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I see that you aren't a particle physicist, Pyro!

Originally Posted by Pyrotex

The particle finds itself in violation of local speed laws! (And this is where everything gets hazy) The particle then "brakes" down to a speed just under cL, by giving off photons--Cherenkov light. But this leaves big questions. How far does the particle enter the material before it "knows" the cL has dropped? Does the particle actually travel at speeds > cL for some tiny distance before its Cherenkov light brakes it to a lower speed? Is this even possible to conjecture? HOW does the particle know what cL is? And on and on and on...

We particle physicists don't consider it a problem with SR at all. Never forget: It isn't c that's the speed of light, it's the speed of light that's c. In vacuo that is. The fact that propagation is slower than c in a material medium doesn't have any bearing at all on the geometry of space-time.

Also, Cherenkov light isn't really the same thing as bremstrahlung radiation. A high energy particle can well maintain velocity for quite a while through a material, energy loss can be very gradual. The beam is often passed through layers of material before being used, further to the thin walls of the pillboxes that actually accelerate the particles and maintain their velocity compensating for the loss by synchrotron raditation.

See also: "Before starting the description of the Cherenkov effect it must be emphasized that the Cherenkov radiation is entirely unrelated to the bremsstrahlung, which is emitted by the moving electron itself when it collides with atoms in the medium. The Cherenkov effect involves radiation emitted by the medium under the action of the field of the particle moving in it. The distinction between the two types of radiation appears with particular clarity when the particle has a very large mass: bremsstrahlung disappears, but the Cherenkov radiation is unaffected." for instance, from:

http://www.gae.ucm.es/~emma/tesina/node4.html