If I had 2 charged slabs that were moving together at relativistic speeds would both slabs
emit cherenkov radiation. In each of the rest frames of the slabs the other slab is approaching it at a speed that is faster than the group velocity of light in its material.
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 Mentor Only if each one is moving faster than c/n in the medium. The medium's speed matters in this case.
 okay im not saying anything travels faster than c. Cerenkov radiation occurs when an E field is being forced through a material faster than light in that material. so we are talking about speed lass than c. Does Cherenkov radiation happen in both dielectric slabs or just one. I was typing this up the same time vandium posted.

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What are both slabs moving through? If they are moving through a medium at a velocity higher than c/n (the speed of light divided by the refractive index of the medium), then they would emit cherenkov radiation.

And what do you mean when you say that an E field is being forced through a material. Electric fields have no "speed", they simply exist. Changes in the field propagate at c however.
 the slabs are moving through free space but they are moving by each other and their E fields exist in each others slab. I know its c/n but we are dealing with relative speed here. in slab A's frame its at rest and slab B is moving towards it and vice versa for the other slab. So is their Cerenkov radiation in one slab or both? I know E fields don't travel, but in a sense the slab is outrunning its E field that is being setup in the other slab. kind of like retarded potentials
 Mentor The only thing that matters is the charge's velocity relative to the medium. Any slab moving faster than c/n will radiate.

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 Quote by Vanadium 50 The only thing that matters is the charge's velocity relative to the medium. Any slab moving faster than c/n will radiate.
The slabs are not in a medium, he's talking about the electric field from each slab somehow causing radiation to be emitted as they pass by each other.
 Mentor If there's no medium, there is no Cerenkov radiation, since the definition of Cerenkov radiation is the radiation produced by a charged particle moving faster than light in that medium.