Ennio de Giorgi: Difference between revisions

Revision as of 15:41, 7 August 2013

The four-frequency of a photon is defined by

N^{a} = (ν, ν n)

where $ν$ is the photon's frequency and $n$ is a unit vector in the direction of the photon's motion. The four-frequency is always a future-pointing and null vector. An observer moving with four-velocity $V$ will observe a frequency

\frac{1}{c} η (N^{a}, V)

Where $η$ is the Minkowski inner-product (+---)

Closely related to the four-frequency is the wave four-vector defined by

K^{a} = (\frac{ω}{c}, k)

where $ω = 2 π ν$ , $c$ is the speed of light and $k = \frac{2 π}{λ} n$ and $λ$ is the wavelength of the photon. The wave four-vector is more often used in practice than the four-frequency, but the two vectors are related (using $c = ν λ$ ) by

K^{a} = \frac{2 π}{c} N^{a}

References

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+The '''four-frequency''' of a [[photon]] is defined by
+:<math>N^a = \left( \nu, \nu \mathbf{n} \right)</math>
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+where <math>\nu</math> is the photon's [[frequency]] and <math>\mathbf{n}</math> is a unit vector in the direction of the photon's motion. The four-frequency is always a future-pointing and [[Null vector (Minkowski space)|null vector]]. An observer moving with [[four-velocity]] <math>V</math> will observe a frequency
+:<math> \tfrac{1}{c}\eta(N^a,V) </math>
+Where <math>\eta</math> is the [[Minkowski Space#The Minkowski inner product|Minkowski inner-product]] (+---)
+Closely related to the four-frequency is the '''wave four-vector''' defined by
+:<math>K^a=\left(\frac{\omega}{c}, \mathbf{k}\right)</math>
+where <math>\omega=2 \pi \nu</math>, <math>c</math> is the speed of light and <math>\mathbf{k}=\frac{2 \pi}{\lambda}\mathbf{n}</math> and <math>\lambda</math> is the [[wavelength]] of the photon. The wave four-vector is more often used in practice than the four-frequency, but the two vectors are related (using <math>c=\nu \lambda</math>) by
+:<math>K^a=\frac{2 \pi}{c}N^a</math>
+==References==
+<references/>
+*{{Cite book |title=Special Relativity |last=Woodhouse |first=N.M.J. |authorlink= |coauthors= |year=2003 |publisher=Springer-Verlag |location=London|isbn=1-85233-426-6 |pages= }}
+{{DEFAULTSORT:Four-Frequency}}
+[[Category:Minkowski spacetime]]
+{{Relativity-stub}}

Ennio de Giorgi: Difference between revisions

Revision as of 15:41, 7 August 2013

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