Sunday, November 04, 2007

The Casimir Effect

When asked about experiments that confirm quantum field theory, most people think about the Lamb-shift, Compton scattering, decay rates or particle cross-sections. The most stunning experiment for me however is the Casimir effect. Though it's neither particularly spectacular nor actually a surprising computational result, it is one of these cases where quantum effects tamper with our classical intuition.

Vacuum Energy

In school, we have probably all made experiments with charged objects and the electrodynamical forces. Consider two conducting and charged plates, parallel to each other. If both plates have the same charge, they will repel, if they have opposite charges they will attract. This force acting on the plates can be measured. So far, so good. Now take away the charges, just stick with the two conducting plates. What will happen? Surprisingly, the two plates will still attract each other!

This seemingly weird finding of quantum field theory is a very weak effect that can only be measured at smallest distances of the plates, typically of the order nanometers. Roughly speaking one can understand it as follows: quantum field theory teaches us there is no such thing as a really 'empty' vacuum. Instead, there are constantly particle pairs created. They come into life for a very short time, then annihilate and vanish. They are called 'virtual particles'. As is common for quantum objects, their energy is related to a wavelength. The higher their energy, the smaller the wavelength.

The troublesome thing about these particles is that their energy can actually become arbitrarily large, in fact, it can be infinitely large. This then results in a seemingly enormous 'vacuum energy'. However, as long as we neglect gravity, we can not really measure absolute values of energy anyhow. We can only measure differences between energies. Therefore, one can be bothered by the result of this calculation, but for practical purposes it never actually becomes problematic.

Now come back to the two conducting plates. The relevant fact is that they act like mirrors for the electromagnetic field and define a boundary: There is an area between the plates which has a finite extension into one direction, and there is the part outside the plates which is infinite on both sides. The wavelengths of the virtual particles have to fit between the plates (see figure below). In such a way, the plates select only some of the total of all possible waves in the vacuum.

Now if we ask for the energy differences between the in- and the outside, there is more virtual stuff on the outside than on the inside. The result is an inward directed pressure on the plates, which appears like an attractive force.

Though this pictorial explanation looks very nice it certainly can't replace a sensible calculation. E.g. for a cube the resulting force is confusingly repulsive, and the sign also depends also on whether the field is fermionic or bosonic. If one does the calculation for the case of parallel plates, one finds that the force F depends on the distance d between the plates as F~ 1/d4. The closer the plates are together, the larger the force between them.

Casimir and his Effect

Weird, eh? But experimentally confirmed! Hendrik Casimir and Dirk Polder, who where working at a Philips Research Lab, predicted the existence of such a force in 1948 and proposed an experiment to detect it (Phys. Rev. 73, 360 - 372 (1948)). Though the first experiments were performed already ten years later by Sparnaay, the data had large error-bars and the results were inconclusive. It has only been in the last ten years that these doubts were erased (Lamoreaux '97; Bressi, Carugno, Onofrio & Ruoso 2001), and Casimir's prediction has been confirmed.

Now during the last decade the Casimir force has received an increased and still increasing amount of attention, because more and more devices are 'nano' - and thereby come into the range where they are sensitive to the Casimir effect. The number of citations of Casimir's original paper has been exponentially growing (see Figure below)

[Graph from D. Budker's powerpoint presentation]

Weird and Weirder

But that's actually not the reason why I find the Casimir effect so interesting. No, the reason is that if one computes the energy density between the plates, it turns out to be negative! Please keep in mind, there is nothing in the known universe with negative energy density. The obvious question to ask then is how does that system couple to gravity? Is this really a negative contribution to the total mass? Does it get repelled by the earth?

I find this question intriguing because it addresses the question how manifestations of the quantum vacuum energy gravitate.


Piture credit: Baughman et al., Science 297, 787 (2002)
Five or six years ago I read an article on superconducting nano-tubes and began to wonder about their Casimir energy. As roughly cylindrically symmetric conducting tubes, would they be subject to the Casimir effect? In a very idealized case, I estimated the contribution to the density to be not too far off the current precision for the equivalence principle in an Eötvös experiment. I can't recall the details though -- maybe some orders of magnitude, not too desperate a situation. I am still not sure whether this makes sense, because I then unfortunately thought about the realistic situation - most notably the tubes are not actually cylindrical but already so small that their molecule structure is relevant.

