If a sun is giving off photons in every direction in space, does that not mean that all of empty space is full of photons? I know photons have no mass but that still means it is not a perfect vacuum right?
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It's correct that open space isn't a perfect vacuum because you can always find at least a few hydrogen atoms floating around. If you're still in the solar system you'll get whatever type of particles the sum is throwing off too, normally different types of radiation. I'm not sure if the presence of photons technically negates a vacuum though. My guess is no, you could in theory create a vacuum in a lab, shine a light though it, and its still a vacuum. I could be wrong though.
BTW, it is worth pointing out that photons, being bosons, can occupy the same space without bumping into each other, meaning you can't "fill up" a volume of space with photons. (This would explain why they aren't counted when assessing a vacuum. If you can forever fill a container with something, yet it is never full, then it might as well be empty.)
This is unlike matter (electrons, protons, neutrons), which is fermionic. Fermions take up space, meaning it is possible to "fill up" a volume of space with matter.
Neutrinos are leptons, so they do take up space, but since they are electrically neutral, they almost never interact with regular matter. I suppose, if you could figure out a way to manipulate them, you could fill up a volume of space with neutrinos.