  Condensed matter systems provide alternative `vacua' exhibiting emergent
low-energy properties drastically different from those of the standard model. A
case in point is the emergent quantum electrodynamics (QED) in the
fractionalized topological magnet known as quantum spin ice, whose magnetic
monopoles set it apart from the familiar QED of the world we live in. Here, we
show that the two greatly differ in their fine-structure constant $\alpha$,
which parametrizes how strongly matter couples to light:
$\alpha_{\mathrm{QSI}}$ is more than an order of magnitude greater than
$\alpha_{\mathrm{QED}} \approx 1/137$. Furthermore, $\alpha_{\mathrm{QSI}}$,
the emergent speed of light, and all other parameters of the emergent QED, are
tunable by engineering the microscopic Hamiltonian. We find that
$\alpha_{\mathrm{QSI}}$ can be tuned all the way from zero up to what is
believed to be the \textit{strongest possible} coupling beyond which QED
confines. In view of the small size of its constrained Hilbert space, this
marks out quantum spin ice as an ideal platform for studying exotic quantum
field theories and a target for quantum simulation. The large
$\alpha_{\mathrm{QSI}}$ implies that experiments probing candidate
condensed-matter realizations of quantum spin ice should expect to observe
phenomena arising due to strong interactions.