I tried to convince an undergrad to look into the matter, but well. It didn't go anywhere. The topic had a brief revival for me some time later when I read a paper that proposed an experiment to test the weak equivalence principle for the gravitational coupling of vacuum energy... HA! I just found the paper. Not sure whether I should be surprised that it's by John Moffat ( Moffat & Gillies, New J. Phys. 4 (2002) 92) It seems whatever I look for, he has written a paper on it.

Anyway, the problem with the gravitational interaction of vacuum energy is if one takes gravity into account, it is no longer true that only energy differences are measurable. So what ought we to make out of an infinite result? If it was really a huge contribution that coupled to gravity, we would already have noticed (worse, we wouldn't even exist then). We can still just define some specific state as 'empty' in the sense that it does not have an energy that couples to gravity. However, the problem is that the definition of this vacuum depends on what an observer calls a particle. Unfortunately, this can differ from one observer to the other*. Either way one turns it, the definition of the vacuum depends on the definition of a particle, and the corresponding annihilation and creation operators. Concepts which in a curved background are not unique.

The actual reason for this post is that I recently came across a paper on the arxiv:

    Gravitational and Inertial Mass of Casimir Energy
    By Milton, Fulling, Parashar, Romeo, Shajesh, & Wagner
    arXiv: 0710.3841
where it is computed how quantum vacuum energy gravitates. The authors do indeed find "after a certain confusion" (p. 11, the confusion being that the result seems to depend on the coordinate system) that it couples as one would naively expect and therefore should result in a "small upward push" (p.4) . However, throughout the paper I see happy use of expectation values without any definition of annihilation and creation operators. I.e. what I thought is the actual problem here doesn't seem to bother the authors at all. I am admittedly somewhat confused by this. If anybody could tell me whether this is a justified procedure, I'd be interested to learn.


There's an incredibly large amount of virtual particles popping in and out of existence - right in front of your eyes, in exactly this moment. If if one does it the right way, one can measure them. Thanks to Casimir's ingenuity.


*This is essentially the reason for the Unruh effect - the one's vacuum is a thermal bath of particles for the other. Do these particles gravitate?

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  1. I'm kind of busy right now, but I'll contribute some information that might be useful, since this falls under the obscure physics of Julian Schwinger.

    Kimball Milton is(was) a student of Schwinger. Schwinger didn't believe in the usual Casimir calculations. He found an alternative method of QFT ("Source Theory") showing that one could get the same results without assuming a vacuum.

    See the collection of links to Schwinger's Casimir papers by Milton.

    PS. blogger's anti spam technology is painful and abusive. You should come over to WordPress like Tommaso, which also allows LaTeX comments.

  2. Hi Carl,

    Sounds interesting. Regarding blogger, I am working on moving the blog and running wordpress. Progress is slow but existent. I've considered just changing to wordpress, but found I can't import comments because I haven't changed to the beta blogger version (I couldn't stand the widgets). Sorry about the anti-spam crap, but I just don't have the time to delete all the viagra ads we get otherwise. Best,


  3. Bee, I blundered into a lecture by Schwinger on his source theory that mentions the application to the Casimir effect:

    The theory of the Casimir effect, including its temperature dependence is rederived by source theory methods, which do not employ the concept of (divergent) zero point energy. What source theory does have is a photon Green’s function, which changes in response to the change of boundary conditions, as one conducting sheet is pushed into the proximity of another one.

    The lecture itself is mostly about Green, the fascinating man who found Green's functions. My version of "the idea behind source theory" is that everything should be written as a propagator. My version of QFT is similar.

    But I go further, thinking that everything should be written as virtual propagators, which just happen to translate everything from spinors into density matrices, hence my interest in the subject.

    Now let me steal some time from the boss and take a look at the papers you linked.

  4. Yes, the first paper referenced by the Milton paper you read gives the "alternative" view of the Casimir effect: it does not prove the existence of the zero point energy.

    Sorry for dominating your comments on this, but I suspect that I'm the only reader who cares much about Milton and Schwinger, or knows much about how they do Casimir point calculations.

