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

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Discussion Overview

The discussion centers on the mechanics of the Casimir effect, specifically whether sliding plates parallel to each other requires the same energy as pulling them apart. Participants explore the implications of forces acting on the plates and the nature of work done in this context, touching on theoretical and practical aspects of the effect.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions how sliding the plates apart requires the same energy as pulling them apart, suggesting that the net forces at the edges are balanced and thus should not require work.
  • Another participant counters that shifting the plates introduces a force component opposing the direction of the slide, indicating that both edges contribute to this force.
  • A repeated point emphasizes that real plates, unlike infinite plates often discussed in textbooks, have a component of the Casimir force that is not normal to the plates, particularly near the edges, which complicates the situation.
  • It is suggested that if sliding the plates laterally could be done without work, it would imply the ability to extract energy from the vacuum, leading to a hypothetical scenario of harnessing energy from the Casimir effect.

Areas of Agreement / Disagreement

Participants express differing views on the mechanics of sliding the plates and the implications of the forces involved. There is no consensus on whether sliding requires the same energy as pulling apart, and the discussion remains unresolved.

Contextual Notes

Participants note that the calculations typically found in textbooks assume infinite plates, which may not accurately represent real-world scenarios involving finite plates and their edge effects.

Christofer Br
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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.
 
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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.
 

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