency.
<!-- It would be nice if someone could expand on this, for example by providing a derivation from the Lorentz transformation laws on the electric and magnetic fields applied to a plane wave. -->

As a consequence, since [[Planck's law]] describes the [[black-body radiation]] as having a spectral intensity in frequency proportional to <math>\frac{f^3}{e^\frac{hf}{kT} - 1}</math> (where <math>T</math> is the source temperature and <math>f</math> the frequency), we can draw the conclusion that ''a black body spectrum seen through a Doppler shift (with arbitrary direction) is still a black body spectrum'' with a temperature multiplied by the same Doppler factor as frequency.

This result provides one of the pieces of evidence that serves to distinguish the [[Big Bang theory]] from alternative theories proposed to explain the [[cosmological redshift]].<ref name="Wright_tired_light">{{cite web |last1=Wright |first1=Edward L. ("Ned") |title=Errors in Tired Light Cosmology |url=http://www.astro.ucla.edu/~wright/tiredlit.htm |website=Ned Wright's Cosmology Tutorial |publisher=Astronomy Department, University of California, Los Angeles |access-date=17 October 2018}}</ref>