Update 12.temporary_ins/44.relativity/40.n4/10.special-relativity/07.coherence/textbook.fr.md

12.temporary_ins/44.relativity/40.n4/10.special-relativity/07.coherence/textbook.fr.md

@@ -31,6 +31,36 @@ lessons:
 
 Invariant ou intervalle
 
+$`\begin{align}
+ds^2&=c^2 dt^2- dx^2- dy^2- dz^2\\
+&=c^2 dt'^2- dx'^2- dy'^2- dz'^2\\
+\end{align}`$
+
+$`x^0=ct\;;\;x^1=x\;;\;x^2=y\;;\;x^3=z`$
+
+$`\begin{align}
+ds^2&=(dx^0)^2 -(dx^1)^2 -(dx^2)^2 -(dx^3)^2\\
+&=(dx^0')^2 -(dx^1')^2 -(dx^2')^2 -(dx^3')^2
+\end{align}`$
+
+$`\begin{align}
+ds^2&=(dx^0)^2 -(dx^1)^2 -(dx^2)^2 -(dx^3)^2\\
+\\
+&=g_{ab}dx^a dx^b
+\end{align}`$
+
+tensuer métrique associé aux coordonnées $`(x^0\;,\;x^1\;,\;x^2=;,\;x^3`$
+
+$`g_{ab}`$
+$`\;=\begin{pmatrix}
+1 & 0 & 0 & 0 \\
+0 & -1 & 0 & 0 \\
+0 & 0 & -1 & 0 \\
+0 & 0 & 0 & -1
+\end{pmatrix}`$
+
+
+
 
 
 *Le vocabulaire fondamental de la relativité restreinte*