# Talk:Casimir effect

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## Demonstration? Test photos?

I have looked for media and videos of the effect but can't find any.--Ericg33 (talk) 08:10, 13 May 2011 (UTC)

How do you photograph a force? Also, remember that it is only significant at submicron lengthscales which requires fairly delicate experiments.
One can certainly find photographs of the experimental apparatuses that are used to measure the force, and plots of measured data. e.g. you can find some such pictures in this review article. However, we can't just copy pictures from papers into Wikipedia because of copyright reasons. We might be able to contact one of the experimental groups (e.g. Steve Lamoreaux's group is an obvious candidate) to see if they will donate a picture of their apparatus. I'm not sure how illuminating this kind of apparatus picture will be for readers of the article, though.
— Steven G. Johnson (talk) 18:04, 13 May 2011 (UTC)
interesting --Ericg33 (talk) 08:07, 16 May 2011 (UTC)

## Old, untitled discussions

How big are theses forces ? Can they be sufficiant in order to enable to separate the two plates ?

If you mean, to keep the plates apart from each other, overcoming gravity between the two? or overcoming the gravity of one on top? Hardly, since the force can only attract the two plates. If you mean, to oppose gravity enough to keep one on the bottom up against gravity (hardly what I'd call "separating", but just in case), it's hypothetically possible, for thin enough plates close enough together, but not in a useful, let's-use-this-for-antigravity kind of way. -- John Owens 04:45 Apr 9, 2003 (UTC)
It says you can make them repulse as well. - Omegatron 20:24, Aug 16, 2004 (UTC)
In certain configurations, not parallel plates. For example, it can be repulsive inside an enclosed sphere - but not enough to break apart spheres of almost any known composition. Even if some configuration were found where it was repulsive between two surfaces not bonded to one another, the separation would be fairly tiny: by the time the surfaces got a few microns apart, the force would drop to effectively zero.
See below

Is this supposed to use permittivity or permeability for the first variable on the right side of the equation? Ever since the equation was introduced in the history, it's been ${\displaystyle \eta }$, eta, but the only use for that in electromagnetics is measuring the electromagnetic moment, which I really don't think is what belongs there. Permittivity uses ${\displaystyle \epsilon }$, epsilon, the other Greek 'e', so I suspect that's what was meant; permeability uses ${\displaystyle \mu }$, mu. -- John Owens 04:47 Apr 9, 2003 (UTC)

Here's a quote from The role of the Casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS), Journal of Applied Physics, Volume 84, Number 5, September 1998:

η depends on the dielectric permittivities of the plates and of the medium between them ( η = 1 for perfectly conducting plates with vacuum between them).

I found it at http://www.quantumfields.com/aip98.pdf. η appears to be a dimensionless quantity. -- Heron

η is just a correction factor (η ≤ 1) used to account for imperfectly-flat surfaces, imperfect vacuum, finite electrical conductivity, etc. —Preceding unsigned comment added by 64.180.6.212 (talk) 16:58, 16 March 2008 (UTC)

## Constants

Isn't ${\displaystyle \hbar }$ the Dirac's constant, equals ${\displaystyle {\frac {h}{2\pi }}}$?

BW from it.wikipedia August, 3, 2004
Yes - fixed. -- ALoan (Talk) 11:32, 3 Aug 2004 (UTC)

## Magnetic dipoles???

"Similarly, fluctuations in the electronic structure of molecules cause transient magnetic dipoles which lead to the Van der Waals force."

The van der waals and london force articles do not mention magnetic dipoles. They seem to refer to electrostatic dipoles, which is what I was under the impression of as well. - Omegatron 20:24, Aug 16, 2004 (UTC)
You (and the other articles are right). I think that was my error, although I can't think why I wrote it. I've deleted the word "magnetic". -- ALoan (Talk) 20:32, 16 Aug 2004 (UTC)

## Speed of light

Doesn't suppressing the vacuum fluctuations also increase the speed of light slightly? About how large is this effect? --Carnildo 06:27, 19 Jan 2005 (UTC)

## ships

whoever wrote the bit about ships gets a big gold star. that's cool! - Omegatron 18:13, Apr 3, 2005 (UTC)

Glad you like it :) Taken from a lecture by John Barrow at Gresham College earlier this year. -- ALoan (Talk) 10:27, 18 May 2005 (UTC)
The bit about ships has just been debunked: [1]. :)--Joel 18:51, 5 May 2006 (UTC)
That seems to require paid subscription to the site. -BlackTerror 05:26, 20 August 2006 (UTC)
I can't get access to that article either, but I found a summary of it here. It's by Fabrizio Pinto, who is CEO of the modestly named Interstellar Technologies Corporation, one of those companies that's just on the verge of producing free energy. An article on his website [2] explains how he thinks his perpetual motion machine works, so I wouldn't put too much faith in his ability to 'debunk' myths. Also, he says that the density of ZPE is infinite, so I hope I'm not standing nearby when he switches that thing on. ;-) --Heron 16:35, 21 August 2006 (UTC)
I agree that Pinto is not a reliable reference, but to me this section sounds too strongly worded based on the available verifiable references. "It is for this reason that naval vessels, when resupplying or transferring personnel at sea, must use lines and maintain a minimum distance from each other..." This makes it sound like all ships do this today, when the only reference I could find was 170 years old (and Pinto found a naval architect who's never heard of it). It just may not be relevant to modern ships for whatever reason. I would suggest to strike that last sentence, or at least qualify it a bit. Unless someone can find a sailor who can prove or disprove it? Kiracofe8 00:12, 7 February 2007 (UTC)

Isn't that due to the bernoulli principle ? In the same way that air flowing over the top of a plane's wing goes faster then underneath, the pressure is less, generating lift. Similarly the water between two ships flows faster, reducing the pressure, drawing them together ? Not sure why it would flow faster - just what I was told long ago. Scale is quite different from Casimir, though !

I was wondering if Casimir forces were related to the precision engineering practice of 'wringing' very flat metal surfaces together so that gauge blocks could be stacked ? Or does that requre a trace of oil ?

Does it relate to the strength of the material ? If perfect surfaces are wrung together then surely you no longer have surfaces - it becomes a single piece of material ?

--195.137.93.171 10:22, 6 August 2007 (UTC)

A better discussion ! Bernoulli principle between two surfaces is called Venturi effect. Also capillary effects and original diagrams show row-boat between ships - unable to pulll them apart !

195.137.93.171 20:20, 6 August 2007 (UTC)

## application through technology

I would assume in the future that materials (plates) can be produced for a repulsive effect, it would be the to the benefit of these plates to be able to change in material structure dynamically to interact with different materials encountered over time during the repulsion phase of movement, and to increase or decrease repulsion energy strength.

Parallel plates can't repulse. That's a fundamental property of the physics involved, which won't change with technology. A quick research seems to indicate it's only repulsive in enclosed spaces - hollow spheres or the like - but I'm not finding enough data to be sure that's the only case. It may simply be that no one's thoroughly investigated this yet. Even if there were an alternate geometry where plate-like structures repulse - say, if the plates were covered with hollow half-spheres - the need to keep them close to keep the repulsion going would mean this would mainly be useful for "reduced friction" systems, like magnetic levitation but with specially-shaped surfaces instead of magnets.
At present, no one has ever observed a repulsive Casimir force between two objects in vacuum. The theoretical prediction that a sphere would show a repulsive force has come under fire in the last few years, but no disproof has yet been given. Another prediction is that parallel plates could have a repulsive Casimir force in vacuum, if one plate has a very high magnetic permeability over a large frequency range. No such materials are presently known, but they are being researched for use in the negative index metamaterials.
I believe a repulsive net Casimir force has been observed between objects separated by a fluid. This is more in the short distance, van der Waals limit.
Vortmeester 02:39, 2 December 2005 (UTC)

Repulsion seems to require a perfect lens with negative refractive index to be inserted in the gap !
No, I don't understand any of that either, but it is being researched at the University of St Andrews and reported by the BBC Experts float levitation theory also Perfect lens could reverse Casimir force
195.137.93.171 10:36, 6 August 2007 (UTC)
Repulsive Casimir Force: Casimir-Lifshitz force experimentally verified.
85.104.31.133 10:36 8 January 2009 (UTC)

## sum of positive integers

Can somebody fix the part where it's stated that the sum of positive integers is -1/12? This is of course not valid when renormalization is not used. AFAIK this is results from taken the difference of the sum of posivive integers and the integral from zero to infinity of x dx.

