"You can use the metric to raise an index" is what I found in one or the other physics text book. Surely I missed some context each time, so I couldn't help to swear: 🤢 , I like the indexes where they are, what is the point of raising or lowering them.

I found the answer in Gravitation, by Misner, Thorne, Wheeler but felt the need to write it down in a way I understand it best: https://miamao.de/blog/2024-06/04.Raising_or_Lowering_an_Index.html

#physics #tensor #metric #vectorspace #dotproduct #raisinganindex #mtw