Let object A move at relativistic velocity relative to a frame O. In 4D space-time (Minkowski diagram) the space view of O at any given moment of its own time is a space-like hypersurface (hyperplane, if O is inertial). What O observes of A at any time is the cross-section of A's world-tube by O's corresponding constant-time hypersurface.
If so, are there any formal objections to saying that "moving objects are observed in space-time cross-section"?
Note: By "observed" I mean "described in measurable coordinates", not optical observation by a human observer or a camera.
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