  Observable signatures of the quantum nature of gravity at low energies have
recently emerged as a promising new research field. One prominent avenue is to
test for gravitationally induced entanglement between two mesoscopic masses
prepared in spatial superposition. Here we analyze such proposals and what one
can infer from them about the quantum nature of gravity, as well as the
electromagnetic analogues of such tests. We show that it is not possible to
draw conclusions about mediators: even within relativistic physics,
entanglement generation can equally be described in terms of mediators or in
terms of non-local processes -- relativity does not dictate a local channel.
Such indirect tests therefore have limited ability to probe the nature of the
process establishing the entanglement as their interpretation is inherently
ambiguous. We also show that cosmological observations already demonstrate some
aspects of quantization that these proposals aim to test. Nevertheless, the
proposed experiments would probe how gravity is sourced by spatial
superpositions of matter, an untested new regime of quantum physics.
