What if elementary particles do have size

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Is it possible that they have the structure something like we used to picture them as? For example, what if we captured an electron and zoom in with a microscope that see infinitly small distances. Is it possible that if we zoomed into the electron close enough that we would see an object? Maybe something like a ball or something? And if no why not
 
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with a microscope that see infinitly small distances.

Such a thing does not exist. One can view particle accelerators as an attempt to create such a thing, but they have limits to their resolution too.
 
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seeing an electron is tantamount to bouncing a photon off of it. individual photons don't really have great resolutions to "see" anything. if you want to see the structure of particles, you collide them in super-colliders like the LHC. modern theory tells us that particles are nothing but field excitations, so we don't expect it to have "structure" in the classical sense.