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Units if conversion between covariant/contravariant tensors

  1. Nov 30, 2015 #1


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    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.

    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.
  2. jcsd
  3. Dec 5, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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