In relativity, space and time are just different directions in spacetime with a single pseudometric determining separation between events. With this understanding, the time/space distance metaphor is more literal than most people think.
The correspondence isn’t exact since it’s a pseudometric and not a standard metric, and everyday units of time correspond to much greater than everyday units of distance, but it’s still more than just a metaphor.
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).
In relativity, space and time are just different directions in spacetime with a single pseudometric determining separation between events. With this understanding, the time/space distance metaphor is more literal than most people think.
The correspondence isn’t exact since it’s a pseudometric and not a standard metric, and everyday units of time correspond to much greater than everyday units of distance, but it’s still more than just a metaphor.
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).