# Quantum friction due to vacuum energy

Hi,
I am writing an essay on quantum friction (the hypothetical force based on the casimir force). I am having trouble finding information on this concept. Wiki does not have a page on it, nor does Britanica. I have found only three Journal articles on the subject. There is more stuff about a quantum description of friction, but I need to write this specifically on the role of vacuum energy in providing a lateral force on two uncharged plates. I'm hoping someone can help guide me to where I can get an overview of this topic, as I'm having trouble understanding it.

I need to be able to discuss it at an advanced undergraduate level. I have studied quantum mechanics, but not QFT. I will obviously need to borrow a little from QFT, but cannot provide detailed explanations based on QFT because I haven't studied it and only have a short time to complete the essay.

One aspect I am having trouble with is this:

One explanation talks about a moving plate, with virtual photons striking from random angles. In the rest frame of the plate, the photons traveling in the same direction as the plate (according to OUR rest frame) are redshifted, and the ones travelling in the opposite direction are blueshifted. This causes momentum to be transfered to the plate, causing it to slow down.

Now, the hypothesised quantum frictional force is only thought to exist between TWO plates, so this doesn't happen with one plate. This makes sense, because the vacuum should look the same in the rest frame of the plate, as it does in our rest frame, so there can't be a force from the vacuum that accelerates a plate. However, clearly this symmetry does not exist when there are two plates.

The thing I don't understand though, is how the presence of a second plate can affect the behaviour of the other plate. The only way I can think of it, is if the momentum of the photon is being transfered FROM ONE PLATE TO ANOTHER. This is clearly the case, but how does that relate to the description of the doppler shift of the virtual photons? Are the virtual photons originating at the surface of the other plate? I don't see why they should. They are a manifestation of the vacuum energy itself, so I don't see how a single virtual photon can exchange momentum BETWEEN the two plates. Mind you, we are talking about UNCHARGED plates, so there are no photons associated with an electromagnetic field of the material itself.

In class, we were taught about the casimir effect, and asked to write out essay on one of the 'related topics' given in class, so I gather that the explanation for the Casimir effect given in class may be able to be used to explain quantum friction...perhaps. The explanation was that there are more modes of the vacuum energy outside of the plates than inside because the plates are nodes and therefore require integer values of photon energy, whereas outside the plates the number of modes is uncountable.

Hope I've been clear on all this, and hopefully someone can shed a little light on this topic. Thanks. :)

alxm
Sounds weird to me. The Casimir effect is a conservative force, classical friction is not. So the analogy makes no sense to me.

What are you trying to describe, the ordinary Casimir effect, or something else?

Staff Emeritus
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First, I think it's a very bad idea to take something you don't understand (for example, something that requires QFT to understand if you haven't had QFT) as a subject of an essay.

Second, it's not clear there even is such an effect: see http://arxiv.org/abs/0810.3750" [Broken] of 6 weeks ago where they claim that in an exact calculation the magnitude of the force is zero.

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Yes, I have read that paper, but I think controversy is okay because it gives me something to discuss. I agree that it is not ideal to write an essay on a topic that I don't understand, but I have little choice. The topics include topological defects, dark energy, and condensed matter systems, among others, and all require relating the topic to vacuum energy. Some might be easier to understand than others, but I don't know much about any of them, and thought it best to just pick a topic and get going with it.

The particular unit I am taking seems to be pretty much aimed at stretching the students. The professor who runs the unit knows that we have not learnt QFT. We generally get a quick overview on a topic (usually over the course of a one hour lecture) and then have to solve-problems, give a talk, write an essay etc. within a couple of weeks. Other topics we have covered have are variational calculus and the principle of least action, and number theory.

Thanks for the input.