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The Casimir Effect 138

Posted by michael from the touchy-feely dept.
HobbySpacer writes "A recent article in Physics World provides a lucid description of the the Casimir effect, which is an attractive force between two surfaces caused by electromagnetic fluctuations in the vacuum. The article discusses some practical application such as the nanotech machines mentioned here earlier."
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The Casimir Effect More

The Casimir Effect

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  • isn't the force two objects excert on eachother called gravity? seriously though, I wonder how these forces are effected by non-vacumes - i.e. a virtual vacume with one lonely hydrogen moluecule. Is the H2 excerting forces on the two mirrors? are these forces the same magnitude as that the mirrors excert on eachother in pure vacume? more? less? 1/distance squared?
    • all objects exert gravity.

      The Casimir effect is something beyond that.

    • Re:forces between objects? (Score:4, Informative)

      by jgardn ( 539054 ) <jgardn@alumni.washington.edu> on Saturday September 07, 2002 @04:19PM (#4213197) Homepage Journal
      Physicists are able to take into account all the forces interacting between two objects. It is exactly this precise accounting that led Casimir to investigate the experimental results that were contrary to their predictions.

      Gravity is proportonal 1/d^2, while the Casimir force is proportional 1/d^4. Therefore, the Casimir force is much stronger at smaller distances, but practically non-existant at larger distances. As you halve the distance between two objects, the gravity increases by 4 times, but the Casimir force increases by 16 times.

      The other force they mentioned is the Van der Waals force, which is really an electric force caused by the polarization of atoms and molecules at very small distances.

      At the scale they were dealing with, the mass of the objects was so small and the distances so short that the Van der Waals force and the Casimir force was much much greater (>>) than the force of gravity.
      • I'm pretty sure that the Casimir force was originally "discovered" as a natural consequence of quantum field theory. It was only recently (something like two years ago) that it was first measured by an experiment at Los Alamos. It was very exciting when it was measured because this aspect of quantum field theory predicts that the vacuum of space contains an infinite background energy and that the Casimir force is actually due to the charged plates restricting the wavelenghts of photons which could be created and anhillated by the vacuum. By imposing this boundary condition, the pressure from these photons on the inner surfaces of the plates is less that the pressure on the outer surfaces of the plates and thus the force pushing the plates together.
        • Yes. That is exactly what is happening. However gathering energy from such a source is going to be almost impossible. Just like thermodynamics breaks down on a very small level, so does quantum mechanics. You get to a point where nothing can be predicted, things are being created and destroyed, conservation of energy is violated constantly, and all the laws of physics are turned upside down and become meaningless traffic laws. But if you scoot back and look at the larger picture, you'll see that there is a pattern to this madness. You see how a photon was created and destroyed, but how it really was "moving" from one localized area to the next, and it really was a "real" photon, transferring energy from one spot to the next. It has a life beyond the small localized areas. While at this level, things aren't as predictable as you hope (which hole did the photon travel through?), it is still predictable to a large degree. Then you scoot back some more, and the probablities begin to add up, and things begin to become predictable with high accuracy. The laser beam doesn't change course, the people around you don't vanish and reappear, and you can be sure that there is going to be a sunrise tomorrow. The point is, even in thermodynamics, you can get violations of energy conservation -- or so it seems. The problem is that you were only looking too close at what was happening, and by looking to close, things don't make "sense" anymore. Things are truly random. However, the rolling of those millions and billions of dice end up with predictable results. Gathering energy from these statistical anomolies is going to be as possible as predicting with high accuracy the roll of a die. Until you can sit on the throne of Einstein's God who doesn't roll dice, it will be impossible.
      • I predict the existence of forces which are proportional 1/d^8, 1/d^16, 1/d^32, 1/d^64,... Gravity then would come from the fourth folded-up spatial dimension, the Casimir force from the fifth...

    • Force due to non-vacuum (Score:2, Interesting)

      by jgardn ( 539054 )
      The forces between two plates in a non-vacuum are difficult to predict, at best. At that scale, the laws of thermodynamics begin to become inapplicable.

