Yes. It's not a settled question.
I'm not a physicist, but... as to whether neutrinos and photons have an infinite life, I don't think so. Like everything else, they were set in motion because of the energy generated by the Big Bang, and they continue to consume energy as they zip around. Seems like they'd eventually run out of energy just like everything else. I don't think they're exempt from the 2nd Law of Thermodynamics.
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