-- ... when s = −1 then the analytic continuation of ζ(s) gives ζ(−1) as −1/12.

-- The Ramanujan sum of 1 + 2 + 3 + 4 + · · · is also −1/12.

you could fix it yourself, click on edit

## Hawking radiation "analogy"

What does Hawking radiation have to do with an analogy of the Casimir effect? This should be explained or removed from the article. -D. Estenson II 12:25, Jun 23, 2005 (UTC)

Hawking radiation is another quantum effect that is caused by an object acting on virtual particles. --Carnildo 18:19, 23 Jun 2005 (UTC)
Then the paragraph should be in an article about virtual particles or quantum theory. As is, it doesn't fit in this article, especially where it is placed. I think it should be removed altogether. -D. Estenson II 10:46, Jun 24, 2005 (UTC)

## Any comments on this paper?

The standard explanation of the Casimir effect has never made sense to me; I thought that vacuum fluctuations by definition interacted only gravitationally. If they're defined in such a way that they interact electromagnetically with real particles, then surely any other calculation involving non-trivial Feynman diagrams could also be taken as evidence of vacuum fluctuations. I don't understand what's supposed to be special about the Casimir effect.

Now there's a paper called The Casimir Effect and the Quantum Vacuum by R. L. Jaffe which seems to support this view.[3] Can anyone comment on this? Should the Wikipedia article be modified?

-- BenRG 21:27, 13 September 2005 (UTC)

The Casimir effect is often given as evidence that vacuum fluctuations carry zero point energy. Jaffe's article points out that this is not the only interpretation for the effect. You are correct that most QED effects (the Lamb shift being a prime example) show that vacuum fluctuations exist; it's just that these effects have nothing to do directly with the zero point energy.
Vortmeester 02:44, 2 December 2005 (UTC)

## casimir in statistical mechanics

Unless I'm mistaken this article speaks only of casimir effect as a product of quantum fluctuations. In statistical mechanics, the term "Casimir effect" is also used to describe entropy-driven forces arising from thermal fluctuations. BTW, although the article does not mention it, I really think that the casimir effect which is present in dipoles and is at the origin of Van De Waals between induced dipoles is one of a thermal origin, not quantic. Another example of a thermal casimir effect is the elastic response of an ideal chain, which I'll soon write something about.(ThorinMuglindir 09:46, 26 October 2005 (UTC))

Regarding the thermal-fluctuation-driven Casimir effect, I've seen it called the "critical Casimir effect" to distinguish it from Casimir's original effect. This is appropriate because the critical version will only be appreciable near a critical point, where thermal fluctuations exist at all length scales.
Regarding the van der Waals force, it is correct to say that it is a quantum effect. It can be derived at zero temperature using standard quantum mechanical perturbation theory (first done by one of the London brothers in the 1930's). On the other hand, thermally driven dipole moments could conceivably modify this.
Vortmeester 01:58, 2 December 2005 (UTC)

## Virtual Particle Dispute

I thought that the dominant characterization of vacuum energy was that it is caused by the fleeting existance of virtual particles. However, User:KazuiKier claims that the casimir effect is not caused by virtual particles, and that the VP explanation is widespread, yet erroneous. However, it is certainly widespread enough to be the explanation of choice for several reputable Stephens sources.

• Stephen Hawking uses the VP explanation.
• Stephen Reucroft and John Swain have a scientific american article which talks about 'vacuum waves' which can become real waves.This sounds like virtual particles to me. Also, does the picture on that page seem familiar to anyone else? heh.
• Stephen K. Lamoreaux's 1997 experiment paper cites another paper(E. Elizalde and A. Romeo, Am. J. Phys. 59, 711 (1991).) for the modern theoretical background. This other paper states "The van der Waals forces admit two other interpretations: two photon exchange (my note:I read this as the QED-style interpretation) and zero point fluctuation (my note:sounds like SED to me)... The photon exchange would be described by Feynman diagrams containing a closed photon loop (my note:this screams virtual photon), standing for the vacuum fluctuations of the e.m. field, perturbed by two insertions representing two particles. The integration would be over all possible momenta of the virtual intermediate photons." This paper also cites another Casimir paper, this one written by...
• Stephen Wolfram. At his ScienceWorld cite, one can see that its Virtual Particle Article(oh that is fun to say!) clearly corroborates the VP explanation.

I think that this confusion may be caused by the mismatched ontologies of QED and older QM. Whereas QED explains things by postulating virtual particles, earlier quantum thought was guided by the uncertainty principle. Don't believe me? In QED (book), Feynman has this to say about the uncertainty principle:

"I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas(such as, light goes in straight lines). But at a certain point the old-fashioned ideas began to fail, so a warning was developed that said, in effect, "Your old-fashioned ideas are no damned good when..." If you get rid of all the old-fashioned ideas and instead use the ideas I'm explaining in these lectures- adding arrows (my note:an arrow is Feynmanese for the complex number representing the 'probability' of an event) for all the ways an event can happen- there is no need for an uncertainty principle!"

Anyways, an ontology using the uncertainty principle predicts the vacuum energy without talking about virtual particles. Conversely, Feynman's QED ontology predicts the vacuum energy without talking about an uncertainty principle. Aren't the legion of ontologically incompatible interpretations of quantum mechanics fun! Seriously though, virtual particles are the dominant and a valid way of explaining the Casimir Effect. As a disclaimer, I just read this stuff for fun- I'm no fuzzycyst. Maybe I'm completely wrong about all this. If not, I hope someone with a good head for the philosophical issues in science could add a discussion of this tricky issue (including the Feynman quote) to the uncertainty principle article. I think it would be a great addition. It seems to me that the invalid mixing of the path integral formulation with the uncertainty principle is a tricky danger many may not even be aware of. -- Intangir 08:08, 26 December 2005 (UTC)

I don't know who has the better side in this dispute, but I did get a few comments from the person who is making these changes. See User_talk:Karol_Langner#Casimir_effect and User_talk:Karol_Langner#Casimir_effect. I thought that the zero-point fluctuations are virtual particles and that both explanations are legitimate, User:KazuiKier, however, says that VP only mediate the transitions to stronger fluctuations, and that the Casimir effect is explained by the lowest fluctuations alone. Karol 10:05, 26 December 2005 (UTC)
This person's user page says they're an 18-year-old student. They're making claims that contradict all of the external references I can find. I'm reverting, adding more reference links, and putting this up on Wikipedia:Pages needing attention/Physics for bona fide experts to look at (I know there are several lurking). --Christopher Thomas 19:57, 26 December 2005 (UTC)

I've moved the controvertial content here, so it can be vetted by physicists before being added again. I'm not saying it's incorrect - I'm saying that I don't trust User:KazuiKier's unsourced addition of it. I've kept the other editing tweaks that have been made, and have added another reference to the article, as well as moving the content in question, so this isn't a straight revert. --Christopher Thomas 20:14, 26 December 2005 (UTC)

(Begin quoted text.)

The Casimir effect is caused by the fact that space is filled with electromagnetic energy. Even "empty" space contains a small amount of electromagnetic energy. This is a result of the nonzero energy ground state of the electromagnetic field, the so-called zero point oscillations. The lowest energy expectation value for the electromagnetic field is

${\displaystyle {E}={\begin{matrix}{\frac {1}{2}}\end{matrix}}\hbar \omega \ .}$

When two reflective plates are placed parallel to each other, however, the wavelength of the oscillations between the plates can only occur in discrete values, while outside the plates there is a continuous spectrum present. This leads to an energy gap—between the plates there is less energy density than outside. It can be shown mathematically that this energy difference, called the Casimir energy, is finite. As the plates move closer together, the distance between them decreases and the interval between "allowed" wavelengths gets smaller. This decreases the difference in energy density between the plates vs. outside the plates. Since the total energy can be decreased by moving the plates closer together, the plates feel an attractive force.

The Casimir effect is often explained in terms of virtual particles. This explanation is mistaken since the electromagnetic zero point field has nothing to do with virtual particles. One zero point oscillation is always present while virtual particles pop in and out of existence.

(End quoted text.)