      However, you can use the ideal gas equation to get an idea of what is happening:

      PV = nRT

      P is the Pressure, V is the Volume, n the number of molecules of gas, R the Rhydberg constant, and T the temperature. If you hold the temperature and the number of molecules constant and then decrease the volume (the case you mentioned above, where a single hydrogen atom has gotten in between the plates), the pressure will begin to grow linearly.

      Because you are moving the plates together, the volume reduces in proportion to the distance between the plates. This means the pressure rises in proportion to the distance between the plates. I'll also make an assumption (a dangerous thing) that the temperature will remain constant because we'll give it time to cool off, and the number of particles remain the same. The last assumption is due to the plates being much larger than the distance between them, so only a very few number of particles on the edges will ever get to escape.

      The force on the plates due to pressure is only the area of the plates times the pressure. As the pressure rises, the force rises proportionally.

      Because the plates are attracted by the Casimir effect, and the casimir force grows quadratically as the plates draw nearer, eventually, even the pressure will be insignificant compared to the Casimir force. I think that's a pretty good conclusion using rough estimates.

      In reality, you can't control the number of particles in the system unless you build some sort of box to hold stuff in between the plates. Also, the laws of thermodynamics depend on there being a large number (millions) of particles, so you can't use them with nay degree of reliability in these kind of situations. My conclusion is suspect, because it is really only an educational guess.

      It is much easier to make a vacuum, thus making the problem a lot easier.

      • Re:Force due to non-vacuum (Score:4, Insightful)

        by Idarubicin ( 579475 ) on Saturday September 07, 2002 @07:50PM (#4213882) Journal
        However, you can use the ideal gas equation to get an idea of what is happening:

        PV = nRT

        Er. Well, not quite. The ideal gas is exactly true only under a certain set of limiting conditions. These conditions include high temperature and low density, among others. For typical gases (oxygen, nitrogen, helium, carbon dioxide--you know, the stuff that comes to mind when we think 'gas') it's not a bad approximation at room temperature and one atmosphere of pressure. Allow a ~10% engineering fudge factor and you're pretty safe.

        In the experiment you described, the particle density would become extremely high. A number unplesant (from a calculation standpoint) effects would make themselves known. For example, the volume occupied by gas molecules would have to be accounted for--something neglected by PV=nRT.

        Depending on the gas used and the operating temperature used, you might also force a phase change (gas -> liquid or gas -> solid). Again, all bets are off when something weird like that happens.

        Because the plates are attracted by the Casimir effect, and the casimir force grows quadratically as the plates draw nearer, eventually, even the pressure will be insignificant compared to the Casimir force. I think that's a pretty good conclusion using rough estimates.

        Nope. There are other effects you might see, as well:

        chemical interactions between the gas between the plates and the plate surface

        physical deformation of the plates by the high-pressure material between them

        limits on compression of the 'gas' because its constituent atoms are pretty close to incompressible

        Of course, as you mentioned this experiment would be impractical in reality, because gas would escape around the edges of the parallel plates--it's a tough device to seal. (And it's hard to get around this by trying to move the plates together quickly. Gas molecules at room temperature typically move with speeds on the order of hundreds of meters per second--they don't stay in one place very long.)

        Oh. Right. Casimir effect. It should go away when there's crud (gas or otherwise) between the states. Establishing standing waves between the plates requires empty space between them. A few gas molecules will weaken the effect--anything near one atmosphere (or worse) will kill it completely.

    • Correct me if I'm wrong, but Gravity only effects marcoscopic objects.

      • Re:forces between objects? (Score:1)

        by Anonymous Coward
        You are wrong.

        Gravity is just very very weak in comparison to the other forces at a small scale. The masses at that level are so small that you can safely ignore their influence for easier calculations, but the force is still there.
      • Correct me if I'm wrong, but Gravity only effects marcoscopic objects.

        You're absolutely right. It's a good thing our atmosphere is only made up of macroscopic objects.

