Editing Photon (section)

=== Relativistic energy and momentum ===
{{See also|Photon energy|Special relativity}}
[[File:Light cone colour.svg|thumb|right|The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency ([[radians per second|rad⋅s<sup>−1</sup>]]) and the "space" axis represents the angular wavenumber (rad⋅m<sup>−1</sup>). Green and indigo represent left and right<!-- I do not know a "correct" assignment --> polarization.]]
In empty space, the photon moves at {{mvar|c}} (the [[speed of light]]) and its [[energy]] and [[momentum]] are related by {{math|1=''E'' = ''pc''}}, where {{mvar|p}} is the [[magnitude (mathematics)|magnitude]] of the momentum vector {{math|'''''p'''''}}. This derives from the following relativistic relation, with {{math|1=''m'' = 0}}:<ref>See {{harvnb|Alonso|Finn|1968|loc=Section 1.6}}.</ref>
: <math>E^{2} = p^{2} c^{2} + m^{2} c^{4} ~.</math>

The energy and momentum of a photon depend only on its [[frequency]] (<math>\nu</math>) or inversely, its [[wavelength]] ({{mvar|λ}}):
: <math>E = \hbar \, \omega = h \nu = \frac{\, h\,c \,}{\lambda}</math>
: <math>\boldsymbol{p} = \hbar \boldsymbol{k} ~,</math>
where '''{{mvar|k}}''' is the [[wave vector]], where
* {{math| ''k'' ≡ {{abs|'''''k'''''}} {{=}} {{sfrac| 2''π'' |''λ''}} }} &emsp; is the [[wave number]], and
* {{math| ''ω'' ≡ 2 ''πν''}} &emsp; is the [[angular frequency]], and
* {{math| ''ħ'' ≡ {{sfrac|''h''| 2''π'' }} }} &emsp; is the [[reduced Planck constant]].<ref>{{cite web |first=Davison E. |last=Soper |title=Electromagnetic radiation is made of photons |department=Institute of Theoretical Science |publisher=[[University of Oregon]] |url=http://pages.uoregon.edu/soper/Light/photons.html |access-date=2024-03-21 |archive-date=2023-04-08 |archive-url=https://web.archive.org/web/20230408082934/https://pages.uoregon.edu/soper/Light/photons.html |url-status=live }}</ref>

Since <math>\boldsymbol{p}</math> points in the direction of the photon's propagation, the magnitude of its momentum is
: <math>p \equiv \left| \boldsymbol{p} \right| = \hbar k = \frac{\, h \nu \,}{c} = \frac{\, h \,}{\lambda} ~.</math>