    I believe that you will find Milton, as I have, a friendly correspondent who has time to suggest papers etc.

    Rereading your post, I should comment on "However, throughout the paper I see happy use of expectation values without any definition of annihilation and creation operators."

    The creation and annihilation operators are used to create quantum states that are mathematically in spinor form. Since I reject spinors in favor of their density matrix form, i.e. I always convert |a) to |a)(a|, I can't use creation and annihilation operators by themselves.

    Instead, in my version of QFT, one must always pair creation and annihilation operators. When one annihilates a ket, one must create a bra. This turns a pair of annihilation and creation operators into an operator of the density matrix sort.

    This is compatible with Schwinger's source theory. I should mention that source theory has a sort of a finite degree of freedom version (for spin and the like) called the measurement algebra, which I'm more direcly connected with (that's one of my websites).

    The odd thing is that Feynman also flirted with similar ideas. When he first was exposed to creation and annihilation operators, he rejected them as unphysical, since particles cannot appear out of nothing. It was only later, after he saw their calculational convenience, that he began using them.

    In my own mind, the creation and annihilation operators, and the zero point energy and all that, are not parts of the physical world, but instead are just mathematical conveniences. In fact, most of the ways where I (and probably Milton as well) disagree with the standard view amount to disagreement over what is a part of the physical world, and what is just mathematical symbols.

    I think that there is a strong tendency in the physics community to confuse mathematics with physical reality. I bet that the Perimiter Institute is the best place on the planet to do otherwise.

  5. Casimatter! Al reflects 93% 100-120 nm. MgF2 has refractive index 1.63/121 nm. Two vacuum deposition sectors continuously add 70 nm of Al to a flat rotating ring promptly covered by 37 nm of MgF2 in a never-ending bifilar spiral. Cut. Casimatter, average density 2.86 g/cm^3, is 38 wt-% ZPF-depleted MgF2.

    LiF goes to RI = 1.777 at 110 nm. 60:40 MgF2:LiF has thermal expansion mismatch of 0.1x10^(-6)/degree versus Al. 37 nm of fluoride alloy and 70 nm Al give Casimatter 2.79 gm/cm^3 of which 37 wt-% is ZPF-depleted fluoride alloy.

    OTOH Casimatter would make a curious Eötvös balance experiment opposing bulk Al and MgF2/LiF. OTOH, it would not. Highly crystalline graphite with 100% intercalcation to separate each monolayer?

  6. The Casimir effect is certainly very
    interesting, and the measurement of the Casimir force between macroscopic objects is an impressive feat. I am not convinced, however, that the Casimir effect has any special relevance to the question how quantum fields and quantum fluctuations couple to gravity.

    The mass of most objects is dominated by quantum fluctuations (QCD, electroweak, the Casimir-Polder force, ..), so any test of the equivalence principle verifies that these conytibutions couple to gravity in a universal way.

    The Casimir effect is not really fundamentally different from any of these effects. The only thing which is superficially different is that the Casimir force contains Planck's constant, but not the fine structure constant. Bob Jaffe recently wrote a nice little paper ( in which he explains why this is not correct (the Casimir effect vanishes in the limit that alpha goes to zero).

  7. This comment has been removed by the author.

  8. Great post!

    Can you say a bit more about what happens to the creation and annihilation operators in curved spacetime? Back when I was a student I asked a lot of people what was wrong with QFT+GR. A few people said "it doesn't work" but no one would ever explain why.

  9. carlbrannen said "Sorry for dominating your comments on this, but I suspect that I'm the only reader who cares much about Milton and Schwinger"

    WRONG !

    ", or knows much about how they do Casimir point calculations."

    well, that might just well be the case.

    Very interesting post, Bee. When can we expect your book for the really interested layperson ? You might even get your own TV-show !

  10. Interesting Bee.

    Is it necessary for there to be a "vacuum" for the virtual particles to be creted in, or do they also pop up inside other more or less dense materials?

