In his popular book on relativity theory, Einstein says that distance is just what measuring rods measure. I am having a hard time making sense of this in Einstein’s operationalist setting.
Either Einstein is talking of real measuring rods or idealized ones. If real ones, then it’s false. If I move a measuring rod from one location to another, its length changes, not for relativistic reasons, but simply because the acceleration causes some shock to it, resulting in a distortion in its shape and dimensions, or because of chemical changes as the rod ages. But if he’s talking about idealized rods, then I think we cannot specify the relevant kind of idealization without making circular use of dimensions—relevantly idealized rods are ones that don’t change their dimensions in the relevant circumstances.
If one drops Einstein’s operationalism, one can make perfect sense of what he says. We can say that distance is the most natural of the quantities that are reliably and to a high degree of approximation measured by measuring rods. But this depends on a metaphysics of naturalness: it’s not a purely operational definition.
