Casimir effect, where is the energy loss?

[ArthurDent]

Firstly my knowledge of science is armchair tv level so any overly complicated explanations will be lost on me.

What is going on it terms energy conservation with the casimir effect.

As I understand it virtual particles created outside the plates have a greater range of wavelengths than those in the gap causing a pressure that pushes the plates together. But if the plates move then work is done and energy has been created, since you can't create energy where is the loss in this process to balance things out?

 

[Nugatory]

But if the plates move then work is done and energy has been created, since you can't create energy where is the loss in this process to balance things out?

Someone had to put the two plates in their initial separated positions, and that required adding energy to the system; we're just getting that energy back when the plates move closer.

Suppose I show you two weights connected by a stretched spring. When I let go of the weights, the spring pulls them together, doing work. Where did that energy come from? It came from the work I did stretching the spring in the first place; it was already there as potential energy when I first showed you the experimental setup.

 

[ArthurDent]

I'm not sure I understand your answer.

Someone had to put the two plates in their initial separated positions, and that required adding energy to the system; we're just getting that energy back when the plates move closer.

Why would you need to add energy to the system to put the plates into position?
As I see it you're just converting/using existing energy to move the plates into position.

Suppose I show you two weights connected by a stretched spring. When I let go of the weights, the spring pulls them together, doing work. Where did that energy come from? It came from the work I did stretching the spring in the first place; it was already there as potential energy when I first showed you the experimental setup.

I kind of get the idea that its recovering the amount of energy needed to overcome the plates gravitational attraction in order to push them apart. Is this what you mean?

 

[Nugatory]

I'm not sure I understand your answer.
Why would you need to add energy to the system to put the plates into position?
As I see it you're just converting/using existing energy to move the plates into position.

Suppose I start with the two plates touching. If there's a force that draws them together then I cannot get the system into the plates-separated state without doing work, which shows up as an increase in the potential energy as I separate the plates to set up your initial condition. And if I start with the plates widely separated and bring them closer to set up the experiment, then the potential energy was there all along. Either way, energy conversation works out.

I kind of get the idea that its recovering the amount of energy needed to overcome the plates gravitational attraction in order to push them apart. Is this what you mean?

Pretty much, yes.
None of this has anything to do with quantum mechanics or the Casimir effect; it's just how forces, potential energy, and energy conservation work in ordinary classical physics.