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Tychoxi: And I'm not a physicist either but I'm pretty sure they can't! Though the joke's on me cause before reading this, I "knew" electrons were one of those fundamental particles (ie. particles that can't be split into anything smaller).
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JudasIscariot: So how do you find out what a particle is made from in the first place? I mean, as far as I know an electron isn't made out of ...itself...or however one can describe something not divisible being made out of something.
Well, that's the thing, electrons aren't made up of anything but themselves. They just are and we happen to have named these fundamental particles "electrons". We found out that atoms are made of protons/neutrons/electrons. That neutrons and protons are made up of quarks. So it is possible to find out, I'm sure at most the limitation will be a technical one.

All the fundamental particles (which are only fundamental as far as we know) like quarks, neutrinos, photons and electrons are just what they are, you could say they are all energy if you want to know what they are "made of". String theorists will tell you they are all made up of vibrating strings, but this doesn't mean they can be split into these "strings", it means that a "string" in a given energetic state will be what we call an "electron", and that another "string" in a different state will be what we measure as a "photon".