After some reading about the Large Hadron Collider and it's very impressive instruments to detect and investigate the collision results, there is a remaining question.
What would happen if the scientists would use leptons instead of hadrons?
Especially: What would happen if they would collide electrons?
Isn't it intrinsic that all particles consist of smaller particles? With current technology, could we detect them?
Answer
First of all -- it wouldn't be called "the Large Hadron Collider", right?
Looks like one would rather call it something like "Large Electron-Positron Collider".
In that case one definitely would need another abbreviation for it. Something like "LEP" instead of "LHC"...
Now, guess what was there in the same tunnel before?
Edit: since my shenanigan got popular, I'll elaborate.
Yes, they actually was colliding electrons and positrons, not electrons-electrons. Mainly because of the richer physics of such collisions. (But for my theoristish point of view: positron is just an electron going back in time.)
Why the same tunnel? Perhaps surprisingly, tunnel is taking a substantial part of the cost of an accelerator. Digging a new one for LHC would have definitely burnt a large hole in CERN's pocket.
Given a fixed circular tunnel (it's radius) you actually have a bound on energy you can have for your particles. Due to synchrotron radiation -- see @emarti answer for more.
27 kilometers seems to be a reasonable limit on the size of a circular tunnel. (Actually people think about 233 km, but that sounds crazy to me.) So the next accelerator most probably will be linear and it will be electron-positron.
P.S. Have you heard of a Photon Collider?
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