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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?

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    $\begingroup$ Positronium is held together electromagnetically, i.e. by virtual photons. $\endgroup$ – G. Smith Jul 16 at 16:42
  • $\begingroup$ @G.Smith ... good point. I feel dumb now. $\endgroup$ – Logan R. Kearsley Jul 16 at 16:53

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