The zero-point energy of the vacuum is interpreted as either the contribution of virtual particles to the vacuum or the zero point energy of harmonic oscillators. Neither approach is incorrect, although calling it the zero point energy of oscillators is more concrete, as virtual photons cannot be directly observed. Nonetheless, the basic idea of virtual particles is correct, and one could calculate the zero-point energy by drawing Feynman diagrams with no external legs. Saying that the "electromagnetic zero point" has nothing to do with virtual particles is simply incorrect: in its ground state, because of the uncertainty principle, the harmonic oscillator is not static. Likewise, in its ground state, the electromagnetic field is not a static E = B = 0 state. It is convenient to think of the fluctuations of the vacuum as photons. KazuiKier says on his user page that "One zero point oscillation is always present while virtual particles pop in and out of existence." Saying that "virtual particles pop in and out of existence" is a classical statement: we can never actually say "a virtual particle of type X appeared here, travelled so far over such a time and disappeared". What is real is the aggregate quantum mechanical effect. This effect is amenable to either intepretation. –Joke 21:33, 26 December 2005 (UTC)

This dispute also spills over to additions User:KazuiKier added to the Virtual particle article(its even more fun the second time!). I've directed the discussion to here. In it he wrote:

Note that it is often believed that the Casimir effect has to do something with virtual particles. This is not directly true since the Casimir-effect results from an external perturbation of the zero point oscillations of the electromagnetic quantum field through two plates placed in the vacuum. -- Intangir 21:58, 26 December 2005 (UTC)

If I may ... My PhD thesis had the words "Casimir effect" in the title, if I remember correctly. So, now that I've claimed authority... The disputed text is more or less correct, with the exception of the last three sentences. Its slightly misleading; its not just the fundamental mode of the cavity that counts, its all of the modes. For fermions, this also includes the negative-energy modes. I will try to amend the article shortly, adding a technical explanation, and then checking the rest against that. linas 02:41, 27 December 2005 (UTC)
Not to be rude, but why did you back out the other changes to the article, like added references and "see also" links? I'd explicitly stated above that I'd added these in addition to moving the material under discussion. Cut and paste doesn't take _that_ much more time than a reversion. --Christopher Thomas 02:57, 27 December 2005 (UTC)
I'm not sure what you are referring to. I did not make a careful study of the edit history of the article. I mostly just re-wrote it. Its late at night here, so I'm done for now. Restore any refs that I may have chopped. The see-also section only contained the van der waals link, and I incorporated that directly into the discussion. Not sure what other "see-also's" there might be.
The experimental section is surely wrong; I thought there were measurements performed in the 60's or 70's or something like that. I vaguely remember that Landau and Lifshitz "theory of continuous media" (a copy of which I sadly do not own) has several long, complex section of related effects in dielectric media, complete with calculations showing dependence on cutoff frequency, and comparisons to experimental results for a variety of dielectrics. Maybe I'm confusing a related effect, since L&L was written in the 50's ... linas 06:28, 27 December 2005 (UTC)
It shows most clearly on this diff, at the bottom ("see also" and "references" sections). I'm puzzled as to how you could miss it, as you presumably diffed to see what _I'd_ done. In any case, they've been added again. Thanks for the monumental effort that went into the rewrite! --Christopher Thomas 06:42, 27 December 2005 (UTC)
--> reason one: virtual particle has momentum hbar*k, is reflected from wall. Thus per spin direction (two) the plates get momentum 2*hbar*k. And thus a total momentum of 4*hbar*k (from virtual photons of wave vector k (two polarization directions). This leads to a Casimir force that is twice stronger than the one obtained by Casimir.
--> where do we put the vacuum polarization contribution of the virtual photons? Why do we only take virtual photons and not electrons and positrons (and myons and antimyons) that are created from the virtual photons?
(p.s. I know that only the expectation value of the electric and magnetic quantum field are zero. But the standard deviation isn't. And I never sayd the harmonic oscillations are static. But there always exist (at every space point) fluctuations of every frequency - thus they are always present).
KazuiKier, 27.12.05

Can we stop, already?

1) I gave a very simple, super-low-brow derivation that I hope any undergrad with advanced calculus can understand. I don't believe its possible to simplify this derivation any further. I hope it provides a good idea of the mechanics of computing these things.

2) "Virtual particle" is not really a well-defined term in physics. Its a concept that is loosely used to describe a variety of things and effects, but it is not a technically accurate phrase. That said, the Casimir effect is a first-class example of what a "virtual particle" looks like. The sum/integral is a sum/integral over all virtual particles between the plates. That's what it is. If some book doesn't say this, its probably because the author doesn't want to use the words "virtual particle" precisely because this phrase is rather useless. Its useless because it clings to an old-fashioned view of the world, as if it were made of "particles". Its not. (Its made of fields)

3) Same remarks for "vacuum polarization". Again, cute phrase, and illuminating because it has analogies to solid state physics, but, if taken to seriously, it is again misleading and imprecise. linas 23:36, 27 December 2005 (UTC)

What momentum do virtual particles have? Is their momentum defined over the relativistic energy momentum relation? I think yes. They've momentum p. If we make the "vacuum pressure approach" with such a momentum we yield a Casmir-force per area that is double the one you got, linas. If we say virtual particles are zero point oscillations what are then virtual photons mediated from one electron to the other? Virtual particles have a clearly defined momentum and zero point oscillations haven't. KazuiKier, 9:36,28.12.05
And also remember that the energy expectation value of the electromagnetic zero point oscillation is hbar*omega/2. We can not derive (I think, perhaps I'm wrong here) a similar energy expectation value for virtual photons. KazuiKier, 20:23, 29.12.05

I'm not sure where you are trying to go with all of this. Virtual particles can be on shell and off shell, so no, they do not obey "the relativistic energy momentum relation". They also do not "have" momentum p; in fact they can "have" any momentum, because they correspond to terms in feynman diagrams where the momentm is integrated over. One could easily choose a different basis (instead of momentum) to define the domain of integration. In fact, choosing a different basis leads to other interesting phenomena, such as the infrared catastrophe. Virtual particles do not even exist in Category:exactly solvable models; they are a symptom of perturbative expansions. As such, virtual particles "do not exist", however, they are a convenient figment of the imagination, which are useful to informally describe the mechanics of certain complex calculations. linas 20:58, 29 December 2005 (UTC)

Word. –Joke 07:18, 30 December 2005 (UTC)

## Relation to Van der Waals force

The passage in the beginning of the article mentioning the Van der Waals force leaves an interesting story untold. It would be very enlightening to expand on the relation between the Van der Waals force and the Casimir effect - quantum origin and whatnot. In particular, as far as I can make out, the calculations below refer fo the Casimir force alone and do not account for a VdW force that must surely also be present in the experiment. How is it then accounted for? Are there other forces that could influence the results of the experiment?

Schnolle 08:35, 4 March 2006 (UTC)

Check out this article: [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005PhRvD..72b1301J&db_key=AST&data_type=HTML&format=&high=42e8fc0ad502668 Casimir effect and the quantum vacuum], which was cited earlier on this discussion page. It describes how the Casimir effect can be derived from either vacuum energy or Van Der Waals force, with the same end result. Apparently, it's the same force, we don't necessarily know where it comes from. But there's been enough controversy around this (wikipedia) article that I don't trust my interpretation enough to add it. --Keflavich 04:17, 3 April 2006 (UTC)

R.L. Jaffe is a trustworthy author. FWIW, I beleive that they are indeed the same thing, and there's some nice math (no reference to physics) that can be used to demonstrate this. Basically, one considers a pair of differential equations, which have solutions characterized by a spectrum of eigenvalues (the spectrum may have discrete and continuous parts). One then considers placing these two diff eq's "some distance apart" from each other, and asking how the solutions behave as a function of this distance (or more generally, some parameter). You may visualize each diff eq as, for example, the Schroedinger eqn for the hydrogen atom, and the spectrum of solutions as the discrete and continuous parts of the hydrogen spectrum. So, as one varies this parameter in the diff eqs (e.g. vary the "distance" between the "hydrogen atoms"), the spectrum of solutions will vary. The total "attractive force" is the derivative (w.r.t. the parameter) of the sum of the eigenvalues. If you can visualize this, you can see that the Casimir effect is one and the same as the van der Waals force. However, I'm not aware of any rigorous treatment of this. Thus, while "blatently obvious" to me, I also dread any potential arguments. linas 14:24, 21 April 2006 (UTC)

I am still unclear as to why the van der Waals force is mentioned as a 'similar effect': i.e., "The van der Waals force between a pair of neutral atoms is a similar effect." The van der Waals force is simply an electromagnetic force between dipoles. --Geremia 19:25, 16 January 2007 (UTC)

