Casimir Effect Force in a Collapsing Sphere

In summary, the Casimir effect is an attractive force between two static spheres. The calculation for a physical material is much more complicated, and considers emission in all directions.
  • #1
nst.john
163
1
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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  • #2
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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  • #3
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
I could Google "Casimir" and "Lifschitz" or "Casimir" and "Boyer", but it seems inefficient for me to do that, and type in the results.
 
  • #5
Sounds good thank you
 

1. What is the Casimir Effect Force in a Collapsing Sphere?

The Casimir Effect Force in a Collapsing Sphere is a phenomenon in quantum physics where two uncharged parallel plates placed in a vacuum experience a force due to the presence of virtual particles. When the plates are brought closer together, the virtual particles have less space to exist between them, resulting in a net force pushing the plates towards each other.

2. How does the Casimir Effect Force in a Collapsing Sphere work?

The Casimir Effect Force is a result of the uncertainty principle in quantum mechanics. According to this principle, there is a limit to how precisely we can know the position and momentum of a particle. This means that for a short period of time, particles can exist in a vacuum, even if they do not have enough energy to do so in the long term. These virtual particles can create a force between the plates due to their interactions with the surrounding vacuum energy.

3. What causes the Casimir Effect Force to occur?

The Casimir Effect Force is caused by the presence of virtual particles in the vacuum. These particles are constantly popping in and out of existence and can create a force between two uncharged plates due to their interactions with the vacuum energy. The force is strongest when the distance between the plates is very small and decreases as the plates are moved further apart.

4. What are the applications of the Casimir Effect Force in a Collapsing Sphere?

The Casimir Effect Force has potential applications in nanotechnology and microelectromechanical systems (MEMS). It can be used to create nanoscale machines and devices, such as nanosensors and nanoswitches. It can also be utilized in the development of new types of energy harvesting and storage technologies.

5. Is the Casimir Effect Force in a Collapsing Sphere a significant force in our everyday lives?

No, the Casimir Effect Force is a very weak force and is only significant on a very small scale, such as in the nanoworld. It is not noticeable in our everyday lives due to the small size and distance between objects. However, it is an important phenomenon in the field of quantum physics and has potential applications in various technologies.

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