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If billions of neutrinos reach us from the Sun why there is no any reflection of photons emitted from Earth to be reflected from them? Is this they are not interacting at all?

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Yes, neutrinos (and other fundamental particles with no electric charge) do not interact directly with photons. They can interact indirectly, by mediation of virtual charged particles, but such interaction is very weak and in most cases negligible.

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There is one kind of photons, as seen in the table of elementary particles. Neutrinos interact only with the weak force. To interact with the matter of the earth it needs higher order Feynman diagrams, which give very small probability of interaction. So they are interacting, and specially designed experiments can record the interactions, but not at the level of giving detectable to the eye radiation.

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