You are absolutely right, Geremia. Fluctuations in the electric dipole of a molecule have nothing to do with vacuum fluctuations or virtual particles or anything similar. --141.154.218.210 (talk) 05:25, 6 March 2008 (UTC)
No, not "absolutely right". It does have something to do; quite a lot, in fact. Thinking that electric fields at an atomic scale can be fully treated classically (without "virtual particles") is incorrect. If you read the cited [4], there is a nice box explaining how Casimir found about the effect investigating on the van der Waals force. And actually, his first article describing the effect [5], also in the references, is a quantum electrodynamics treatment of van der Waals force; the same treatment applied to extended plates is what we now know as Casimir effect. But I agree that the statement was too generic and the article is better off without it - or maybe with a more clear statement. --Sergio Ballestrero (talk) 17:27, 6 March 2008 (UTC)

Just to add to your discussion to clear what you have already partially said: van der Waals interaction and Casimir force are two sides of the same phenomenon, two-photon exchange between the interacting particles (atoms, nanopraticles, surfaces, etc.). The "electromagnetic" Casimir force is a particular case of van der Waals interaction, when the electromagnetic properties of the boundary of the interacting particles get to the extreme. For example, when dielectric constant tends to infinity, electromagnetic field does not penetrate inside the particles. In can be described in a mathematically simplified manner as a change of zero-point (vacuum) fluctuations. The result depends on the distance between the particles. As a result, a force occurs. This is called the Casimir force. Such a mathematical way of calculation of this Casimir/van der Waals interaction has become quite popular. It was used for other fields beyond electromagnetic, like scalar, hypothetical vector fields, curved space, non-trivial topology, etc. It sounds "sexy" but the only experimental verification has been done for the electromagnetic Casimir, which is almost trivial van der Waals force. It was a part of my Ph.D. I stopped doing it ~15 years ago. So, I do not have refs handy. My feeling is that it was described in exisiting monographs, in addition ot the refs cited above. Best, Igor

## Bad ship analogy

I removed this section:

A macroscopic effect analogous to the Casimir effect was observed by 18th century French sailors. Where two ships are rocking from side to side in conditions with a strong swell but light wind, and the ships come closer together than roughly 40 m, destructive interference eliminates the swell between the ships. The calm sea between the ships has a lower energy density than the swell to either side of the ships, creating a pressure that can push the ships closer together. If they get too close together, the ships' rigging can become entangled. As a countermeasure, a handbook from the early 1800s recommends that each ship should send out a boat rowed by 10 to 20 sailors to physically pull the ships apart.

Because of this article. It is a myth. -Ravedave 17:12, 5 May 2006 (UTC)

While it's right to remove that, maybe it's better to reword the section to demonstrate that it's a myth? After all, the Nature article mentions that it has become "almost obligatory" to mention the supposed macroscopic casimir effect as an analogy. --Keflavich 19:16, 5 May 2006 (UTC)
Go ahead, be bold. I didn't have the expertise to re-write it so I will leave that up to you. -Ravedave 20:14, 5 May 2006 (UTC)
This is OT, but y'all will probably be amused by one of my favorite "whatifs". At noon 10 April, 1912, R.M.S. Titanic (46000 tons) sailed from Pier 44 at Southhampton to commence her maiden voyage. As the ship accelerated down channel on her way out of port, under the direction of harbor pilot George Bowyer, she passed a smaller liner, S.S. New York (built 1892; about 10000 tons) moored at Pier 39. In those days, the sometimes violent effect of the passage of a large vessel in a narrow channel was not sufficiently appreciated, and Titanic was traveling too fast (six knots) for safety. The New York broke free from her moorings and was rapidly drawn toward Titanic. The dramatic scene was captured by a student riding as a first class passenger on Titanic, Francis Browne, later Fr. Browne (who was due to get off at Queenstown before the ship proceeded to cross the Atlantic bound for New York City). The ship's officers were horrified because Titanic's sister ship R.M.S. Olympic had previously been involved in a dangerous collision with H.M.S. Hawke under similar circumstances. In fact, George Bowyer had also been piloting Olympic on that occasion. Fortunately, quick action by the crew of one of the tugs attending to Titanic and some workmen who happened to be on board the New York prevented a collision. With a collective sigh of relief, the officers of Titanic proceeded on their way, whereupon, a few days later... ---CH 21:43, 5 May 2006 (UTC)
I just spotted the removal of that paragraph. I am quite surprised; I wish I could read that Science article. My direct experience with sailing and sailboats indicates that Science is flat-out-wrong, and that the removed section is correct. You need only spend an hour or two among moored boats at a harbor before you notice that, e.g. a dinghy will get pushed towards a sailboat, in such a fashion that you have to keep pushing away from it every few minutes. This is easy to spot: the owner is yelling at you not to scratch or dent the boat :) So I just can't imagine what that Science article is about. linas 18:09, 23 July 2006 (UTC)
I'd go along with Linas. It's only one guy that claims to have 'debunked' the myth. I've given references in the section on 'Ships' above. --Heron 16:44, 21 August 2006 (UTC)

## fundamental force

I don't see an explicit mention in the article concerning which fundamental force is responsible for this. My guess would be electromagnetic between the virtual particles? Btyner 17:01, 21 July 2006 (UTC)

Read the article again. The effect is not directly due to any fundamental forces; its an effect of quantization. linas 18:13, 23 July 2006 (UTC)

## Fold "overview" into intro

There seems to be no reason for the Overview section. It seems to me the information in it -- which is useful IMHO -- could easily be put right into a slightly modified intro. Any objections? Maury 21:55, 31 July 2006 (UTC)

I'd actually prefer turning that around, and folding a large chunk of the intro into the "overview" section. Introductions are supposed to be a short capsule summary, whereas the present version is anything but short. --Christopher Thomas 21:58, 31 July 2006 (UTC)

## negative energy?

It is sometimes claimed that the Casimir effect can be a source of "negative energy". As far as I know, there is no such thing as truly negative energy. In my class notes, we calculated the vacuum energy between two plates, and the vacuum energy in an equivalent space with no plates. Both quantities are positive. The Casimir energy is taken as negative just in order to get an attractive force, kind of like how classical potential energies are often considered negative relative to some reference, even though of course they aren't really "negative energies". So, is it at all valid to interpret the Casimir energy as a negative energy? Perhaps there should be a small section addressing this. It is often confused, e.g.: in this article Faster-than-light#Option_H:_Distort_the_space-time_fabric (which has numerous other issues aside from the negative energy). Rotiro

According to scientists the amount of vacuum energy contained in a volume of space as large as our own planet Earth is only enough to boil a teacup of cold water, so Casimir-tech powerplants will not solve mankind's fossil fuel problem. Others (mostly SF writers) say scientists are wrong and a pair of door-sized Casimir plates could give enough energy to drive fast interpalnetary spaceships. 82.131.210.162 09:53, 15 June 2007 (UTC)

That is a completely missleading thing to say. The ammount of energy you can make to affect the two surounding plates totaly depends on how close they are. You could fill a large room full of devises which had one centimeter in distance between the plates and get zero energy extracted from it.

You could also fill the room with devises that had only a few nanometers in distance between the plates and get a usefull amount of energy out of it. This is the reason to why it is missleading to say that so and so much region of space ( the earth for example) only can create a fixed output of energy. It totally depends on the technology we use to extract it with. As nanotechnology in the future will be many times more advanced, and able to be mass distributed, it will surly make this form of energy extraction become many times more efficient. --Nabo0o (talk) 10:54, 29 April 2008 (UTC)

Well effectively the energy you can extract from the Casimir effect is the zero-point energy of the vacuum. See vacuum energy. Two estimated values are given for the vacuum energy in the lead of that article. They're VERY different, in fact this discrepancy has been referred to as "the worst prediction in the history of theoretical physics." It seems that the boiling-a-cup-of-tea calculation used the smaller value which assumes that the vacuum energy is responsible for cosmic expansion. If, on the other hand, the vacuum energy is truly the sum of the energies of all the vacuum oscillators above the Planck scale (which gives the larger value), then yes, subatomic devices extracting zero-point energy could solve the world's energy crisis. And physicists would have to think a bit harder about what causes the expansion of spacetime. — Preceding unsigned comment added by 92.27.55.215 (talk) 15:50, 11 May 2012 (UTC)

## GA Re-Review and In-line citations

Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. Currently this article does not include in-line citations. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:20, 26 September 2006 (UTC)

