Queries, comments, suggestions? Please contact us.



Area Physics for electrotechnology / Relativistic physics for electrotechnology

IEV ref 113-07-61

en
flat space-time
space-time in which the metric tensor for real components x _ _ :=( x 1 , x 2 , x 3 , x 4 =ct) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaWaaWqaaeaacaWG4baaai aacQdacqGH9aqpcaGGOaGaamiEamaaBaaaleaacaaIXaaabeaakiaa cYcacaWG4bWaaSbaaSqaaiaaikdaaeqaaOGaaiilaiaadIhadaWgaa WcbaGaaG4maaqabaGccaGGSaGaamiEamaaBaaaleaacaaI0aaabeaa kiabg2da9iaadogacaWG0bGaaiykaaaa@43E9@ can be expressed as a diagonal one, each diagonal component having one of the values 1 or −1

EXAMPLE Metric tensor with g μ λ =0 for μλ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaKiVdiabgcMi5kaajU 7aaaa@3763@ , g 11 = g 22 = g 33 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaam4zamaaBaaaleaaca aIXaGaaGymaaqabaGccqGH9aqpcaWGNbWaaSbaaSqaaiaaikdacaaI Yaaabeaakiabg2da9iaadEgadaWgaaWcbaGaaG4maiaaiodaaeqaaO Gaeyypa0JaaGymaaaa@3EA4@ , and g 44 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaam4zamaaBaaaleaaca aI0aGaaGinaaqabaGccqGH9aqpcqGHsislcaaIXaaaaa@3855@ describes a flat pseudo-Euclidean space-time. 3D subspace of it for μ, λ=13 is a flat Euclidean space.

Note 1 to entry: Special theory of relativity is based on the space-time described in the example.


fr
espace-temps plat, m
espace-temps dans lequel le tenseur métrique pour des composantes réelles x _ _ :=( x 1 , x 2 , x 3 , x 4 =ct) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaWaaWqaaeaacaWG4baaai aacQdacqGH9aqpcaGGOaGaamiEamaaBaaaleaacaaIXaaabeaakiaa cYcacaWG4bWaaSbaaSqaaiaaikdaaeqaaOGaaiilaiaadIhadaWgaa WcbaGaaG4maaqabaGccaGGSaGaamiEamaaBaaaleaacaaI0aaabeaa kiabg2da9iaadogacaWG0bGaaiykaaaa@43E9@ peut être exprimé comme un tenseur diagonal dont chaque composante diagonale prend une des valeurs 1 ou −1

EXEMPLE  Un tenseur métrique g μ λ =0 pour μλ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaaKiVdiabgcMi5kaajU 7aaaa@3763@ , g 11 = g 22 = g 33 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaam4zamaaBaaaleaaca aIXaGaaGymaaqabaGccqGH9aqpcaWGNbWaaSbaaSqaaiaaikdacaaI Yaaabeaakiabg2da9iaadEgadaWgaaWcbaGaaG4maiaaiodaaeqaaO Gaeyypa0JaaGymaaaa@3EA4@ , et g 44 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacmabaaGcbaGaam4zamaaBaaaleaaca aI0aGaaGinaaqabaGccqGH9aqpcqGHsislcaaIXaaaaa@3855@ décrit un espace-temps pseudo-euclidien plat. Un sous-espace 3D de cet espace-temps pour μ, λ=13 est un espace euclidien plat.

Note 1 à l’article: La relativité restreinte est basée sur l’espace-temps décrit en exemple.


Publication date: 2022-06
Copyright © IEC 2022. All Rights Reserved.