  11. Hi Rillian:

    Sure. In a nutshell the problem is the following: in flat space you expand the field in a complete set of solutions to the wave equations, exp(i(kx-wt)) and their complex conjugate. They have an energy that is defined through the derivative in the time-like direction E = i \partial_t. The coefficients for each mode are the annihilation and creation operators (a, a^\dag). The vacuum state is the one defined through the property that acting with an annihilation operator on it gives zero, i.e. it's empty a |0> = 0 for all a.

    Now try to do the same thing in curved space and you run into a problem. There isn't usually a set of coordinates with a specific time-like dimension that you could define your modes' energy with. You can pick one, sure. For example in the Schwarzschild case it seems only natural to chose Schwarzschild coordinates. But the problem is that if you change into a different coordinate system, or a different observer, that observer can have a different set of modes, and make a different expansion of the quantum field - resulting in another set of annihilation and creation operators (b, b^\dag). These he can use to define another vacuum state with b |0> = 0.

    Generally, these two sets will not be identical. One can transform the one into the other - this is called a Bugolubiov transformation - and what you find is that generally, the one's vacuum state will not be empty with respect to the other one's particle definition.

    This is basically the reason for the Hawking and the Unruh effect.

    Note that if space-time is flat, performing a Lorentz-Transformation on the coordinates leaves the vacuum state invariant.

    A really good introduction into all this is

    Birrell and Davies
    Quantum Fields in Curved Space

    Hope this is helpful. Best,


  12. Consider two conducting and charged plates, parallel to each other. If both plates have the same charge, they will repel, if they have opposite charges they will attract. This force acting on the plates can be measured. So far, so good. Now take away the charges, just stick with the two conducting plates. What will happen? Surprisingly, the two plates will still attract each other!

    The traditional calculation as shown in QFT textbooks such as Itzykson and Zuber should be viewed, IMO, with grave suspicion.

  13. Dear Arun:

    The paragraph you quote above actually didn't refer to a calculation, but to actual measurements. But regarding your previous comment, do you have a reference on that? I'd be interested to see, it is not clear to me how good one can resolve and understand material dependence. What I find somewhat 'suspicious' is that one can calculate the qft effect for a lot of fields, and they should all exist, but afaik the only one that has ever been measured is the one for the electromagnetic field. That of course begs for the question whether it's actually as general an effect as believed, or somehow related to electromagnetism. Best,


  14. Lightspeed depends upon the permeability and permitivity of the vacuum. A Casimir etalon's depletion region contains the Scharnhorst effect,
    Phys. Lett. B236 354 (1990)
    Phys. Lett. B250 133 (1990)
    J Phys A26 2037 (1993)

    If c is dependent upon boundary conditions both GR and QFT emerge from increasingly poor foundations when things begin to get interesting.

  15. Thanks, Bee. That was quite helpful, and I will try the rest of the reference you suggested.

    I see what you mean now, and what Carl meant about a and a^\dag not being real, although surely "the wrong mathematical construct" is more accurate?

  16. Bee,
    Thomas above gave this Jaffe preprint

    which argues I believe that the Casimir effect goes to zero as the fine structure constant goes to zero; the Itzykson-Zuber type calculation is the limit when the fine structure constant is infinite.

    I'm basing all this on a vague memory of having seen it before, so it is possible I'm entirely wrong.

  17. Ah,

    thank you for reminding me of that idea of yours :-)

    BTW, although a bit off-topic, it seems that with the methods used by Jaffe, one can now calculate Casimir forces between arbitrary compact objects (arXiv:0707.1862v2, PRL 99 (2007) 170403)...

    Best, Stefan

  18. Hi There,

    First an apology for being brief, but I am pretty much tied up this week with the previously mentioned workshop on Experimental Search for Quantum Gravity. The IT guys are impressively fast, the fist talks are already online (I successfully avoided having my intro recorded).

    Hi Carl,

    I admittedly don't understand what you mean with

    The creation and annihilation operators are used to create quantum states that are mathematically in spinor form. Since I reject spinors in favor of their density matrix form, i.e. I always convert |a) to |a)(a|, I can't use creation and annihilation operators by themselves.

    Well, what about scalar fiels? Vector fields?

    I bet that the Perimiter Institute is the best place on the planet to do otherwise.

