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Area Physics for electrotechnology / Relativistic physics for electrotechnology

IEV ref 113-07-58

Symbol
d s 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaciizaiaadohadaahaa Wcbeqaaiaaikdaaaaaaa@3671@

en
squared interval, <in general theory of relativity>
space-time step
squared distance between two events that are infinitesimally close in space-time

d s 2 = μ,ν g μν d x μ d x ν

where g μν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4zamaaBaaaleaaca aH8oGaaqyVdaqabaaaaa@3749@ is a component of the metric tensor and d x μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaciizaiaadIhadaahaa WcbeqaaiaajY7aaaaaaa@3667@ , d x ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaiizaiaadIhadaahaa Wcbeqaaiaaj27aaaaaaa@3666@ are components of a quasi-infinitesimal position four-vector

Note 1 to entry: From the mathematical point of view, the squared interval is rather a “squared length of interval” or “squared space-time range” rather than a “squared interval” or even an “interval”. These two terms are also used in literature.

Note 2 to entry: The coherent SI unit of squared interval is metre squared, m2.


fr
carré d’intervalle d’espace-temps, <en relativité générale> f
intervalle carré d’espace-temps, m
carré de la distance entre deux événements infinitésimalement proches dans l’espace-temps

d s 2 = μ,ν g μν d x μ d x ν

g μν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4zamaaBaaaleaaca aH8oGaaqyVdaqabaaaaa@3749@ est une composante du tenseur métrique et d x μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaciizaiaadIhadaahaa WcbeqaaiaajY7aaaaaaa@3667@ , d x ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaiizaiaadIhadaahaa Wcbeqaaiaaj27aaaaaaa@3666@ sont les composantes d’un quadrivecteur position quasi infinitésimale

Note 1 à l’article: Du point de vue mathématique, le carré d’intervalle d’espace-temps est plutôt le “carré d’une longueur d’intervalle” ou le “carré d’une étendue d’espace-temps” qu’un “carré d’intervalle”, voire un “intervalle”. Ces deux termes sont également utilisés dans la littérature.

Note 2 à l’article: L’unité SI cohérente du carré d’intervalle d’espace-temps est le mètre carré, m2.


Publication date: 2022-06
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