  The recently proposed ER=EPR correspondence postulates the existence of
wormholes (Einstein-Rosen bridges) between entangled states (such as EPR
pairs). Entanglement is famously known to be unobservable in quantum mechanics,
in that there exists no observable (or, equivalently, projector) that can
accurately pick out whether a generic state is entangled. Many features of the
geometry of spacetime, however, are observables, so one might worry that the
presence or absence of a wormhole could identify an entangled state in ER=EPR,
violating quantum mechanics, specifically, the property of state-independence
of observables. In this note, we establish that this cannot occur: there is no
measurement in general relativity that unambiguously detects the presence of a
generic wormhole geometry. This statement is the ER=EPR dual of the
undetectability of entanglement.