    Without doubt, Perimeter Institute is the best place to do "Otherwise" ;-)

    Hi Thomas,

    You are of course right, we know that quantum contributions to particle's bare masses gravitate as usual. But usually this contribution isn't negative? What I was referring to as what I find exciting about the Casimir energy is that it's actually the 'empty' space question in a curved background (our universe) which is addressed here.

    Hi Oxo,

    Is it necessary for there to be a "vacuum" for the virtual particles to be creted in, or do they also pop up inside other more or less dense materials?

    These particles pop up everywhere, it's an always present contribution. Besides this, on a microscopic level even dense materials are mostly "empty". Best,


  19. Bee, Well, what about scalar fiels? Vector fields?

    Sorry, I do live in my own little version of physics. I only care about the foundations, and I want them as simple as possible.

    There are no known, observed, fundamental scalar particles. As for the vector particles, my guess is that they are composites made also from spin-1/2 sorts of things. This, you know how to do, so it isn't much of a stretch to believe. This makes the scalar and vector particles just mathematical conveniences for representing certain bound states, not parts of the fundamental reality. Hence they do not require analysis.

    It really boils down to this. Did Nature really go to the trouble of making a whole zoo of fundamental particles widely divergent in type? Or did she make only one truly fundamental particle type, and the bosons and fermions we see are made from even and odd bound states from that fundamental particle type? What would Jesus do?

    To build the particles up from preons, you have to begin with spinors (or their density matrix equivalent). Can't make fermions out of bosons.

    Stefan: The note on calculating Casimir forces for arbitrary shapes is important; I hadn't seen it before.

    The way that new physics paradigms advance is not by convincing old established researchers of the error of their ways so much as by convincing the next crop of grad students that they can use the new techniques to make calculations that will get them their damned degree (or tenure) faster than the old methods.

    There are about a dozen interrelated places where physics has two (or more) alternative ways of answering the question "what is mathematical convenience versus physical reality" that I think the majority got wrong. The ZPE is one of them. Most of them amount to stuff that "everybody knows for certain" that is simply untrue.

  20. Hi Carl, I see - you're a composite fan. How do you get the photon to be massless? Best, B.

  21. Hi Anonymous,

    When can we expect your book for the really interested layperson ? You might even get your own TV-show !

    Book: not until I'm tenured. TV: categorically not. But thanks for the nice words,


  22. Have you head to talk about Podkeltnov?

    A few years ago, around the 98 or so, he claimed that he had found some gravitatory shielding in experiments with a very complicate superconducting device he was studiying for diferent purposes.

    The effect hasn´t been reproduced, among other reasons because he refuses to give the exact nature of the orignial (and subsequent) experiment.

    I readed sometime ago an paper where he and a colleague, tried to explain the effect based on something similar to the cassimir effect. They considered gravitational modes and arged that their superconductor, representable as a ginstpurg-Landau lagrangian, cancelated some modes anda that caused a modificaton in the (assumed existent) value of the cosmological constant resulting in the observed gravity shielding.

    Since them other people have claimed to have found anomalies in gravitation associated to sperconductors. But the problem is that experiments usually are plagued with a lot o incertities and are not too fiables. Anyway I think you could be interested to know if You didn´t already do.

  23. No, I have only one head and I prefer using it to talk about well documented, reproducible experiments and reliable calculations. You might be interested in this, that's about far as I will go into this direction. Best,


  24. Ok. I just wanted to let you know. Not being an experimentalist the point I usually see in this caes is that the persons who do the experiments are condensed matter physicians and not experts in quantum gravity theory so their temptative explanations usually are a bit naive.

    In brief, my opinion is that they are curiosities wotrting to be aware of them, but not to expend too mucch time wondering specifically aobut them.

  25. What I find somewhat 'suspicious' is that one can calculate the qft effect for a lot of fields, and they should all exist, but afaik the only one that has ever been measured is the one for the electromagnetic field.

    That might have something to do with the fact that it is quite easy to experimentally impose Dirichlet boundary conditions on the e.m. field (conducting plates will do just fine), but I am not aware of a way to do it to e.g. the gluon field...

