I mean “spacetime” doesn’t necessarily require you to have a certain view of the metric, just that they need to be inseparable/mixed/importantly viewed as a single thing in some way.
As another example: electromagnetism (because in special relativity, a moving frame can see an electric field as a magnetic field and vice versa, but they’ll still agree upon the net effect of the fields), and the curvature of spacetime uses the same math as the curvature of regular surfaces like my water bottle (though is, admittedly, much less intuitively a curvature).
I mean “spacetime” doesn’t necessarily require you to have a certain view of the metric, just that they need to be inseparable/mixed/importantly viewed as a single thing in some way.
As another example: electromagnetism (because in special relativity, a moving frame can see an electric field as a magnetic field and vice versa, but they’ll still agree upon the net effect of the fields), and the curvature of spacetime uses the same math as the curvature of regular surfaces like my water bottle (though is, admittedly, much less intuitively a curvature).