A more accurate spacetime diagram would only use a preferred geodesic as any one of the axises on the diagram/graph.
That would give a picture that is much more revealing of the actual fundemantal physical nature of timeless spacetime.
It would likewise mean that no massive objects and thus also no observers could travel on or parallel to any of the axises.
In fact, in the most accurate diagram, any object with mass would presumably have to have a non-straight worldline, such that shortest path between any two points is a straight line (straight on the graph), meaning all straight lines on the graph correspond to preferred geodesics.
Granted, the paths of massive objects could be approximately represented as as a line with width with the understanding that the actual path of the photons and massless waves making up the object are themselves zigzaging (i.e. non-straight) lines.
The short simple point is that even when we are mapping special relativity in flat spacetime, non-preferred geodesics don't exist, and the flaw of the diagrams is that they use a non-preferred geodesic as the t axis.
A non-preferred geodesic instead needs to be represented as a zigzag.
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