I am still at the stage of trying to assimilate contravariant and covariant tensors, so my question probably has a simpler answer than I realize.(adsbygoogle = window.adsbygoogle || []).push({});

A covariant tensor is like a gradient, as its units increase when the coordinate units do. A contravariant tensor's components decrease when the coordinates increase. In other words, covariant is inversely proportional to length; contravariant, proportional.

This means that if I use the metric to transform a contravariant vector to a covariant tensor, I have changed the units by a factor of length^2. Yet, the metric is dimensionless, at least the Minkowski one is.

What have I misunderstood? I suspect the units don't change, but then my idea of what makes a tensor co- or contravariant is all wrong.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Units if conversion between covariant/contravariant tensors

Loading...

Similar Threads for Units conversion between |
---|

I Difference between vectors and one-forms |

I Difference between diffeomorphism and homeomorphism |

I Mapping between two spaces |

**Physics Forums | Science Articles, Homework Help, Discussion**