Asymmetrical Casimir force?

[gildomar]

So I was reading an excerpt from Lifshitz about the Casimir effect, and besides the obvious dependency on plate separation and geometry, he indicated that the strength of the force also depends on the dielectric value of the plates. What I'm wondering is what the force distribution for the plates would look like if one of the plates was one kind of dielectric, and the other plate was another kind?

 

[Vanadium 50]

Momentum conservation requires the force to be the same on both plates, and pointing in opposite directions.

 

[gildomar]

I guess I could see that for the inner side of the plates, since they're facing each other and can have a field interaction to balance the forces there. But what about for the outer side of the plates? How would they "know" that the forces there need to be balanced?

 

[Vanadium 50]

Momentum is conserved whether the plates "know" about it or not - that's one of the beautiful things about conservation laws.

 

[gildomar]

There might be an interesting research paper in exploring the exact mechanics of how conservation of momentum is maintained in such a situation.

 

[Vanadium 50]

Perhaps, but given how few research papers there are showing that momentum is conserved when one does a proper calculation in other systems, I kind of doubt it. Nobody doubts momentum is conserved, which is why you don't see people writing about it.