## Ivory tower

I complain that the current article has no word on CE's practical uses, ranging from scanning tunneling microscopes to reactionless starship propulsion. Dammit, I just saw a tabloid report of someone's weird patent-application for a real quidditch-type flying broom, powered by a multiple-piston casimir drive hidden inside the handle-stick and effecting repulsion via a bunch of contra-rotating "Podkletnikov piezo-discs" hidden inside the bunch of fibres at the rear! Bullshit is bullshit, but if the patent is granted we have no choice but include it. 82.131.210.162 09:44, 15 June 2007 (UTC)

But if the laws of physics say it's impossible, then we say that too. Bullshit is bullshit, which is why it is made perfectly clear in most well-reviewed articles that even patent-earning inventions that cannot work, cannot work. SamuelRiv 00:45, 1 December 2007 (UTC)

## Levitation

Here's an article that says the Casimir effect can be used for levitation:

Yes, the reversal of the Casimir effect does it. This groundbreaking info should be added, stat. Cowicide 18:06, 7 September 2007 (UTC)
It was added several weeks ago when it was breaking news. See 'reversal', down near the bottom of the page. Also, note that "levitation" is slightly misleading... Levitation on the nano- scale, yes. Flying cars, not so much. :-) Angus Lepper(T, C, D) 19:49, 7 September 2007 (UTC)
Is this really what is going on in this video then? Btyner (talk) 00:03, 20 October 2011 (UTC)
No, it appears that Tel Aviv University is trying to commandeer the terminology to reenergize interest in decades old superconducting levitation ideas. Note they own the website http://www.quantumlevitation.com/ which was registered just last month. 85.170.167.60 (talk) 01:06, 20 October 2011 (UTC)

## Merge Casimir Force

I'm suggesting that Casimir force is merged into this article, the Casimir effect. Casimir force is looking lonely and could easily find a home in this article. --h2g2bob (talk) 09:54, 26 August 2007 (UTC)

## Gauge blocks

Could the adhesion of wrung gauge blocks be a manifestation of Casimir effect? 71.116.83.87 03:23, 22 October 2007 (UTC)

Let's see....Baez calculates that for parallel surfaces 1 square meter at 1 micron separation, the attractive force would be .13 grams. Rectangular gauge blocks have an area of about 35mm x 9mm, so the force is 3200X lower than .13 grams. But the measured separation of wrung blocks is 10nm - than makes the force 100^4 = 100,000,000X higher! This nets out to 31,250 x .13 grams = over 4kg. (NIST says a wrung force up to 300N or 30kg, which corresponds to a wrung separation of 6.1nm). I guess it could be. —Preceding unsigned comment added by 64.180.6.212 (talk) 05:02, 16 March 2008 (UTC)
This is kind of surprising to me! We can see an example of virtual photons creating a force we can feel in something we can hold in our hands? This should be in the article.

## Not accessible

{{ safesubst:#invoke:Unsubst||$N=Technical |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} It should be explained in the intro whether this is a pull-together or push-apart force. A diagram or two showing some simple situations and the resulting forces would be immensely helpful. -- Beland (talk) 00:34, 18 November 2007 (UTC)

## Semi-protection

I have semi-protected this article for 1 week, due to recent high level of vandalism from newbies and IPs. Bearian (talk) 02:13, 1 February 2008 (UTC)

The use of "newbies" and "IPs" here constitutes registered editor snobbery. —Preceding unsigned comment added by 86.138.8.24 (talk) 21:32, 3 January 2010 (UTC)

## Delisted from GA

In order to uphold the quality of Wikipedia:Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 12,

2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR.

The major reason for delisting is a lack of inline citations throughout the first half of the article. Note that inline citations where only required by Good article criteria starting in 2006, so this article may have passed prior to that change.

Additionally, this article's use of jargon renders it less accessible to a general audience. Terms such as "resonance" and "all-pervasive energy fields" need to be avoided if possible or explained if they're crucial to the subject.

Once these changes have been addressed, if the article meets all of the wp:Good article criteria, it should be renominated. --jwandersTalk 22:53, 12 February 2008 (UTC)

For the "jargon", I've tried to reword the introduction (I didn't like it either); but the matter of the fact is that the Casimir effect is intrinsically a second quantisation effect, and cannot be "reduced" to something conceptually easy for the layman. Explaining what a quantised field is in few words is even more difficult, I'd say it's better to leave it and link to the proper pages where people can learn about quantisation; the text below anyway gives what I would consider the simplest possible explanation. But maybe someone is a much better writer than me and will manage to explain it in few words ;-) - Sergio Ballestrero (talk) 19:26, 23 February 2008 (UTC)
Yeah, you're right that the bulk of this article will never be accessible to a general audience. I think we could at least give them a couple of sentences in the lead before we delve into heavy jargon, though. For example, what do you think of opening with:
The Casimir effect or Casimir-Polder force is a highly advanced subject in the study of physics. It defines the how the interactions between individual particles of matter effect the smallest amount of energy that matter can contain.
In physics, the Casimir effect or Casimir-Polder force is a physical force exerted between separate objects due to their influence on the zero-point energy of a quantized field in the intervening space between the objects.
I'm sure that description isn't as precise as some people would like it, but when speaking to a general audience precision isn't as important as clarity. Thoughts? --jwandersTalk 20:55, 23 February 2008 (UTC)
Well, if that is what you got from what I wrote, then I really must rewrite it, because didn't do a good job! :-) Because the point of the Casimir effect is that is really does not involve matter; the matter (the conductor) only changes the boundary condition for the field; and the minimum energy of the EM field (in the space - it's not matter what counts) is still infinite, which is still renormalised to zero... a real mess, I mean, but it works. I agree with you on clarity, just let's try not to make it wrong. I've given it another shot, trying to use the "virtual photon" picture which may be easier, and comparing to the classical picture, to let readers understand what's so special about it. Let me know what you think... - Sergio Ballestrero (talk) 11:59, 24 February 2008 (UTC)
Wow, completely unintended, but what a perfect example of why clarity is important, even between people with a physics background! I really like what you've done with the first para, much gentler than before. I polished it a bit further. For example, the expressions "in a quantum mechanical treatment" I think would be mis-leading to a lay reader, as they wouldn't be used to "treatment" meaning "mathematical study". I just imagine I'm trying to explain stuff to my parents, and suddenly it's much easier to work out what not to say ;-) --jwandersTalk 16:43, 24 February 2008 (UTC)
Well done, I like it! Now let's wait for the bashing by a theoretical physicist :-) - Sergio Ballestrero (talk) 22:19, 25 February 2008 (UTC)
Now, coming to the inline citations. It's mostly for myself to understand and possibly improve other articles, because the Casimir effect is not really my backyard, so I wouldn't be of much help. The way I understand the guideline (provides in-line citations from reliable sources for direct quotations, statistics, published opinion, counter-intuitive or controversial statements) if something is well established, it's not really necessary to spend time on this; and the basic physics of the Casimir effect are well established, both in theory and by experiment, and references are given in the "Further reading". The "Vacuum energy" section may seem lacking, true, but since it is (should be) just a summary of the main article, the reference should be there instead. The more "controversial" parts like reversal, faster than light, seem to have sufficient references, and to be written in a sufficiently skeptical tone. I know that cranks are attracted to the Casimir effect, so one has to thread carefully, but maybe it's not necessary to overdo it. - Sergio Ballestrero (talk) 12:33, 24 February 2008 (UTC)
The inline citation guideline in the good article criteria is how we try to ensure GAs meet Wikipedia's verifiability policy. The goal as I think of it is that the reader should be able to check every fact in the article in an independent, reliable source. How an article achieves this is up to the editors, but the preferred method is through lots of inline citations. Inline citations make it crystal clear where the fact they label has come from, whereas a general "references" section for the whole article leaves a lot of ambiguity.
You're right that articles on excepted scientific subjects are a bit of a special case. My advice would be to find two or three good text books, and put an inline citation to all of them at the end of every paragraph that covers the basic material (you can use the <ref name="label"> tag for repeated refs). Paragraphs that go beyond the basics or discuss controversial theories will then be referenced to the specific arguments.
Also careful with that "sufficiently skeptical tone" ;-) If you merely cite the arguments on each side of a debate with appropriate sources, the reader should develop their own skepticism; if you tried to impart it through the tone of writing, many readers will instinctively fight against it, and wonder if the "cranks" might have something you're trying to cover up! --jwandersTalk 17:00, 24 February 2008 (UTC)
Sad but true, I have to agree. You've made good points above too - especially the book references, much better than articles, which often are also not accessible for free to those who do not belong to an academic institution. - Sergio Ballestrero (talk) 22:19, 25 February 2008 (UTC)

