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If you are talking about [1], I think nobody knows how they are possible.

https://en.wikipedia.org/wiki/Oh-My-God_particle

That article links to a much better written one that appears to discuss this exact issue: https://en.wikipedia.org/wiki/Greisen–Zatsepin–Kuzmin_limit. Thanks!

Those rays are unlikely to be photons, so EM-self interaction is not likely to stop them. The articles linked in this sub-thread all speculate/assume that the cosmic rays were protons.

They're not gamma rays :)

But a similar limit happens to protons (the GZK limit at 50 EeV, where protons and CMB photons can make a Delta+). For heavier nuclei, photodisintegration will happen at even higher energies.