Casimir Effect Force in a Collapsing Sphere

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SUMMARY

The Casimir Effect Force is defined by the equation F=(π h c A) / 480 L4, but calculating this force for non-ideal geometries, such as a bubble or a collapsing sphere, introduces significant complexity. Boyer's 1968 calculation for a vacuum bubble in a sea of metal yielded a repulsive and infinite force, which lacks practical relevance due to the absence of an external environment. Proper calculations must account for emission in all directions, diverging from the idealized assumptions of perfect materials. The challenge increases for dynamic scenarios like a collapsing sphere, necessitating advanced understanding of the Lifschitz approach and its implications.

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  • Understanding of the Casimir Effect and its mathematical formulation
  • Familiarity with Lifschitz theory and its application to physical materials
  • Knowledge of Boyer's calculations and their implications for vacuum forces
  • Basic principles of quantum field theory related to vacuum fluctuations
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nst.john
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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.
 
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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.
 
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Do you have any places I can learn more about the messy calculation and how the casimir effect really works and all about it?
 
I could Google "Casimir" and "Lifschitz" or "Casimir" and "Boyer", but it seems inefficient for me to do that, and type in the results.
 
Sounds good thank you
 

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