      • Correct me if I'm wrong, but Gravity only effects marcoscopic objects.
        Marcoscopic objects? Is that something you can see only if your name is "Marco"?

        Or did you mean narcoscopic objects, objects which can only be seen under the influence of narcotics???

    • isn't the force two objects excert on eachother called gravity?

      Uhh...yeah...gravity. That's right, kid, it's just gravity. Head back to your classroom, now. I think the teacher's finished reading "Charlotte's Web" and is starting a lesson on decimal addition. Don't worry too much; you'll learn all about gravity when you get to high school. You might even learn about magnetism. /sarcasm
      Seriously...what has happened to science education? I'd read about the four forces when I was in junior high (and there were still four...electroweak hadn't been proved/discovered/demonstrated yet). I knew that magnets had nothing to do with gravity before I was ten. I'm nobody special, so what gives?
    • isn't the force two objects excert on eachother called gravity?
      Obviously not. Gravity is inversely proportional to the square of the distance, whilst the Casimir effect is inversely proportional to the 4th power of the distance.
  • A while ago, I read Neal Stephenson's The Big U [amazon.com]. The protagonist (well, one of them) was named Casimir, and, if I remember correctly, he built a rail gun.

    Did Stephenson have a special reason for naming his protagonist after this strange force? Was it a metaphor for how he was mysteriously attracted to his female friend? Or am I just trying too hard to explain an author's choice of names? ;-)

  • another Casimir (Score:3, Interesting)

    by Debillitatus ( 532722 ) <devillel2 AT hotmail DOT com> on Saturday September 07, 2002 @04:07PM (#4213161) Journal
    There's this other thing called a Casimir, when you have a Hamiltonian on an odd-dimensional space, you're guaranteed (by anti-symmetry) to have a null direction for the flow at any point, and this is called the "Casimir" for the flow. Does anyone know if this is the same thing?
    • Yet another one, but only for French people: Casimir [axeria.com] is our equivalent for Barney the dinosaur.
      It's even the first choice on google [google.com]!
      So, it felt strange when I read the 'Casimir Effect' :-P
    • You are probably thinking of a Casimir Operator [wolfram.com].

      If so they are not related.
    • I believe this Casimir is related to Electromagnetic vacuum fluctuations. That two sufficiently large (the traditional physics textbook calculation is for infinitely large) plates allow you to somehow focus or otherwise alter the vacuum fluctuations in a region of space so that they are greater or less than in other regions.

      For those that don't know, vacuum fluctations are everywhere. It's a quantum mechanical thing that I won't attempt to explain, but basically, try to remove everything, all energy and matter, that you can from a region of space, and because of the heisenberg uncertainty principle, there will still be energy left.

      The problem is, that this energy is everywhere, so to use it you have to find a place that has LESS energy in it, so the energy can flow. That's what I believe this Casimir effect is. The SECOND problem is to figure out how to do work from the energy flow.

  • How it works (Score:2, Insightful)

    by Liquidity ( 62369 )
    In simplistic terms this works because photons of certain wavelengths are excluded from the space between the plates. This doesn't happen on the outer faces of the plates, and the difference in the vacuum energy inside versus outside leads to an "attracting" force.

    It only works on uncharged plates.
    • It only depends on how "opaque" the plates are to the light at those frequencies, and has nothing to do with charge. Photons are unaffected by charge.

      Besides, having a charge on the plates means you are going to get a force between the plates -- attractive or repulsive, depending on the charge -- that is inversely proportional to the distance squared.

      The Casimir force is inversely proportional to the distance to the fourth power, and so the electric force will become insignificant as the distance becomes very small.
      • I have no idea what "how 'opaque' the plates are to the light at those frequencies" is supposed to mean; but whether the light is able to penetrate the plates or not, what most people mean by "opaque", has nothing to do with it. Charge, however, does have something to do with it.

        I hope you're sitting down for this, but photons are affected by charge. Quantum mechanics says photons constantly form electron-positron pairs, which then mutually annihilate to reform the original photon. These particles are charged and are affected by surrounding charges. This is not some kind of mathematical theory; it has been verified experimentally, and is the underlying reason for the refractive index of materials.

