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Can you see or accurately visualise sub atomic particles or are they known only by maths and/or inference?

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What is your definition of visualize? If we draw something using mathematical equations, isn't it a visual representation? Do you want to see it under light? Mind it, whatever techniques we use to visualize subatomic particles do actually use mathematical equations to draw something on computer. –  SS-3.1415926535897932384626433 Dec 7 '12 at 4:17

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You can see a nucleus and the nucleus of a hydrogen atom is a proton which is the same. You can't see below that at least with a source of neutrons that ISIS produce, but you can see down to the level of the proton.

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The limit at ISIS is basically set by the beam energies and the strong nature of the neutron--nucleon interaction, higher energy facilities can problem finer distance scales. –  dmckee Dec 7 '12 at 3:34

We can image the sub-structure of nucleons by a number of different techniques involving high energy scattering. The results are generally presented in terms of "parton distribution functions" or "structure functions".

One such experiment that I had some small relationship with (though not enough to be an author) was NuSea (E866) at Fermilab in the mid 1990s, which used muon Drell-Yan as the a probe to image the QCD sea in particular.

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