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I am having trouble with coordinates in curved space time lately, allow me to demonstrate my issue.

Take the metric of flat space in spherical coordinates for example, a diagonal metric with values 1,r^2 and r^2sinΘ. It appears to me that only when we know that the Θ and ψ variables are dimensionless, can we transform this back into the usual flat spacetime in cartesian coordinates.

However what if I made an abitrary transformation of coordinates and did not reveal to you the dimensions of the various coordinates, how would one know whether the metric is flat or not?

The problem seems to be that the cartesian system of coordinates is held on a pedestal, and I think this should not be.

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# Coordinates in general relativity

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