Open or closed Casimir system?

[gildomar]

If you had the Casimir effect pushing two plates together, would that be an open or closed system? And why? I haven't been able to find a satisfying answer/explanation to that.

 

[PeterDonis]

would that be an open or closed system?

What is your definition of these terms?

 

[gildomar]

That's the thing: I'm not sure how they'd be defined here. It's obviously easy if you have a classical system, but things get fuzzy when you have virtual energy.

 

[PeterDonis]

It's obviously easy if you have a classical system, but things get fuzzy when you have virtual energy.

I'm not sure why you would think so. But let's start with the classical definition: what do you think that is?

 

[gildomar]

Isn't it closed if no energy/matter is entering or leaving the system, and open otherwise?

 

[PeterDonis]

Isn't it closed if no energy/matter is entering or leaving the system, and open otherwise?

That'll work. Now, if we have two plates sitting in vacuum, nothing else present, what energy or matter could be entering or leaving the system?

 

[gildomar]

Possibly the virtual photons. But due to their nature, I'm not sure if that would constitute entering/leaving the system, or if they would be considered to be already part of the system. Hence my confusion.

 

[PeterDonis]

Possibly the virtual photons.

The virtual photons are part of the system. They aren't coming in from outside.

More precisely, "virtual photons" is only a heuristic way of describing what is causing the Casimir Effect. A better way is to say that the presence of the plates changes the vacuum state between the plates, in such a way as to create a force that attracts the plates to each other.

But no matter how you describe it, it should be evident that there is nothing entering or leaving the system as a whole; you could draw a boundary around the whole apparatus and measure energy flow across the boundary and find that it is zero. That's part of the specification of the scenario.

 

[gildomar]

Fair enough. Would that also be related to it apparently being a conservative force?

 

[PeterDonis]

Would that also be related to it apparently being a conservative force?

Not really; conservative forces are not limited to closed systems, unless you want to consider the entire universe as part of the "system".

 

[gildomar]

Fair point. :P