Casimir Effect Force in a Collapsing Sphere

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Discussion Overview

The discussion revolves around the calculation of the Casimir Effect Force in the context of a collapsing sphere, exploring theoretical implications and complexities involved in different configurations, such as a bubble or a sphere in a vacuum.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes the standard equation for the Casimir Effect Force but questions how to apply it to a sphere or bubble, particularly regarding the area calculation.
  • Another participant explains that the calculation for a perfect metal differs significantly from that for physical materials, referencing Lifschitz's work as more complex.
  • The same participant mentions Boyer's 1968 calculation of the Casimir effect for a vacuum bubble, which is described as repulsive and infinite, but questions its relevance due to the lack of an external contribution in Boyer's configuration.
  • Concerns are raised about the assumptions made in Boyer's calculation, particularly regarding emission directions and the need for a more comprehensive approach for physical materials.
  • There is a suggestion that a proper calculation for a collapsing sphere would be even more complicated than for a static one.
  • One participant seeks resources for further learning about the calculations and workings of the Casimir effect.
  • Another participant suggests using search engines to find information but expresses concern about the efficiency of that approach.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and relevance of existing calculations, with no consensus on the best approach for calculating the Casimir effect in the context of a collapsing sphere or bubble.

Contextual Notes

The discussion highlights the complexity of the calculations involved, particularly regarding the assumptions made about material properties and emission directions, which remain unresolved.

Who May Find This Useful

This discussion may be of interest to those studying theoretical physics, particularly in the areas of quantum field theory and the Casimir effect, as well as individuals exploring advanced topics in material science.

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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