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haushofer
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Ok, that's something I definitely missed, thanks! :P
No. Those are dielectric functions ##\epsilon## treated as a classical non-dynamic background field.haushofer said:Just to make sure i get it: in Jaffe's paper fig.3, those external legs are the conducting charges of the plates, right?
Orstevendaryl said:If I understand what the two approaches to deriving the Casimir force are, they sure seem very different:
The two approaches seem to be focusing on completely different subsystems, and are making completely different approximations about what to treat classically and what to treat quantum mechanically.
- Treat the electromagnetic field classically, but assume that the charges inside the metal plates are undergoing random internal motion. Then you get a Van der Waals type force between the plates.
- Treat the plates classically (as just boundary conditions for the electromagnetic field), and treat the field modes of the E&M field quantum mechanically.
That's exactly why I have writtenHaelfix said:Just so people are clear, this business is deeply controversial in the literature and not settled. There are quite a few subtleties involved, and really requires going through the entire analysis with a scalpel.
Yes. See Secs. IV.B and IV.C, as well as the discussions around Eqs. (14) and (78) in my https://arxiv.org/abs/1702.03291haushofer said:Is there any simple/intuitive way of seeing why these two seemingly completely different approaches lead to the same answer?
I hope my https://arxiv.org/abs/1702.03291 helps to get a better mental picture.Vanadium 50 said:The issue comes about when one tries to paint a mental picture of the results of this calculation.