In the Casimir effect, can you slide plates unopposed by force?

Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
3 replies · 2K views
Christofer Br
Messages
51
Reaction score
0
How would sliding the plates parallel to each other in order to separate them (they are prevented from contacting to avoid friction) require the same amount of energy as pulling them apart? You're not pushing against the force (the net force at the edges pulling it back is balanced by opposite force on opposite edges). I am sure it has to be the same amount of work in both cases to conserve energy, I just don't know how it works.
 
Physics news on Phys.org

Discussion

As soon as the plates are shifted with respect to each other there is a force component against the direction you slide them. Both edges contribute to that.
 
Christofer Br said:
How would sliding the plates parallel to each other in order to separate them (they are prevented from contacting to avoid friction) require the same amount of energy as pulling them apart? You're not pushing against the force (the net force at the edges pulling it back is balanced by opposite force on opposite edges). I am sure it has to be the same amount of work in both cases to conserve energy, I just don't know how it works.

In textbooks you will only find a calculation of the force for infinite plates. But real plates, which can be separated by sliding, are not infinite. For real plates there is a component of Casimir force that is not normal to the plates. This component is most pronounced near the edges of the plates. The "opposite" forces on opposite edges are forces on different plates, so they don't cancel out. (To see this, try to draw a picture with forces, being careful about which force acts on which plate!) Therefore, you are pushing against the force.

In fact, the Casimir force is a red herring here. The same apparent "problem" exists also for classical force between oppositely charged plates.
 
If you could slide the plates laterally without doing work, then you could draw energy from the vacuum. You would start with some spacing, let the Casimir force pull them together and harness the free energy released. Then slide them apart so that they are non-overlapping with enough margin - you wouldn't be doing work, per our assumption. Then move them along the normal axis and get back to the original plane-to-plane spacing. Finally slide into initial configuration and repeat.