What fills the 96% empty space in atoms?

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PRodQuanta
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I was having a little discussion with my teacher this evening, and I had a funny idea. I recalled that an atom is composed of something like 4% matter (be it protons, neutrons, electrons, quarks, gluons, ect...)and 96% empty space. I was thinking, and wondering, if it was all empty space, or if it was actually something else. Does anybody know much about this? Or am I way off track here. Any insight is appreciated.

Paden Roder
 
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Surely you could say that it is just distance between matter points.

Note that matter, due to QM, is not localized about any concrete point. And note that the force fields, filling these space, can also be seen as particles, due to corpuscle/wave duality.