  We propose an experimental realisation of the protocol for the counterfactual
disembodied transport of an unknown qubit -- or what we call counterportation
-- where sender and receiver, remarkably, exchange no particles. We employ
cavity quantum electrodynamics, estimating resources for beating the classical
fidelity limit -- except, unlike teleportation, no pre-shared entanglement nor
classical communication are required. Our approach is multiple orders of
magnitude more efficient in terms of physical resources than previously
proposed implementations, paving the way for a demonstration using existing
imperfect devices. Surprisingly, while such communication is intuitively
explained in terms of "interaction-free" measurement and the Zeno effect, we
show that neither is necessary, with far-reaching implications in support of an
underlying physical reality. We go on to characterise an explanatory framework
for counterportation starting from constructor theory: local wormholes.
Conversely, a counterportation experiment demonstrating the traversability of
space, by means of what is essentially a 2-qubit exchange-free quantum
computer, can point to the existence in the lab of such traversable wormholes.
