Let's say you've got a digging machine, and you want to dig a *perfectly* flat tunnel 50 miles long through the earth. Ignoring the earth's curvature, just a perfectly straight and flat surface. How do you do this?

You can't use lasers to level the surface, because they are affected by gravity. You can't use any physical object, because they bend and are also affected by gravity. According to relativity, any measuring stick you observe will also appear distorted and bent. There are NO straight rulers.

In that case, doesn't the concept of "straight" lose all meaning? Doesn't the whole idea of a coordinate system lose meaning?