# Fields other than the photon field in the Casimir effect?

• bcrowell
In summary, according to this argument, the Casimir effect can be explained by considering only the zero-point energy associated with the photon field, while ignoring other fields.
bcrowell
Staff Emeritus
Gold Member
Can anyone tell me if the following argument correctly explains why the Casimir effect, as observed in experiments to date, can be explained by arguments that consider only the zero-point energy associated with the photon field, while ignoring other fields?

Between two parallel, conducting plates separated by a distance L, the longest wavelength you can have is essentially L. (Let's not worry about factors of 2.) Then the low-energy cutoff on the modes of oscillation of the EM field is $hc/\lambda$. This cut-off energy sets the scale for the zero-point energy, which determines the strength of the Casimir attraction between the plates.

On other other hand, suppose you have a particle of mass m. It seems like the experiments have been done with L in the micrometer range, and then if we're talking about the electron-positron field, the low-energy cutoff is obtained when the particles are nonrelativistic, so it occurs at $E=p^2/2m$, which (again ignoring factors of 2) comes out to be $(hc/\lambda)(v/c)$. Therefore it's down by a factor of v/c compared to the energy cutoff for photons.

To get the field of massive particles to contribute comparably to the photon field, you could try looking for less massive particles, which might be relativistic even when their wavelengths were comparable to L. But the only particles we have that fit this description are neutrinos, I think, and since they're electrically neutral, the existence of the conducting parallel plates doesn't impose any boundary condition on them.

Is this right?

Yes, you need to impose boudary conditions on the relevant field. But for massive fields, the effect will fall of exponentially like
exp(-L/lambda) where Lambda is the Compton wavelength.

Suppose you have just one plate. Then that modifies the boundary conditions of the field there and a distance L away where you wan to put the other plate, the effect is already exponentially suppressed by exp(-L/lambda). So, putting the other plate there will always yield an exponentially small effect if L >> lambda.

Thanks, Count Iblis, that's very helpful!

## 1. What are the other fields involved in the Casimir effect?

The other fields involved in the Casimir effect are the electromagnetic field, the gravitational field, and the quantum mechanical fields such as the electron field or the Higgs field.

## 2. How do these fields contribute to the Casimir effect?

These fields contribute to the Casimir effect by interacting with each other and creating a force that can attract or repel objects in the vacuum between two parallel conducting plates.

## 3. Can the Casimir effect be observed with all types of fields?

No, the Casimir effect is primarily observed with electromagnetic and quantum mechanical fields. The effect is not as significant with gravitational fields due to their relatively weak strength.

## 4. Are there any real-world applications of the Casimir effect with other fields?

While the Casimir effect is most commonly studied with the electromagnetic field, there have been studies on its potential applications in the field of quantum computing and nanotechnology. However, further research is still needed in this area.

## 5. How does the presence of multiple fields affect the Casimir effect?

The presence of multiple fields can complicate the calculation of the Casimir effect and may result in different outcomes depending on the specific combination of fields. However, the overall concept of the effect remains the same regardless of the number of fields involved.

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