Special and General Relativity Special and General Relativity Physics Help Forum Oct 1st 2016, 01:10 PM #1 Junior Member   Join Date: Oct 2016 Posts: 1 Tensor calculation in Lorentztransformations Hi, I have difficulties understanding the following relations. Given the Minkowski metric $\displaystyle \eta_{\alpha\beta}=diag(1,-1,-1,-1)$ and the line segment $\displaystyle ds^2 = dx^2+dy^2+dz^2$, then how can i see that this line segment is equal to $\displaystyle ds^2 = \eta_{\alpha\beta}dx^\alpha dx^\beta$. Further, we want the line segment to be unchanged under this metric. And i don't understand why the following equivalences hold true: $\displaystyle ds^2 = ds'^2$ if and only if $\displaystyle c^2d\tau^2 = c^2d\tau'^2$ and $\displaystyle \Lambda^{\alpha}{}_{\gamma} \Lambda^{\beta}{}_{\delta} \eta_{\alpha}{\beta} = \eta_{\gamma}{\delta} \iff \Lambda^T \eta \Lambda = \eta$ I am thankful for any kind of hints and tips and tricks. Thank you very much.  Tags calculation, lorentztransformations, tensor Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post botee Equilibrium and Elasticity 4 Feb 1st 2013 09:11 PM purakanui Special and General Relativity 1 Jan 16th 2011 06:24 PM universitytextbooks Advanced Electricity and Magnetism 0 Dec 27th 2009 07:32 PM galactus Special and General Relativity 2 Dec 26th 2008 12:20 PM kala Kinematics and Dynamics 0 Dec 4th 2008 07:01 AM 