## The Casimir effect and the quantum vacuum

The Casimir Effect and the Quantum Vacuum by R. L. Jaffe was uploaded to the arXiv in March of 2005 and published in Phys. Rev. D in July. According to the paper:

• The Casimir force is just like any other QED force; it can be derived without any reference to vacuum energy (vacuum fluctuations, zero point energy) and provides no evidence one way or the other for the reality of vacuum energy. It is a van der Waals force.
• The Casimir force between parallel plates has the unusual property of remaining finite in the α → ∞ limit. The result obtained from Casimir's vacuum-energy argument is that limit. In other similar cases (like the Casimir pressure on a conducting sphere) the force diverges in the limit and the vacuum-energy derivation doesn't work at all, while the ordinary approach still does. Jaffe describes the vacuum-energy argument as "heuristic".
• Casimir originally derived the magnitude of the force using ordinary methods, and the unusually simple form of the result inspired him to find the vacuum-energy derivation for which the force is now famous.

The paper has so far accumulated 27 citations, none of which rebut (or claim to rebut) any part of it. A couple of the papers cite Jaffe in support of a conclusion that directly opposes Jaffe's, presumably out of simple carelessness. A couple of them give the usual vacuum-energy explanation and then suggest reading Jaffe for a contrary view, without elaboration. In one paper I wasn't able to find a reference to Jaffe despite the CiteBase listing. The rest cite him in support of their own arguments.

As far as I can tell Jaffe's claims are not even controversial, much less wrong. He's a respectable physicist and PRD is a respected journal; if he'd made a mistake I would expect someone to have pointed it out by now, at least on the arXiv. He wrote in a matter-of-fact style suggesting that he didn't himself think that what he was writing would be controversial. As far as I can tell, everyone who has carefully considered his arguments has concluded that he is correct.

As such I think the Wikipedia article needs to be rewritten to completely remove the claim that the Casimir effect requires the existence of zero-point energy. Ideally we should also state outright that the Casimir effect doesn't prove the existence of zero-point energy, though I would understand if people are concerned about the lack of accessible references for this. But at the very least the current claims about zero-point energy need to be deleted because, all issues of verifiability aside, they're not correct.

Jaffe's paper is already cited in the article (in the introduction, as evidence of a controversy which I don't think exists); it's also mentioned in two earlier threads on this talk page: 1 2. -- BenRG (talk) 18:33, 6 March 2008 (UTC)

As far as I know, Jaffe's paper is not particularly controversial. You can't use Casimir forces to prove the existence of a zero-point energy per se, although they certainly establish an interaction energy (basically, you can only measure energy differences, or energy derivatives in the form of forces, so the raw vacuum energy cancels out). On the other hand, it's also well-established that the QED path-integral/partition-function force viewpoint is mathematically equivalent to differentiating Casimir's frequency-summation calculation (and also to Lifshitz/Pitaevskii/Dzyaloshinskii's field-fluctuation viewpoint, for that matter). So, the Casimir force is at least consistent with the zero-point energy picture. — Steven G. Johnson (talk) 00:30, 9 July 2010 (UTC)

## Derivation

The derivation of the Casimir formula is at least incomplete and lacks simplicity. It needs to be improved or removed in favour of a good and accessible reference. Aoosten (talk) 23:18, 17 June 2008 (UTC)

I choose for improving the existing text instead of such a dramatic act as removing this text altogether. I should add that it is very much debatable what constitutes a rigorous, or "complete", derivation of the Casimir formula; quantum electrodynamics is not as closed a subject matter as one might imagine or wish: it is a hotchpotch of things that turn out to work, but rigorous in the strict sense of the word it is not. In the Foreword of Landau and Lifshitz' Quantum Electrodynamics (Volume 4 of Course of Theoretical Physics) one reads: "This branch of theoretical physics [i.e. relativistic quantum theory] is still far from completion, even as regards its basic physical principles. ... But even quantum electrodynamics, despite the remarkable achievements of the last twenty years, still lacks a satisfactory logical structure." Kind regards, --BF 04:47, 18 June 2008 (UTC).

## Popular Culture section

I've added the reference to the Orientation video from Lost. However I don't know if a reference can be cited for "The Big Bang Theory" bit. If it can't be found, I say we delete that bit and leave just the information about Lost.StorminMormon (talk) 06:29, 4 May 2008 (UTC)

## New image

Please comment on corrections / alterations you would like to the new images at Wikipedia:Graphic_Lab/Images_to_improve#Casimir Effect. Please provide captions that correctly distinguish between the two. I think the article should use these images as lead images, rather than tucked away half way down the page. Thoughts? Dhatfield (talk) 11:15, 28 June 2008 (UTC)

## Need explanation of the thermal aspect of the Casimir effect

The Wikipedia article confirms my understanding that the Casimir effect results in a net attractive force between metal plates.

However, United States Patent #7,379,286 has recently been granted to Jovion Corp., which is associated with the University of Colorado, to exploit a different aspect of the Casimir effect. (See [6]). Namely, a thermal effect, by which gas passing through Casimir "strips" or "tunnels" is heated.

The Wikipedia article does not explain how the Casimir effect could have a thermal aspect like this. Can someone add this to the article please?199.46.199.231 (talk) 19:20, 5 February 2009 (UTC)

Casimir effect restricts longer wavelength vacuum flucuations between 2 closely spaced conductive plates. The plates will be drawn together due to this difference in ratio of short to long vacuum flucuations between the plates VS outside the plates. If the plates are braced apart you create a permanent exclusion zone to the longer wavelength vacuum flucuations where gas atoms experience an anomalous effect broiled in controversey. Dr Mills of Black Light power coined the term "hydrino" with very specific properties outlined in his classical Grand Unified theory most controversial of which is a subzero state orbital. Professor Moddel and Bernard Haisch do not describes a hydrino as defined by Dr Mills; Their SED based theory describes different properties and the way they arrive at it is very different but they also describe an atom that "spins down" below zero state. I contend that the orbital is not subzero but rather temporal axis displacement as already suggested by Professor Jan Naudts in wikipedias hydrino controversey timeline. My only contribution to his suggestion is that a covalent bond is essential to "lock" orbital orientation while inside the exclusion to turn the covalent orbitals into a bucket that forces chaotic Vacuum flux to accumulate organized boundaries as the new molecule tries to exit and finally causes the bond to fail releasing the signature black light plasma as nature restores the atoms to mon atomic energy levels. theoretically the heat could keep the atoms disassociated and the procedure could repeat endlessly supported by the statistical proportion of atoms reforming as H2 while inside an exclusion field Vs outside - Thermally this may actually be a balancing act to prevent the cavities from overheating and melting closed. —Preceding unsigned comment added by Froarty (talkcontribs) 18:38, 6 March 2009 (UTC) Froarty (talk) 20:45, 6 March 2009 (UTC)

## Wording of the article

(Comments moved from the article page. --Christopher Thomas (talk) 20:08, 11 July 2009 (UTC))

In physics, the Casimir effect and the Casimir-Polder force are physical forces arising from a quantized field.

Well, the magnitude of the force is clculated using a quantized field. It ceratinly does not arise from an abstract concept...I would change this sentence. This would be like saying the attraction between planets is a result from Newton´s universal law of gravitation. The law decrbies what happens; is not the cause of the phenomena.

When this field is instead studied using quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force[1]—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization.

