Another question inspired by this one on alternative standard models.
Greg Egan's story Wang's Carpets (or the similar segment of the larger novel Diaspora) sketchily describes a universe with no analog of light, such that the inhabitants can communicate solely by touch. I have long wondered how you could construct such a universe such that atomic matter supporting chemistry could still exist, but upon reading about the higgsless theory, I think I have an idea.
Suppose we eliminate the electromagnetic field. That would initially seem to eliminate any mechanism for electric charges to interact, resulting in a very boring universe. Except, we already have the real-world example of the residual nuclear force being carried by unstable composite particles: pions. An analogous particle is available made from leptons: positronium, a bound state of an electron and positron.
As positronium is not massless, the resulting force-carrying field should produce a exponentially-decaying Yukawa potential, just like pions. And even without photons, positronium should still be unstable, decaying into a pair of neutrinos, so the positronium boson does not act as an analog to real-universe light.
Is my reasoning correct so far? And if so, what does electron structure look like in an atom with a Yukawa-potentialed electric field? Do we even still get bound states of electrons producing neutral atoms?