  • Maybe something based on this force could help out with this [slashdot.org].
  • just to add more confusion to the story... one can show that the casimir force between two objects can also be viewed as a van der waals force. imagine two dielectrics separated by vacuum. in the casimir picture, the two dielectrics will attract because of vacuum zero-point energy fluctuations. as someone else pointed out earlier, this is, in very simple terms, because certain frequencies are not allowed in the vacuum creating a pressure. on the other hand, one can also generate the same force by having the particles in the dielectricum fluctuate, i.e. generate van der waals forces due to "dipoles".

    from a physics point of view one has a hamiltonian (function which describes the whole system) for which one can integrate out the degrees of freedom of the dielectric or the degrees of freedom of the electromagnetic vacuum. if you remove the dielectric degrees of freedom, you get equations for the EM field which will give you a casimir force when you look at the cero point energies of the system with and without the dielectricum. if you integrate out the field, you will get an effective interaction term for the dielectrica and hence a vdW force.

    note also, that both, van der waals and casimir forces depend with a power law on the distance between the objects, usually at a high power and are therefore extremely short-ranged. there are some nice papers and experiments measuring both at the usual archive xxx.lanl.gov [lanl.gov]. just search for casimir...

    • casimir != van der waals (Score:4, Informative)

      by slyborg ( 524607 ) on Sunday September 08, 2002 @12:11AM (#4214560)
      Confusion would be an excellent description. What in Heisenberg's name are you driving at here? The London force or dipole dispersion force varies as 1/r^6, where r is the separation radius.

      The Casimir effect between two parallel uncharged plates in a vacuum at zero kelvin is given by:

      pi^2 h-bar c
      F = ----------- A
      240 r^4

      A = area of the plates and r is the separation distance.

      The Van der Waals interaction can be considered and computed as a semi-classical electrostatic effect. The Casimir effect, although sometimes referred to as a "long-range Van der Waals effect" is fundamentally a quantum concept as shown by the appearance of h-bar in the equation above.

      As you indicate, both forces follow a power law, but the Casimir effect will appear, again, between "neutral, conducting" plates at absolute zero, i.e. in a configuration where electrostatic forces due to charge distribution are not present, and the power relationship differs by an order of magnitude.

      So the two forces are fundamentally different conceptually and similar in that they both describe attractive forces between objects. However the latter similarity would also allow you to say that casimir == ferromagnetism if that is the only metric.
    • as you write, the casimir force is a quantum effect. still, there is more than just the textbook formula you wrote down for the forc between two plates. note that there are also *repulsive* casimir forces.... in any case, i am too lazy to elaborate and would like to refer you to the work of lamoreaux.

      • Re:casimir == van der waals (Score:4, Informative)

        by slyborg ( 524607 ) on Sunday September 08, 2002 @11:31PM (#4218515)
        I'm aware that the Casimir effect can appear as a repulsive force, J. Ambjørn and Stephen Wolfram wrote a detailed paper that can be found at:

        http://www.stephenwolfram.com/publications/artic le s/physics/83-properties1/

        Originally in Annals of Physics 147 (1983). I also came across an interesting paper in the June Physical Review Letters, by P. Bruno at the Max Planck Institute, available at:

        http://www.mpi-halle.mpg.de/~bruno/publis/2002_6 .p df

        on calculating a magnetic Casimir effect for parallel ferromagnetic plates, which shows the resultant effect as antiferromagnetic.

        As classical electromagnetism derives from an underlying quantum formulation, I concede that that Van Der Waals interactions are essentially classical manifestations of an underlying quantum explanation. However the "classical" vacuum parallel plate Casimir effect is one of those quantum manifestations, like superfluidity, that would not be expected or predicted from "common sense" physics. Van Der Waals forces, calculated without recourse to quantum effects, serve to explain all manner of chemical interactions and phase transitions, and, apparently, the adhesion of geckos to walls ;-) So stating a bald equivalence between these two well known forces is a little misleading.