Again, attraction between plates is not the result from a mathematical procedure (used to quantize a field). --—Preceding unsigned comment added by 190.190.87.136 (talk) on 11 July 2009 (moved from article space)

## Casimir´s calculation

In a moment the article says that the sum may be understood to be the Riemann zeta function; it previously says the sum may be analitically continued. It is true that using a general expresssion for the Zeta function, it reduces to the sum when the exponent p is greater than 1. But not for p=-3. So, as written, the calculation is not correct. That is, the sum with p=-3 diverges. At the beginning of the caculation, the sum should be replaced in some way by

${\displaystyle \zeta (p)\!}$

and the manipulation of the expression I think should be done from there. —Preceding unsigned comment added by 190.190.87.136 (talk) 16:33, 12 July 2009 (UTC)

Ok, So the calculation described in article is NOT Casimir's Calculation. He first starts with a conducting plate in a cube of side length L. 99.250.15.176 (talk) 00:00, 16 March 2010 (UTC)

That is not the point. The point is that it seems the calculations in the article are not rigorous, whereas the result can be obtained riguroulsy (using an ultraviolet cutoff, but not suddenly turning a divergent term into a finite one).--190.188.0.22 (talk) 19:36, 17 March 2010 (UTC)

There are many ways to regularize the divergences (at least for interaction energies and forces involving rigid-body motion). Rigorous zeta-function regularization was described in G. Cognola, E. Elizalde, and K. Kirsten, "Casimir energies for spherically symmetric cavities," J. Phys. A. 34, 7311-7327 (2001). — Steven G. Johnson (talk) 00:11, 9 July 2010 (UTC)

## Added external link to Babb bibliography

We are now in 2009 and it seems that this article truly needs a link to an current i.e. up-to-date bibliography on the Casimir effect. Watch out for developments on a repulsive Casimir effect. That's in the works and it will be a breakthrough if they get a result. - Tony 98.234.179.52 (talk) 23:07, 20 September 2009 (UTC)

It is possible (in theory) to obtain a repulsive Casimir effect even in vacuum (arXiv:1003.3487) and experimentally repulsive effects have been obtained in fluids. However, there is a proof that, in vacuum (and air is essentially no different) for metallic/dielectric objects of any shape, you cannot obtain a stable equilibrium with Casimir forces (arXiv:0911.5364).
I agree that there have been a lot of recent developments on Casimir effects in the last few years that are not yet in the article, however. — Steven G. Johnson (talk) 00:08, 9 July 2010 (UTC)

## Can it be interpreted semiclassically?

A newbie inserted this text:

In fact "Casimir's original goal was to compute the van der Waal’s force between polarizable molecules" of the metallic plates. Thus it can be interpreted semiclassically, without any reference to the vacuum energy of quantum fields.

—no citation

I do not think this is true. Can anyone find a good cite? Bearian (talk) 18:54, 26 September 2009 (UTC)

Jaffe could serve as a reference for most of it (in fact the part in quotes appears to be a direct quote from that paper), but the Casimir force is a loop effect and as such I don't think it has a classical counterpart. I'm not sure what "semiclassical" means here. -- BenRG (talk) 23:19, 26 September 2009 (UTC)

The reference is the same used few line above, that is R. L. Jaffe(2005)"The Casimir Effect and the Quantum Vacuum" I have quoted a sentence of the paper and summarized the meaning. You could also find the word Casimir in the paper to have a confirmation of my addition to the article. http://arXiv.org/pdf/quant-ph/0609163

Van der Waals is a classical force, the reference to the vacuum energy, a typical quantum phenomon, is not necessary to derive the Casimir effect. By the way I dropped the adjective "semiclassical".

For further clarifications please ask me. -- N4tur4le (talk 23:26, 29 September 2009 (UTC)

There is a Classical Casimir Effect or "critical Casimir effect' that is a classical analogy to the quantum effect. I added a section describing its detection to satisfy folks who had heard of a classical counterpart. Canuck100 (talk) 18:05, 21 October 2009 (UTC)

I Have removed the "critical Casimir effect" Section. The experiment you cite does not measure the Critical Casimir effect like you say. From the article:

"Finally, other effects are sometimes named after Casimir, which are not quantum electrodynamic in origin but rather the result of thermodynamic fluctuations. The critical Casimir effect is one such phenomenon (see, for example, ref. 29 and references therein); however, this effect is not present in our experiment because it occurs only in binary liquid mixtures near a critical point." Nature 457, 170-173 (8 January 2009) JabberWalkie (talk) 00:31, 16 March 2010 (UTC)

Note that Van der Waals forces are not purely classical phenomena. They include London dispersion forces, which arise from fluctuation-induced dipole moments that occur even in the limit of zero temperature as a consequence of purely quantum effects. And these forces, in turn, are just a short-range approximation (neglecting retardation effects) of Casimir effects (called Casimir-Polder forces for small particles). And although you can derive Casimir forces without directly employing a vacuum energy per se as Jaffe has pointed out, you still need quantum fluctuations.
Finally, it's incorrect to pose "thermodynamic fluctuations" as contrary to "quantum electrodynamic" effects: Casimir effects are precisely thermodynamic fluctuations (including quantum statistics, of course) that arise in the electromagnetic field operators from quantum electrodynamics. (The entire Lifshitz approach centers around fluctuation statistics of the electromagnetic field. Most commonly, however, these fluctuations are evaluated at zero temperature because the temperature corrections are usually near-negligible for forces at measurable lengthscales. The frequency-summation expression in the article is a zero-temperature expression, for example.) — Steven G. Johnson (talk) 23:48, 8 July 2010 (UTC)
Well as I was citing a relatively recent paper and you take up a contrary position, I must assume you have supporting evidence/articles. That being the case it is clear the subject is still a mater of debate, and hence should not be included in the article. JabberWalkie (talk) 01:32, 9 September 2010 (UTC)
I think the sentence you quote in the paper was just poorly phrased, not that this aspect of the physics is particularly controversial. — Steven G. Johnson (talk) 04:44, 9 September 2010 (UTC)

## Negative index metamaterials

Talking about linking the articles over at Negative index metamaterials. Strange things happen when the laws of physics are reversed. Hcobb (talk) 05:04, 27 March 2010 (UTC)

Putting aside practical concerns about making such a metamaterial operate at the lengthscales where Casimir forces become relevant, it turns out that even in theory these don't seem to have any dramatic or interesting impact on Casimir forces. Basically, negative effective indices occur only over narrow bandwidths as a consequence of resonant effects, whereas Casimir effects rely on a broad-bandwidth response that turns out to wipe out the effect. (Mathematically, there are more precise ways to see this based on analytic continuation to the imaginary-frequency axis.) See:
F. S. S. Rosa, D. A. R. Dalvit, and P. W. Milonni, "Casimir-Lifshitz Theory and Metamaterials," Phys. Rev. Lett 1000, 183602 (2008).
Note also that there is a recent proof that no metamaterial made of metal/dielectric constituents can yield a repulsive interaction between two planar surfaces in vacuum (at least, not in the regime where a metamaterial description is valid). See arXiv:0911.5364.
— Steven G. Johnson (talk) 00:02, 9 July 2010 (UTC)

## Summing?

The article currently says "Summing over all possible oscillators at all points in space gives an infinite quantity." But the article provides no rationale for this sum. Intuitively, the sum would be meaningful if energy is not shared between the oscillators, but it is hard to imagine a universe where everything in the universe is totally decoupled from everything else. Not only that but when you physically combine oscillators you reduce their minimum frequency. So, I think that this concept needs a little elaboration. 159.54.131.7 (talk) 15:24, 17 May 2010 (UTC)

## Recent progress in numerical calculation for non-planar geometries

It might be nice to mention the dramatic progress in the last few years on computations of Casimir forces for complex non-planar geometries. (Especially since the current "More Recent Theory" section describes developments that are 50 years old!!)

It's gone from virtually nothing nonplanar 10 years ago (aside from small perturbations around planar cases, or even crude uncontrolled heuristic formulas), to the first cylinder-plate calculation 4 years ago (by Emig, Kardar, Jaffe, et al), to application of advanced computational methods from classical EM in order to compute Casimir forces for essentially any geometry demonstrated in the last 2-3 years.

There are a couple of ways to look at it. First, once you express the unknowns approximately (to any desired accuracy) in a finite basis, the complicated functional path integrals can be turned into log determinants, and the matrix you are taking the log determinant of is essentially a classical scattering matrix of some sort. Second, one can instead think about evaluating the mean fluctuations of the fields via the fluctuation dissipation theorem, which re-expresses the correlation functions in terms of classical Green's functions (fields from currents) that can be solved by standard classical methods. (The two approaches turn out to be mathematically equivalent in the end, and are also equivalent to summing frequencies ala Casimir.) The main wrinkle from the point of view of classical EM calculations is that it turns out that you need in practice to evaluate the scattering problem at imaginary or complex frequencies (where the problem becomes much nicer numerically and analytically), and you need to solve many classical problems for a single Casimir problem.

