ਲੌਰੰਟਜ਼ ਰੂਪਾਂਤ੍ਰਨ ਲਈ ਸਰੋਤ ਵੇਖੋ

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[[Image:Standard conf.png|right|thumb|250px|ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ (ਪਰਿਵਰਤਨ) ਲਈ ਕੋ-ਆਰਡੀਨੇਟ (ਨਿਰਦੇਸ਼ਾਂਕ) ਸਿਸਟਮਾਂ ਦੀ ਸਟੈਂਡਰਡ ਬ]]

ਗਰੁੱਪ O(3,1) ਦੇ ਐਲੀਮੈਂਟਾਂ ਨੂੰ (ਹੋਮੋਜੀਨੀਅਸ) ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਕਿਹਾ ਜਾਂਦਾ ਹੈ। ਹੋਰ ਜਿਆਦਾ ਭੌਤਿਕੀ ਮੋੜ ਨਾਲ ਹੋਰ ਤਰੀਕੇ ਖੋਜਣ ਲਈ ਦੇਖੋ [[ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਦੀਆਂ ਡੈਰੀਵੇਸ਼ਨਾਂ]] । 

[[ਪੋਆਇਨਕੇਅਰ ਗਰੁੱਪ]] ਅੰਤਰਾਲ ਨੂੰ ਸੁਰੱਖਿਅਤ ਰੱਖਣ ਵਾਲੇ ਸਾਰੇ ਪਰਿਵਰਤਨਾਂ ਦਾ ਗਰੁੱਪ ਹੈ। ਅੰਤਰਾਲ (ਇੰਟਰਵਲ) ਨੂੰ 4-ਅਯਾਮਾਂ ਵਿੱਚ [[ਟਰਾਂਸਲੇਸ਼ਨ ਗਰੁੱਪ]] ਰਾਹੀਂ ਸੁਰੱਖਿਅਤ ਹੁੰਦਾ ਅਸਾਨੀ ਨਾਲ ਦੇਖਿਆ ਜਾ ਸਕਦਾ ਹੈ। ਹੋਰ ਪਰਿਵਰਤਨ ਉਹ ਹੁੰਦੇ ਹਨ ਜੋ ਅੰਤਰਾਲ ਨੂੰ ਸੁਰੱਖਿਅਤ ਰੱਖਦੇ ਹਨ ਅਤੇ ਉਰਿਜਿਨ ਨੂੰ ਫਿਕਸ ਰੱਖਦੇ ਹਨ । ਮਿੰਕੋਵਸਕੀ ਮੀਟ੍ਰਿਕ ਨਾਲ ਜੁੜੇ ਬਾਇ[[ਲੀਨੀਅਰ ਅਕਾਰ]] ਦੇ ਦਿੱਤੇ ਹੋਣ ਤੇ, ਕਲਾਸੀਕਲ ਗਰੁੱਪਾਂ ਦੀ ਥਿਊਰੀ (ਖਾਸ ਕਰਕੇ ਪਰਿਭਾਸ਼ਾ) ਤੋਂ ਢੁਕਵੇਂ ਗਰੁੱਪ ਦਾ ਪਤਾ ਚਲਦਾ ਹੈ। ਲਿੰਕ ਕੀਤੇ ਆਰਟੀਕਲ ਵਿੱਚ, ਮੈਟ੍ਰਿਕਸ  Φ ਦੇ ਨਾਲ η (ਇਸਦੀ ਮੈਟ੍ਰਿਕਸ ਪ੍ਰਸਤੁਤੀ ਵਿੱਚ) ਨੂੰ ਪਛਾਣਨਾ ਚਾਹੀਦਾ ਹੈ। 

==ਗਣਿਤ==

ਸਰਲਤਮ ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਵਿੱਚੋਂ ਇੱਕ ਲੌਰੰਟਜ਼ ਬੂਸਟ ਹੈ। ਇਸ਼ਾਰੇ ਵਜੋਂ, x-ਦਿਸ਼ਾ ਵਿੱਚ ਇੱਕ ਬੂਸਟ ਇਸਤਰਾਂ ਪ੍ਰਾਪਤ ਕੀਤੀ ਜਾਂਦੀ ਹੈ; 
:<math>
\begin{bmatrix}
U'_0 \\ U'_1 \\ U'_2 \\ U'_3
\end{bmatrix}
=
\begin{bmatrix}
\gamma&-\beta \gamma&0&0\\
-\beta \gamma&\gamma&0&0\\
0&0&1&0\\
0&0&0&1\\
\end{bmatrix}
\begin{bmatrix}
U_0 \\ U_1 \\ U_2 \\ U_3
\end{bmatrix}, 
</math>