        (Note: I am not a physicist, I only play one on Slashdot ;)

      • i agree with all you write but have to insist that one can show the equivalence of vdW and casimir forces. after all, i wrote my undergaduate thesis on that. : )
    • before i forget: i recommend the book by mostepanenko and trunov. and of course, the standard work "The Casimir Effect" by k. a. milton has a whole chapter devoted to equivalence of the casimir effect and van der Waals forces. happy reading, if you understand it.
  • Here is another article [washington.edu] from John G. Cramer's [washington.edu] Alternate View Articles [washington.edu] in Analog Sci-Fi Magazine [analogsf.com].

    Professor Cramer is the real deal. A physics professor at Washington University who is also a sci-fi fan and writer. He is also an excellent pop-science writer who can get his point across without dumbing things down. Enjoy.

  • hmm (Score:1)

    by prmths ( 325452 )
    is it just me or does this sound like something that would tie into ZPF energy theories?
  • I understand that two parallel mirrors are attracted to each other and presumably meet exactly even, What do perpendicular 90 degreee surfaces do? They said the effect was present but not what the natural motion was.

    It would seem to me that both surfaces would want to become the leg on the T on the other (if both sides of the leg are mirrored). Would the absence of protons cause collapse into the shape of a V on the connected (or close to connected) side? I would think not since the 90 degree would be broken as soon as the force was observed, I'm assuming it would not be the only force because if so wouldn't momentum eventually make the plates paralell and the effect would complete the movement. Sounds like nanites will look like modern art or sports cars, composed of paralellagrams and curves.

    Perhaps structures could use several atom mirrors like velcro in construction? Does the force disappear when the distance is 0?

  • If matter and energy are different aspects of the same thing how can a true vacuum have energy in it?
  • hmm... is "importances" a word?

    at any rate... I think one of the "very important" aspect of this has to do with multi (>3) dimentional physics. I can't remember where I read it, but physicists are theorizing that at millimeter (or less) distances, we will see gravity suddenly becomes disobedient of the inverse square law (which would prove the "we live in half dozen dimentions) theory. Now -- measuring gravity on a millimetre scale is hard enough, but when you throw in all these "fluctuation forces" (Van der Waal, Casmir, whatever), you will seriously screw up any chance you have on the Nobel prize... so people are trying to get all these things sorted out and verify some gravity, etc.
  • Many years ago, I read a book co-authored by Buzz Aldrin (i forget what it's called) about some aliens from the Alpha Centauri system who come to Earth using a spacecraft powered by millions of tiny plates that extracted energy using the casimir effect. Apparently, a paper proposing this has been published somewhere.... Has anyone read this paper, and has anyone read this book - I'd love to know what it was called...
  • My favorite part of the article contained this sentence. "Consider the gap between two plane mirrors as a cavity (figure 1)." You look directly over to the right at figure 1, and all you see is a picture of some droopy, slow-witted looking scientist. Poor guy, the sentence describing his head uses the words "gap" and "cavity". Chalk that one up for one of the worst editorial mistakes ever.
  • I tell ya, man, this quatum physics stuff is almost as hard to comprehand as women.
  • It's when the Indian rock bands and the Pakistani rock bands fight over who'll cover "Kashmir."

    HAH!

  • A primer on Casimir Effect (Score:5, Informative)

    by adipocere ( 201135 ) on Sunday September 08, 2002 @12:34PM (#4216143)
    My Bachelor's in physics is a little rusty, but I did attend a small symposium on the Casimir Effect (C.E.) a couple of years ago.

    Imagine a "vacuum" with two metallic (reflecting) plates in it, sitting near each other. The vacuum isn't pure. Photons could exist in it, momentarily, as governed by Heisenberg's Uncertainty Principle, wherein the energy of the photon is inversely proportional to the time it exists. Gamma rays would exist for a short period of time, radio waves much longer. Eventually, the Universe checks its books and corrects the accounting error, the photons go back to non-existence - conservation of mass-energy is upheld.