There is a new book on Casimir Physics coming out (in the Lecture Notes in Physics series) on the subject of recent Casimir developments. I was invited to contribute a chapter on numerical methods, and I've posted a preprint of my review article (accepted, in press) on arXiv arXiv:1007.0996. This might make a useful reference for the Wikipedia article (although I can understand if you want to wait until the book comes out in print), or in any case the references contained therein (see e.g. the references at the top of page 2) should give an idea of the scope of the recent developments.

(I don't want to add it myself, at least not without another editor taking a look, because of the possible WP:COI since my group is involved in the recent numerical developments.)

— Steven G. Johnson (talk) 22:31, 8 July 2010 (UTC)

## Confusing intro: "this field"

Currently the intro dives into the material with this bit:

without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them.[1] When this field is instead studied using quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field

The use of "this field" halfway through doesn't make any sense, since it doesn't have a clear prior referent. I'm guessing, knowing nothing about the topic, but based on some guessing about how wikipedia articles evolve, that it must refer to the previously mentioned "quantized field", but note that the previous sentences to "this field" refer both to a non-existent external field and a non-existent classical field. So it's rather confusing.

Moreover, if you're going to contrast with classical theory that predicts no field and hence no forces, then you have to be explicit about what the quantum theory is postulating and predicting. If the idea is that given the exact same physical setup, quantum electrodynamics says that there is a quantized field and therefore an observable force, it should say that, in parallel to the classical saying "no external field => no "local" field => no force". Like, I have no idea what the actual idea here is, but it's either something like "but since there's always a quantized field, then this means the plates affect that, and a force arises", or if the quantized field arises in this experiment for some reason that should be addressed, or if the idea is that there's always a field even classically, it's just 0-valued or some such, then say that, but don't say 'no field'. Or don't compare it to classical theory, and just drill down into the forces arising from quantized field, or otherwise rewrite it.

I'm guessing that this would be a lot easier to understand if I already knew what 'second quantization' was. But note that currently, clicking through the link to 'second quantization' leads to an article that does not allow quickly determining what second quantization is; the "definition" is buried in the second paragraph there, with confusing hedging about early literature vs. modern interpretation that guarantees excessive opacity. (And although I can understand the first paragraph there, I don't know what a "field variable" is, and the link only links to 'field', which I know what it is). Which is why I still haven't figured out what the intro is trying to say so that I can figure out what it means by 'this field'. I'm sure if I re-read it three or four times and thought harder I'd get it, but I'm pretty sure it could be easier. 24.16.57.110 (talk) 18:24, 20 July 2010 (UTC)

## Temperature

Does not the expression, for the Zero-Point Energy, assume an Infinite Temperature, and ensuing Uniform Occupation of States (N_n = 1 for all n) ?? Why wouldn't the ZPE have a finite temperature, say, 2.7 K ??66.235.14.162 (talk) 13:27, 17 April 2011 (UTC)

Quite the opposite. The expression here is for zero temperature, and the half-photon occupation of each state is the quantum ground state. At a nonzero temperature, there is an additional factor of ${\displaystyle \coth(\hbar \omega /2kT)}$ (from the Bose–Einstein distribution for occupation of states above the ground state) multiplying the mode summation. (For ${\displaystyle T\to 0^{+}}$, ${\displaystyle \coth \to 1}$.) See e.g. Lifshitz' Statistical Physics text. — Steven G. Johnson (talk) 16:43, 17 April 2011 (UTC)

## Dynamic Casimir effect experiment in Chalmers University, Sweden.

In the section "Analogies and the dynamic Casimir effect" it is said that "An experimental verification of the dynamical Casimir effect is still lacking".

What about the recent experiment (June 2011) at the Chalmers University of Technology in Gothenburg, Sweden, where moving mirrors produced real photons from virtual particles (from the vacuum)? The experiment was reported on Nature and Scientific American. Isn't that an experimental verification of the dynamical Casimir effect? Siaraman (talk) 11:54, 28 June 2011 (UTC)

## How to make it useful.

Making the Casimir effect useful requires preventing the plates from slamming together. That can be done by using repulsive magnetism and keep the outermost plates in place mechanically, or by mechanically holding them in one or two edges but leaving the vacuum between them free. And since they are not supposed to slam together, the plates can be replaced by other mechanisms. One is cylinders within cylinders. That has been tested with two layers, but making a strong effect would require more layers. Another possibility is to use a solid object honeycombed with microchannels or other microscopic holes. Either possibility would enable the use of vacuum energy and manipulation of the vacuum itself.

217.28.207.226 (talk) 09:20, 14 September 2011 (UTC)Martin J Sallberg

## Units for Formula

For the final formula that is produced by the mathematics, what are the units? It may be clear that they are the SI base units, but this will not be clear to some viewers, esp. considering the discussion of nanometers earlier in the article. — Preceding unsigned comment added by 164.107.188.243 (talk) 20:14, 30 January 2012 (UTC)

## Spurious precision

It is rather amusing that the article says "In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.325 kPa), the precise value depending on surface geometry and other factors." while quoting a value precise to 6 figures. I rather doubt that the exact value of the force between two conducting plates 10 nm apart is as quoted. Such spurious accuracy is to be avoided. treesmill (talk) 11:53, 20 February 2012 (UTC)

The distinction has to be made between the theoretical prediction for infinite, perfectly conducting planes, which is an exact analytical result, and the force for the closest physical analogue (where even obtaining 5% accuracy in the theoretical predictions is somewhat controversial, e.g. due to uncertainties in geometry, surface roughness, and materials properties). — Steven G. Johnson (talk) 18:04, 20 February 2012 (UTC)
Still, the lead of this article doesn't seem the right place to give the equivalent of 1 atm in 3 other units (101.325 kPa, 1.01325 bar, 14.69595 psi). And some readers may think that those values represent the actual calculated or measured Casimir force. Unless I'm mistaken and by some amazing coincidence it turns out to be equal to 1.000000 atm at 10 nm... Ssscienccce (talk) 15:39, 12 January 2014 (UTC)
Template:Done Rather than arguing between "101kPa" and "100kPa", I've simply removed the part in brackets (superfluous because atm is already wiki-linked, so anyone who wants it in other units need only click it). Cesiumfrog (talk) 20:50, 12 January 2014 (UTC)

## Prospects for energy

This section appears to have been created mainly to promote a particular patent. RockMagnetist (talk) 19:26, 26 October 2012 (UTC). It’s a new source of energy and the first nanoactuator, which generate this energy by itself. Anatolii j — Preceding unsigned comment added by Anatolii j (talkcontribs) 17:17, 29 October 2012 (UTC)

## Wormholes

This entire section exists on the existence of one short article of speculation on various science fiction topics by well-known theoretical physicists in 1988.[2] No serious theoretical or practical connection has been made between the science fiction concept of wormholes and the quantum mechanics Casimir force before or since. This section has been tagged for more sources since 2009. I am removing this Wormholes section pending the inclusion of scholarly WP:RS sources for it. Otherwise we should include it in a speculation section for this article. Aldebaran66 (talk) 18:21, 26 January 2013 (UTC)

## Water wave analogue: was that known before Casimir?

Was the attraction of plates in vibrating water known before Casimir studied plates in a vacuum? 216.31.219.19 (talk) 21:36, 18 June 2013 (UTC)

## A way to calculate the effects of quantum Casimir forces

just a reference that could be added to the article:

A way to calculate the effects of quantum Casimir forces http://www.sciencecodex.com/a_way_to_calculate_the_effects_of_quantum_casimir_forces

## Should there be a "Cultural References" section?

In the movie Atlas Shrugged: Part I depicts two of the protagonists, Hank Rearden and Dagney Taggert, finding the remains of am abandoned motor that runs off the the Casimir effect. As I recall, in the book, Atlas Shrugged, the motor worked off of deriving energy from static electricity the air. It's a long book, and I did not find the exact quote. Maybe someone more familiar with the book will help on this.

Notice that the book was published in 1957, after the discovery of the Casimir effect.

Should this information be in the main article under "Cultural Reference"?

Josh-Levin@ieee.org (talk) 12:03, 24 August 2013 (UTC)

## bad reference "Chip harnesses mysterious Casimir effect force"

The ref is just a news stub. This is way outside my domain, so I won't post these myself in case they are older/separate work, but I'd guess these are better refs. MIT Review article and Zhou et al. (2013) - Casimir forces on a silicon micromechanical chip — Preceding unsigned comment added by Aaport (talkcontribs) 19:39, 3 September 2013 (UTC)