Hi everyone! I am trying to self- study GR and I am (very slowly) working through Schutz at the moment ( not the clearest at times for a " first course" text). Anyway I have noticed that several times when working with components of physical variables e.g. momentum/ energy, the 'up' index in say p alpha is deliberately 'lowered' in the workings to get p alpha 'down'. for example in - deriving the Consevation law on geodesics so that we can spot if the metric is independent of any x component or - in Shutz page 170 where we work out the scalar product - p.p to show that energy is conserved in a stationary gravity field. i can follow the lines and the equations BUT I don't understand why we keep lowering the index??? Is this something to do with physical variables or with 1-forms?? The answer is probably something very simple but I'm asking anyway Thanks!!!