Casimir Effect Force in a Collapsing Sphere

1. Jan 2, 2015

nst.john

I know that the Casimir Effect Force is calculated by the equation F=(π h c A) / 480 L4. However, how can you calculated the Casimir Force if there is for example, a bubble. If there is a sphere how can you calculate the force because I don't know what the area would be or how to find it.

2. Jan 2, 2015

Staff Emeritus
This doesn't have a simple answer.

Problem 1 - your calculation is for a perfect, ideal metal. The actual calculation (first done by Lifschitz) for a physical material is much messier.

In 1968, Boyer calculated the Casimir effect for a bubble of vacuum in a sea of metal stretching to the ends of the universe. He found this to be repulsive and infinite. This is probably the "classic" calculation, but while not exactly wrong, it's not exactly relevant. In the rectangular Casimir effect, the finite force is obtained by subtracting the contribution from the inside from the contribution from the outside (or vice versa). In Boyer's configuration, there is no outside.

Additionally, Boyer assumed that his sphere only radiates in directions normal to its surface. If you were to look at such a sphere, you would only see one small point - the point that happens to be directly in line of sight. A proper calculation for a physical material needs to consider emission in all directions. I don't know if such a proper calculation has been done - if the Lifschitz calculation is messier, this is messiern squared, but the force would be attractive. (Replace the sphere with an 2n-hedron of parallel plates - the force between all n opposite plates is attractive, so therefore the total force is attractive. Now let n go to infinity)

This is for a static sphere. For a collapsing sphere, it will be even more complicated.

Last edited: Jan 2, 2015
3. Jan 2, 2015

nst.john

Do you have any places I can learn more about the messy calculation and how the casimir effect really works and all about it?

4. Jan 2, 2015