    Here's where it gets weird. The photons kinda-sorta existed (virtually), so they kinda sorta could exert an influence. Whoa. Strange.

    Next, only certain frequencies are allowed. The frequencies allowed to "kinda sorta exist" are modal, that is, they have to terminate with a node on one of the plates. So, clearly, you can't have gigantic radio waves between these two plates - radio waves are meters in length, they're too big to fit between the plates. You can have some blue photons, and all the gammas you can handle.

    Meanwhile, on the OTHER side of the plate, you get all of the radio waves you want - you have an entire universe to stuff them in! And the blue photons, and all the gammas you can handle. So ... there's just a few more potential electromagnetic waves (virtual photons) on the OUTSIDES of the plates than there are on the INSIDE of the two plates - this leads to a net push of the plates together.

    But that's not all - the force experienced by those two plates depends on a lot of things. In the symposium in question, it was demonstrated that, with the right geometry (concentric shells, weird flower-like arrangements) that the Casimir effect can be repulsive.

    In short, it isn't always 1/r^4, and it isn't always attractive.

    Now, for those of you who would like a free lunch out of this effect, it's not going to happen. Why? 'cause you have to push the plates back apart to complete a full cycle for any "free energy" machine you would like to devise. It's like a waterfall - you only get that energy from something falling down ONCE.

    No, it doesn't have anything to do with the Higgs boson. No, it doesn't come from some folded-up dimension. No, it doesn't have to do anything with gravity at small ranges. C.E. results entirely from QM + EM.

    On an aside, correcting other bits of non-information in these posts: no, photons are not influenced by charge. No, photons do not constantly form electron-positron pairs - most photons do not have enough energy to form an electron-positron pair - do the math if you don't believe me. The refractivity of materials comes from something entirely different. Photons don't have a non-zero rest mass - they never "rest" (discussion of the Bose-Einstein condensate usually ignores that the information about the photon was stored) - and many experiments have placed upper limits on the proper mass of a photon as being no greater than 10^-50 grams.

    • One small correction: photons do form virtual electron positron pairs. They are not observable but when you need to calculate the effects of a photon you need to take this into account. Lookup any QED book for "photon propogator" and fermion loop corrections. Its effect does depend on the energy of the photon, but it's always there.

    • first, very nice intro, mostly correct.

      photons are not influenced by charge

      photons are eigenvectors of pure EM hamiltonian. In this approximation, they are indeed uneffected by charge.
      However, there is matter-radiation interaction (the (P-e/c*A)^2 parts) terms in the more general hamiltonian, and radiation does indeed interact with charged matter (not just exciting atoms: lookup bremsstrahlung radiation)

      so, in short: photons are not eigenkets of the general EM+matter hamiltonian, therefore they do interact with charged matter.
  • Sorry about the wierd characters. I had to do some strange things to get this through the lameness filter.

    If two tiny mirrors were attracted to each other with both the forces of gravity and the casimir effect, the work done by their movement would generate energy that could be captured. Once they are together, they could be slid apart, moved back apart while not facing each other and moved to face each other again.

    1)

    _____________
    |
    v
    Casimir effect + gravity
    n
    |
    _____________

    2)

    =============

    ^
    |--Capture the energy of collision.

    3)
    slide right____________
    ____________slide left

    Slide mirrors apart using stored energy.

    4)

    ___________
    ^
    |---------------|
    v
    __________

    Push mirrors apart using stored energy.

    5)
    slide right _________

    _________ slide left

    Push or rotate mirrors to face each other again.

    6) Repeat

    I think if all the energy is captured, steps 3, 4 and 5 should eat up all the energy that was gained by the work that gravity performed. The rest of the energy, the work that was done by the Casimir effect is yours to keep. Do this with a billion little mirrors in a space-based power plant and you're set.

    I must be missing something cause perpetual motion let's all sorts of bad things happen like time travel, superluminal flight and entropy reversal. Sorry about being sloppy with my terminology. I'm probably misusing "work", "force" and "energy" in this context.

    So am I wrong about something or is this scheme truly money for nothing and chicks for free?

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