  26. Even if the Casimir effect has nothing to do with quantum gravity, I rather like Uncle Al's idea of Casimatter--whether it's a candidate for dark matter or for dark energy.;-)

  27. Hi Anonymous: of course

    Hi Cynthia: Well, people have examined all kinds of 'matter' as dark matter and/or energy, depending on the equation of state it comes as one or the other 'essence' or 'field'. I am certainly in favor of trying negative energy densities, but it takes more effort to make it work than just calling it Casimatter. Best.


  28. False Vacuum to the True

    See the "bubble nucleation process" it is not hard to follow what goes on in the early universe in a geometrical sense.

  29. Casimatter is Casimir etalons *only* - alternating stacked minimal thickness of best reflector with shortest possible wavelength transparent dielectric spacer. It does not go below ~115 nm optical spacing (physical gap times refractive index). Casimir force should degrade to van der Waals interaction with decreasing separation, hence the need for falsifying experiment. This is top down and not naturally occuring.

    Bottom up begins with a lamellar crystal (graphite, transition metal chalcogenides, zirconium phosphonates, smectite clays, micas...) then intercalcates the lamellae into Casimir etalons. Perhaps compacted lamellae alone are sufficient. That could be natural occurance, but natural abundance vs. galactic requirements is a poor fit, including carbon nanotubes.

    Adelberger's best reported Eötvös balance is 10^(-13) difference/average mass sensitivity. Casimir depletion is ~10^(-15) relative mass sensitivity given calorimetry arguments (lamellar graphite versus 3-D diamond). Casimatter would need go against theory. Enthalpy of fusion is diagnostic (Al = 660 C mp), and is c^2 more sensitive than mass deficit observations.

    Carbon nanotubes might be pathological. They must be sorted by type (insulating, semiconductor, metallic) then enthalpy of combustion is diagnostic. Energy is the integral of force times distance. The geometry is not promising, but it's worth a look for ease of experiment.

  30. superconducting nanotubes, reduce errorbars

  31. "Hi Carl, I see - you're a composite fan. How do you get the photon to be massless? Best, B."

    If you were going to build photons from fermions like electrons you'd be in a world of hurt cause electrons have mass. But the standard model fermions are built from chiral handed states that are massless, which makes it a little less impossible.

    As to it being possible, you linked to the "Weinberg Witten" theorem. The theorem requires an assumption of perfect Lorentz invariance (as does the Coleman-Mandula theorem). Almost everybody assumes perfect Lorentz invariance pretty much the same way almost everybody assumes zero point energy, etc., and almost everybody makes no progress in understanding mass.

    I guess if some experimenter runs an experiment that verifies that Lorentz invariance is perfect for all particles (including the 96% we can't observe) at all energies (including the Planck mass energy we can't achieve), then I'll have to drop this idea. Until then, I'll just continue deriving results with it.

    The question of Lorentz invariance goes to the foundations of physics in such an intimate way that it makes a difficult topic of conversation. The assumption is that if you see approximate Lorentz invariance in the cold, cold world around us, it must be a perfect invariance at all temperatures. This was the topic I chose for a guest post on Tommaso's blog, you can read my opinions there.

    To see physics the way that I do would require that you study full time from the papers I did for a semester or so. You don't have the time to do this. And you already know what is true about physics, so why should you waste your time with a long reading list put together by an insane amateur? Tell you what. I won't give you the list and you won't ignore it.

    Eventually I'll write a blog post on the subject of the difference between spinors and density operators, and the difference between creation / annihilation operators and Green's functions / path integrals (and how this relates to the zero point energy and Casimir calculations), and the difference between a Hilbert space and a Banach space (hint: inner products), and what all this has to do with how it came to be that an amateur figured out how to generalize Koide's charged lepton mass formula to the neutrinos. But don't anyone hold their breath because I've got a lot of other stuff to do first.

  32. [holy shit, this wasn't posted when I came back. I can't believe the reply wasn't erased by my errant usage of copy and paste!]


    Podkeltnov is a scam artist and a crank. He has given his experimental setup out - repeatedly - and nobody can replicate what he claims he did. He cannot even replicate what he claims he did. NASA has spent millions of dollars trying to replicate Podkletnov, as have others. Everyone - including Podkletnov - has come up empty. He needs to be forgotten or derided, like Bogdanov and Cahill. Rather than given more positive attention.