ਜਿੱਥੇ

:<math>\gamma = { 1 \over \sqrt{1 - {v^2 \over c^2}} }</math>

ਨੂੰ ਇੱਕ ਲੌਰੰਟਜ਼ ਫੈਕਟਰ ਕਿਹਾ ਜਾਂਦਾ ਹੈ, ਅਤੇ

:<math>\beta = { v \over c} \,.</math> ਹੁੰਦਾ ਹੈ|
 
ਹੋਰ ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਸ਼ੁੱਧ ਰੋਟੇਸ਼ਨਲ ਹੁੰਦੀਆਂ ਹਨ, ਅਤੇ ਇਸ ਕਰਕੇ O(3,1) ਦੇ ਸਬਗਰੁੱਪ SO(3) ਦੇ [[ਐਲੀਮੈਂਟ]] ਵੀ । ਇੱਕ ਸਧਾਰਣ [[ਹੋਮੋਜੀਨੀਅਸ]] ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨ ਸ਼ੁੱਧ ਬੂਸਟ ਅਤੇ ਸ਼ੁੱਧ ਰੋਟੇਸ਼ਨ ਦਾ ਗੁਣਨਫਲ ਹੁੰਦੀ ਹੈ। ਇੱਕ ਇਨਹੋਮੋਜੀਨੀਅਸ ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨ ਸਪੇਸ ਅਤੇ ਟਾਈਮ ਵਿੱਚ ਇੱਕ ਬਦਲਾਓ ਰਾਹੀਂ ਹੋਈ ਹੋਮੋਜੀਨੀਅਸ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨ ਹੁੰਦੀ ਹੈ। ਵਿਸ਼ੇਸ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ (ਪਰਿਵਰਤਨ) ਉਹ ਹੁੰਦੀਆਂ ਹਨ ਜੋ ਸਪੇਸ ਨਿਰਦੇਸ਼ਾਂਕਾਂ ਅਤੇ ਟਾਈਮ ਨਿਰਦੇਸ਼ਾਂਕਾਂ ਨੂੰ ਕ੍ਰਮਵਾਰ ਉਲਟਾ ਦਿੰਦੇ ਹਨ, ਜਾਂ ਦੋਵਾਂ ਨੂੰ (PT) । 

ਮਿੰਕੋਵਸਕੀ ਸਪੇਸ ਵਿੱਚ ਸਾਰੇ ਦੇ ਸਾਰੇ ਚਾਰੇ [[ਵੈਕਟਰ]] ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਅਧੀਨ ਉਸੇ ਫਾਰਮੂਲੇ ਮੁਤਾਬਿਕ ਬਦਲ ਜਾਂਦੇ ਹਨ । ਮਿੰਕੋਵਸਕੀ ਡਾਇਗਰਾਮ ਲੌਰੰਟਜ਼ ਟਰਾਂਸਫੋਰਮੇਸ਼ਨਾਂ ਨੂੰ ਸਮਝਾਉਂਦਾ ਹੈ।

== ਫੁਟਨੋਟਸ ==

{{reflist|group=nb}}

== ਨੋਟਸ ==

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== ਹਵਾਲੇ ==

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== ਹੋਰ ਲਿਖਤਾਂ ==
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 |df= 
}}
*{{Citation |first1 = Stephen T. |last1 = Thornton |first2 = Jerry B. |last2 = Marion |title =  Classical dynamics of particles and systems |edition = 5th |place = Belmont, [CA.] |publisher = Brooks/Cole |year = 2004 |pages = 546–579 |isbn = 0-534-40896-6}}
*{{Citation |first = Woldemar |last = Voigt |author-link = Woldemar Voigt |title = Über das Doppler'sche princip |journal = Nachrichten von der Königlicher Gesellschaft den Wissenschaft zu Göttingen |volume = 2 |pages =  41–51 |year = 1887}}

== ਬਾਹਰੀ ਲਿੰਕ ==
{{Wikisource portal|ਰਿਲੇਟੀਵਿਟੀ}}
{{wikibooks|ਸਪੈਸ਼ਲ ਰਿਲੇਟੀਵਿਟੀ}}
*[http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf Derivation of the Lorentz transformations]. This web page contains a more detailed derivation of the Lorentz transformation with special emphasis on group properties.
*[http://casa.colorado.edu/~ajsh/sr/paradox.html The Paradox of Special Relativity] {{Webarchive|url=https://web.archive.org/web/20061206092114/http://casa.colorado.edu/~ajsh/sr/paradox.html |date=2006-12-06 }}.  This webpage poses a problem, the solution of which is the Lorentz transformation, which is presented graphically in its next page.
*[http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html Relativity] {{Webarchive|url=https://web.archive.org/web/20110829032009/http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html |date=2011-08-29 }} – a chapter from an online textbook
*[http://www.adamauton.com/warp/ Warp Special Relativity Simulator]. A computer program demonstrating the Lorentz transformations on everyday objects.
*{{YouTube|C2VMO7pcWhg|Animation clip}} visualizing the Lorentz transformation.
*[http://math.ucr.edu/~jdp/Relativity/Lorentz_Frames.html Lorentz Frames Animated] ''from John de Pillis.''  Online Flash animations of Galilean and Lorentz frames, various paradoxes, EM wave phenomena, ''etc''.

{{Relativity}}

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