ds2=∑μ,νgμνdxμdxν
where gμν is a component of the metric tensor and dxμ, dxν 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.
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