Quote Originally Posted by mojo
It's a straight line through curved spacetime in Einstein's model, but a curved line through flat spacetime in Newton's model.
This is an interesting contradiction. Maybe both are right. Curvature (and indeed flatness) are relative. It's much like time. From your frame of reference, time is normal, it doesn't speed up or slow down from your point of view based on your velocity. It just appears to from the point of view of observers. The same will be true of spacetime curvature. As far as you're concerned, you're in a flat region, and everywhere else is curved. Meanwhile, those in the curved regions, looking at you, will say their region is flat, and yours is in fact curved.

Newton sees a curved path in flat spacetime because he's speaking from an intertial frame of reference.

Einstein sees a straight line in curved spacetime because he's speaking from a non-intertial frame of reference.

Technically, Einstein is right because there's no such thing as an inertial frame of reference... everything is in motion relative to everything else... but because the majority of that motion we observe is close to zero, or at least muc closer to zero than c, Newton's ideas hold up to observation within acceptable parameters. And because we're always in a flat region of space from our own point of view, it's fair to say that the moon is folllowing a curved path relative to us. But it's a straight path from the point of view of the moon, and what Einstein appears to have done so brilliantly is to mentally observe this neither from earth, nor from the moon, but from a third vantage point, and in doing so, he saw both are curved, and that flatness is exlcusive to your frame of reference.