Plainly, the coordinate components E [ X ] _ { \ theta \ theta }, \, E [ X ] _ { \ phi \ phi } computed above don't even scale the right way, so they clearly cannot correspond to what an observer will measure even approximately . ( By coincidence, the Newtonian tidal tensor components agree exactly with the relativistic tidal tensor components we wrote out above .)
22.
Plainly, the coordinate components E [ X ] _ { \ theta \ theta }, \, E [ X ] _ { \ phi \ phi } computed above don't even scale the right way, so they clearly cannot correspond to what an observer will measure even approximately . ( By coincidence, the Newtonian tidal tensor components agree exactly with the relativistic tidal tensor components we wrote out above .)
23.
All the books and articles I've found have assumed the fact quoted in the article ( https : / / en . wikipedia . org / wiki / Yang % E2 % 80 % 93Mills _ theory # Mathematical _ overview ) that " the transition between " upper " ( " contravariant " ) and " lower " ( " covariant " ) vector or tensor components is trivial for a indices " but none of the primary sources I've found explicitly state it and the fact is provided in the article without citation.
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