    Furthermore, I *love* it when people continually make offhanded references to the supposed finding that superconductors tweak gravitation in some odd way. There has yet to be one observation that has made it into a peer reviewed journal. The last one I heard about was from Tajmar who thinks he found some kind of gravitomagnetism that [un]curiously never made it into Physical Review C.


    Casimatter doesn't have the energy density to /be/ dark matter or energy, and you are overlooking the requirement that it be built up from baryonic matter.


    The Casimir effect holds a special place in my heart as the only thing, to my knowledge, that directly upsets GR at any level that is outside an event horizon. This is because the region between the conducting plates directly violates the strong energy condition, which is something that tends to be taken for granted and tends to be used to prove that wormhole and warp drive geometries are not possible.

    Plus there is the amusing possibility that the speed of light may be related to the amount of vacuum energy, and that it would be different in in the depleted vacuum region. Uncle Al calls this the Scharnhorst effect. Unfortunately I haven't the faintest idea how to measure the speed of light in that kind of region. But I like the thought.

    Also, after reading the paper Bee posted, I am even more in love with the Casimir effect. You can't even tell what the SIGN of the force will be without slugging through the math!

  33. Rillian, QFT + Curved space works just fine in the path integral approach, contrary to what you might have heard. People used this to figure out things like the Hawking effect.

    The problem is its still just an effective field theory, and a nasty one at that. Gravity is nonrenormalizable, so you cannot trust its predictions beyond some cutoff (where the energy scale approaches the Planck scale, or when the curvature starts getting too violent).

    The other nastiness comes in the framework of canonical quantization due to the fact that the Hamiltonian constraint is vanishing in quantum gravity. Which is the problem of 'time'.

    There are various ways around this, but their is still controversy to this day.

    Either way, you really want to UV complete the theory in some way, which is what String theory successfully does and one of the reasons people are excited about it.

  34. Hi Carl:

    And you already know what is true about physics, so why should you waste your time with a long reading list put together by an insane amateur? Tell you what. I won't give you the list and you won't ignore it.

    I find this comment pretty much insulting. True, I don't have time to read a whole bunch of your papers, and given that I am not particularly interested in the topic I actually see no reason why so - did you read any of my papers? I was trying to understand what's on your mind, and what I get is this. Sure you can cling to Lorentz invariance not being exactly true, and since every experiment is done with finite precision only, nobody can ever prove you otherwise. I just don't find it particularly compelling or exciting, a perception you might not share.

    Basically, my question with the photon being composit has nothing to do with the potentially existing elementary fermions having masses, but the interaction between the fermions. If the photon is made out of fermions, what about their binding energy? How does the composite system remain massless?

    Hi Anonymous,

    I didn't say QFT in curved space doesn't work, I said the notion of a particle isn't well defined, since the annihilation and creation operators - and so the vacuum state - depend on the choice of modes, and the time-like coordinate and/or energy. I don't see how the path integral approach helps in this regard?



  35. Scharnhorst effect: Measuring increased c within a Casimir etalon is not hurt by the short distance. Pulse gamma photons in vacuum through a grating of thicknesses of Casimatter and void. The photons will visit the detector in two bunches - and one will be too soon. A continuum of scattered background provides more calibration.

    Aluminum, magnesium, lithium, and fluorine are all light elements. Do it along the c-axis of well-crystallized graphite, too, and parallel to the long axes of aligned bundled carbon nanotubes. It is a very doable experiment.

  36. Sorry Bee, I didn't mean to be snipy. And the papers you'd have to read are not my own.

    Sure you can cling to Lorentz invariance not being exactly true, and since every experiment is done with finite precision only

    Actually, I think that the known particles satisfy Lorentz symmetry exactly. I think that there are some people at PI that occasionally write papers messing around with special relativity, uh, that would be you.

    If the photon is made out of fermions, what about their binding energy? How does the composite system remain massless?

    To me, "mass" is an interaction between a left and a right handed state that allows one of the usual particles to (more or less) reverse its direction. To see this idea straight from Feynman in 1+1 dimensions, do a search for "checkerboard model"+ "Feynman". This, by the way, is an example of a non Lorentz invariant underlying theory giving a Lorentz invariant visible particle. To see the Lorentz invariance breaking more explicitly in 3+1 dimensions, see Plavchan'swrite up.

