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Between two extremely close metal plates, there is a force of attraction because the metal plates have to be nodes of any electromagnetic quantum fluctuations and so there are less virtual particles between the two plates than there are outside. This causes a difference in radiation pressure that pushes the two plates together.

casimir effect

I don't understand why there won't be a similar force would be generated by a metal plate in the shape of a 'u', because the shape would cause electromagnetic quantum fluctuations to be a node at the closed end and an antinode at the open end. this would reduce the virtual particles inside the tube and so there would be a radiation pressure pushing forwards.

force similar to Casimir effect

And if this would accelerate this object would it break conservation of energy.

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The plates getting pushed together by the casmir effect also uses energy, there is no requirement that the casmir effect can't do work.

The energy comes from the fields, this is what they mean when they talk about "vacuum energy"

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    $\begingroup$ I think there is a difference though, with the plates getting pushed together by the Casimir effect the energy has always existed as potential energy. whereas with the acceleration of u shaped object, I don't think there is any potential energy being transfered. $\endgroup$
    – Myles_H
    Jan 16, 2021 at 0:37

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