Casimir-Effect: Beyond Virtual Particles & Photons?

[Kruger]

I read in wikipedia that the Casimir-effect is a one-loop quantum electrodynamical effect. This seems to be wrong to me. I always thought that it is raised due to electromagnetic zero point oscillations. And this oscillations have nothing to do with virtual photons either virtual particles. So how must I understand this text in wikipedia?

 

[hellfire]

I had a similar question a time ago. My understanding is now the following: You are right that, in general, the Casimir effect can be understood as a difference in the infinite integral in the Hamiltonian inside and outside the plates. This is the usual way to derive the Casimir effect in textbooks making use of a model of a non-interacting scalar field. However, if you go to more realistic scenarios you should consider the electromagnetic field as the main contributor to the Casimir force. This means, the Dirac field, the photon field and the interaction between both. As soon as there exist interacting fields you are able to talk about virtual particles and loop effects, because the ground state is not equal to |0> of the single fields anymore. I assume that one may describe then the Casimir effect in that terms. I think this is a very subtle topic and I might be wrong.

 

[dextercioby]

I read in wikipedia that the Casimir-effect is a one-loop quantum electrodynamical effect. This seems to be wrong to me. I always thought that it is raised due to electromagnetic zero point oscillations. And this oscillations have nothing to do with virtual photons either virtual particles. So how must I understand this text in wikipedia?

Technically, the em. vacuum includes quantum corrections which means that various loop (electronic-positronic) corrections to the free photon propagator must be added. Fortunately, QED is renormalizable (at any loop order) and these corrections can be computed.

Daniel.

 

[Kruger]

This is weird. Why are then only virtual photons considered. There are also virtual electrons and positrons in the vacuum and myon-anti-myon pair? And I mean a virtual photon has energy homework and these oscillations have energy hw/2.
Sorry Dexter, I was writing, while you was writing. But do we really get the same result? I mean are this vacuum bubbles in quantum electrodynamics the same thing as the oscillations with energy hw/2 in quantum field theory?

 

[vanesch]

It is technically difficult to claim that the Casimir effect is a one-loop effect, because in its expression, the (EM) coupling constant doesn't appear, which I presume it would - by definition - if it were the first order term in a series development towards that coupling constant.
But my reasoning here might miss some subtility of which I'd like to know something more then.

 

[Kruger]

I think, if we can explain the Casimir-effect by a one-loop effect, then there must not be a coupling constant present in the formula. This is because a coupling constant arrises when two particle interract with each other. And virtual particles, coming as vacuum fluctations, don't couple with a real particle.

Dexter, if you know more about this one-loop Casimir-effect, it would be instructive for me and I think others when you can make this point clear.

For me it is a difference if we derive the Casimir-formula witht hese scillations or with virtual particles. Because virtual particles have another origin.

 

[Kruger]

Is this correct:

The zero point oscillations of the electromagnetic field are the same as virtual photons in quantum electrodynamics.

There are a lot of authors (also Milonny: the quantum vacuum) that say that we can explain the Casimir-effect as a pressure coming from virtual particles with momentum 1/2h(bar)k. But this momentum correspondands to the zero point oscillations with energy 1/2h(bar)w. So this should be the momentum of the zero point oscillations and not of virtual particles. Because virtual particles have momentum hk. That is why I ask if the above sentence is correct.

 

[CarlB]

Dexter, if you know more about this one-loop Casimir-effect, it would be instructive for me and I think others when you can make this point clear.

For me it is a difference if we derive the Casimir-formula witht hese scillations or with virtual particles. Because virtual particles have another origin.

Julian Schwinger (co-recipient of Nobel prize for invention of QED) argued against the physical existence of the vacuum for the most of the rest of his life. His students have continued the fight, with the Casimir effect one of the major battlegrounds. Here's a relatively recent paper that shows other ways of calculating the effect:
http://arxiv.org/abs/hep-th/9811054

This is not a subject about which I know much. That it is a one-loop effect comes about from the presence of $$\alpha^4$$ in the formula, I guess.

One of Feynmann's books referenced the concept that a theoretical physicist should know a lot of different ways of showing the same thing.

Carl

 

[Kruger]

Thanks Carl. But where do you see any a^4 in the formula of the Casimir-force?

 

[hellfire]

There are a lot of authors (also Milonny: the quantum vacuum) that say that we can explain the Casimir-effect as a pressure coming from virtual particles with momentum 1/2h(bar)k. But this momentum correspondands to the zero point oscillations with energy 1/2h(bar)w. So this should be the momentum of the zero point oscillations and not of virtual particles. Because virtual particles have momentum hk. That is why I ask if the above sentence is correct.

As far as I know the problem is that the vacuum energy is actually equal to the integral of all "zero point oscillations" only for free fields. In case of interacting fields this is not true anymore, because there are virtual particles creating and annihilating which, I assume, must contribute to the energy of the ground state. I assume that if one considers the ground state of the electromagnetic field only with one-loop corrections, one may be able to calculate the formula of the Casimir force. I guess it is not necessary that the coupling constant appears to say that it is a one-loop effect. Note that h appears, which might be enough. But, as I said before, this is beyond my knowledge and I never have done these calculations.

 

[Kruger]

Is this correct:

The zero point oscillations of the electromagnetic field are the same as virtual photons in quantum electrodynamics.

There are a lot of authors (also Milonny: the quantum vacuum) that say that we can explain the Casimir-effect as a pressure coming from virtual particles with momentum 1/2h(bar)k. But this momentum correspondands to the zero point oscillations with energy 1/2h(bar)w. So this should be the momentum of the zero point oscillations and not of virtual particles. Because virtual particles have momentum hk. That is why I ask if the above sentence is correct.


In my oppinion we must, if we can calculate the Casimir-force in two ways, with virtual particles and with zero point oscillations and get the same result and these things are not the same, we must in order to get the whole Casimir-force make this: Fcas=Fvirtualparticlepressure+Fzeropointoscillation.


If not, then virtual photons in QED must be the same thing as zero point oscillations in QFT.

 

[member 11137]

Is this correct:
The zero point oscillations of the electromagnetic field are the same as virtual photons in quantum electrodynamics.
There are a lot of authors (also Milonny: the quantum vacuum) that say that we can explain the Casimir-effect as a pressure coming from virtual particles with momentum 1/2h(bar)k. But this momentum correspondands to the zero point oscillations with energy 1/2h(bar)w. So this should be the momentum of the zero point oscillations and not of virtual particles. Because virtual particles have momentum hk. That is why I ask if the above sentence is correct.

In my oppinion we must, if we can calculate the Casimir-force in two ways, with virtual particles and with zero point oscillations and get the same result and these things are not the same, we must in order to get the whole Casimir-force make this: Fcas=Fvirtualparticlepressure+Fzeropointoscillation.

If not, then virtual photons in QED must be the same thing as zero point oscillations in QFT.

I am not a specialist of this question but it looks very interesting. Intuitively, I would defend this point of view: EM fields owns fluctuations. These fluctuations could be short life polarisations ... (see my homepage)

 

[hellfire]

we must in order to get the whole Casimir-force make this: Fcas=Fvirtualparticlepressure+Fzeropointoscillation.

I would say this is right.