As evidenced by our continued existence, the activation of the Large Hadron Collider did not result in the end of life as we know it. But then, the scientists and engineers involved in building the LHC knew how to minimise the chances of creating a singularity, opening a portal to an alternate dimension or triggering a regular old explosion. The eggheads of the LEGO world, on the other hand? Yeah, they're just winging it.
According to builder Jason Allemann, the "LBC", or Large Brick Collider, "started out as a joke". But as he started putting it together, the inevitable scientific and mathematical qualities of the project began to surface. Allemann realised with the right parts, he could craft something functional, a device that could actually accelerate an object... and smack it into another object.
Of course, it wouldn't be subatomic particles. For the LBC, a LEGO soccer ball is used instead and it only gets up to 12.5km per hour -- a respectable speed for a toy, but it won't be smashing any records CERN has set. That said, if you watch the video, the LEGO scientist relaying the ball's speed is providing fairly accurate numbers; Allemann says he watched the recording frame-by-frame to figure out the speed in "studs per second".
The grunt work is handled by a set of LEGO wheels and a Power Functions M motor. The rest is just clever construction to keep the ball spinning in a circle... and eventually colliding with something.