 This is a form of indeterminism first highlighted by Earman and Norton (1987) as an interpretive philosophical difficulty for realism about GTR’s description of the world, especially the point manifold M. They showed that realism about the manifold as a part of the furniture of the universe (which they called “manifold substantivalism”) commits us to an automatic indeterminism in GTR (as described above), and they argued that this is unacceptable. (See  the hole argument  and Hoefer (1996) for one response on behalf of the space-time realist, and discussion of other responses.) For now, we will simply note that this indeterminism, unlike most others we are discussing in this section, is empirically undetectable: our two models &lt;M, g, T&gt; and the shifted model &lt;M, h*g, h*T&gt; are empirically indistinguishable.