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# Minkowski Metric

## Intuitive

The Minkowski metric is the correct mathematical tool that tells us how far two events are away from each other in special relativity.

The Minkowski metric encodes the experimental observation that the speed of light has the same value in all inertial frames of reference.

## Concrete

\begin{equation} \begin{gathered} (g_{\mu\nu})_{\mu,\nu}=\left( \begin{matrix} 1 & 0 & 0 & 0\cr 0 & -1 & 0 & 0\cr 0 & 0 & -1 & 0\cr 0 & 0 & 0 & -1 \end{matrix} \right) \end{gathered} \end{equation} Thus $x_0=x^0$, $x_j=-x^j$ for $1\le j\le 3$. For real vectors and tensors lowering and raising indices is made by \begin{equation} A_{\mu}^a=g_{\mu\nu}A^{\nu}_a\\ \quad F_{\mu\nu}^a=g_{\mu\alpha}g_{\nu\beta}F^{\alpha\beta}_a\\ \quad \partial_{\mu}=g_{\mu\nu}\partial^{\nu} \end{equation}

## Abstract

The motto in this section is: the higher the level of abstraction, the better.

## Why is it interesting?

advanced_tools/minkowski_metric.1522077903.txt.gz · Last modified: 2018/03/26 15:25 (external edit)

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