    So a massless particle is simply one where the coupling between the two handedness states is very small or non existent. I realize that this is not very nice according to relativity, but the only important thing is that the composite states be Lorentz invariant. Sausages are made from pigs, not daschunds as their appearance would suggest.

    The real puzzle is not how one gets massless states, but instead how is it that the massless states can have finite energy. To answer that question, you need to do a rather simple QFT calculation that I will eventually blog.

    When you make a radical change to the foundations of physics the change propagates around the foundations until you have changed everything. It is an all or nothing proposition, only an insane person would attempt it. It also takes a long time to understand, and a longer time to do.

    A convenience of relativistic physics is that when you define the quantum state for a particle of energy E and momentum 0, you can use relativity to get the states for arbitrary momenta. And statistics works correctly among these particles. By relativity they are equivalent.

    If you instead assume a preferred reference frame (which is the consequence of losing Lorentz invariance), you will now have that particles with different momenta are not the same. They are distinguishable. Quantum statistics seems broken.

    An elegant solution is to postulate that at the deeply fundamental level, all particles are characterized only by their velocity (which is a constant we can call "c"). Then you get the rest of them by the convenient method of, you guessed it, superposition.

    And this will give you photons with various finite momenta from a massless photon whose only kinematic characteristic is the direction of travel. To do this, however, you have to make a correct guess about the propagator for the "ur" photon, the one characterized only by velocity. You might be surprised at the answer, might not.

    Do me a favor and delete this comment, it is way too long.

  37. Hi Bee, what do you think of arXiv:0711.1206?

  38. Hi Anonymous:

    Thanks for pointing out the paper. I didn't read it, and given that I already have an issue with the first sentence of their abstract (it seems to refer to the paper I have mentioned above, the argument in which I can't quite follow) it doesn't rank especially high on my to do list reading it.


    PS: I have deleted the duplicate comment.

  39. Bee --

    After having seen the EM Casimir effect measured to be real, what interests/worries me most is the implications for vacuum energy, and by extension cosmology. We are now reasonably sure that _changes_ in vacuum energy are real and match with what would be described in QFT as zero-point modes. But at the same time we know that the absolute value of vacuum energy, if GR is to be believed, is much lower than these zero-point modes would imply. Does this strike you as a worrisome contradiction?

    Another way to approach this question is to ask: if I hold up two sheets of aluminum foil parallel and let them go, they will fall together under the Casimir effect force; eventually they will collide and presumably wind up being (slightly) heated. Standing in my kitchen, how do I understand where this heat energy came from? Did the cosmological constant of the universe just go down by a little bit?

    What's to prevent me from repeating the process and "mining" an arbitrary amount of vacuum energy into mechanical/heat energy? I need a lot of aluminum foil which is already separated at some large distance; but what is the fundamental limit on creating all those conducting sheets? Does the Casimir logic also say that it costs/yields energy to take a single conductor and change its shape? Or, does it cost/yield energy to change a piece of material from conducting to non-conducting (as could be done chemically)?



  40. Late to the party.

    Take two small styrofoam balls and cover them with aluminum foil. Suspend them with strings an inch apart.

    Put a negative charge on one of them. The neutral ball will be attracted. The electrons on the front side of the neutral ball will be repelled by the electrons on the charged ball and will tend to retreat to the far side. The remaining positive charges on the neutral ball will attract the neutral ball to the charged ball.

    If neither ball was charged could it work? What if a statistical anomaly put more electrons on the near side of one ball, then electrons on the other ball would flee, the opposite charges would attract, the effect would be reinforced, etc. But that doesn't happen. There are too many electrons to get the statistical anomaly in the first place, and interactions between electrons on one ball outweigh interactions with the other one.

    Now make it two plates a few nanometers apart. Wouldn't statistical anomalies have more chance to act? The effects come sooner and bigger. Small effects can matter more. A small patch of positive charge on one plate is more likely to happen when there is a small patch of negative charge near it on the other plate than another positive patch. You could easily get a small attraction. Maybe a large one.


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