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    Van Der Waals Force Or Gecko Feet Grasping Into Parallel Worlds
    By Sascha Vongehr | March 26th 2012 04:47 AM | 15 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    That relativity theory or quantum mechanics are only important at huge velocities or incredibly small distances and so on is a common misconception. In fact, the yellow color of gold and the stickiness of fridge magnets are relativistic effects. One thing that only works because of quantum mechanics is that a gecko can walk along the ceiling, which is quite astonishing to watch for the first time. I remember washing myself in Thailand, finding beautiful white geckos above me. Not knowing how secure they are up there on the moist ceiling nor whether they were potentially dangerous, this was a quite strange situation, making me jump every time they moved. But they never fell, even although they sometimes just dangled there with merely two feet attached.



    Close-up of the underside of a gecko's foot as it walks on vertical glass.


    Their feet stick to the ceiling because of Van der Waals forces [1], and these are often misunderstood. I was inspired to write this article after watching a MIT lecture on biochemistry where an otherwise very competent lecturer “explained” the Van der Waals-London force* somewhat like in the following description:


    * Different texts refer to different things using the term "van der Waals force". Some include forces due to permanent dipoles in macroscopic objects. I am here focusing on what I learned as the proper VdW force with the 1/R6-dependence (yes I am getting old), which is more specifically called London dispersion force.



    Say we model neutral molecules via chains of electrically neutral beads; here are two long molecules, one above the other:


    000000000000000


    000000000000000


    The mobile electrical charges of a neutral molecule, namely the negative (n) electrons, happen to randomly move about and so most of the time also a neutral molecule is charged, having some negative regions and some positive (p) ones.


    000ppp00nn000n0


    000n0000p000000


    These charge distributions will induce opposite charge distributions in the nearby molecule: The negative parts will repulse the other molecule’s electrons, turn the nearby regions of the other molecule thus positive, and consequently attract these induced positive regions:


    000ppp00nn000n0

    000nnn00pp000p0


    Thus, even two overall neutral molecules do attract each other via such induced random charge distributions.


    A heavy metal ring is supported from a sandpaper surface by a small square of carbon nanotube dry adhesive that works just like the gecko’s feet.


    This explanation has truthiness but is also fundamentally flawed! If it were indeed so that there are random charge fluctuations, if the electrons were to really move about a lot as if they had some excess energy, they would have to calm down over time. Such changing fluctuations would be noticeable via electromagnetic fields and they would ultimately radiate energy away, namely in form of these electromagnetic (EM) fields. However, these fluctuations are actually of quantum nature and never calm down**. Never ever, and that they keep fluctuating makes the force so dependent on the distance according to a 1/R6 law*** - if they were dipoles that just induce each other and then stay as they are, it would be 1/R3 (other assumptions, e.g. one stationary, one induced etc give other dependencies of the involved potential energies). This permanency of the fluctuating means that it cannot radiate away energy, which in turn means that it does not change the electromagnetic environment, which in turn would mean that it cannot induce any charges anywhere else.

    ** QM fluctuations are observer dependent - they "exist" when you describe the situation as one molecule observing the other. To an outside observer, fluctuations are "virtual".

    *** 1/R6 energy dependence is just like two very hot and thus randomly rotating electric dipoles - that is why this dependence looks like permanent ongoing fluctuations. I thank Lagrangiansforbreakfast for pointing out that I should be yet more careful with distancing myself from the picture of there "actually existing" fluctuations in a naive sense.


    If indeed two molecules would stick to each other and forth and back induce random charge fluctuations along each molecule, this would be a source of energy that never stopped, for ever radiating EM fields. Such can be possible only inside a thermodynamic equilibrium, meaning this would be only possible inside a bath of EM radiation that gives the molecules as many random photon excitations as it receives from the molecules; a balance. However, and now comes the big problem: In such an equilibrium background where the random outside excitations have the same energy scale as that of the internal binding forces, the molecules would no longer be bound to each other!


    That something "is bound" means little more than that the binding energy (E) is larger than the thermal energy (kBT). Room temperature thermal excitations are about 0.6 kilo calories per mole of water. That water molecules are bound and do not boil away at room temperature is due to the hydrogen bridges having a binding energy of about 5 kcal/mol. Covalent binding of DNA for example is at about 80 kcal/mol. That is why Neanderthal DNA has been found still intact after many thousands of years. If the thermal excitations are comparable to the binding energy, they rapidly destroy the "bound" structure, i.e. it is not bound.


    This is a fundamental point and not a technicality that depends on how much binding energy is involved: Either the molecules are bound to each other, that means their binding energy is larger than the thermal excitations, or they are in equilibrium with the environment, but then they are no longer bound. Binding can never be due to stuff actually jumping randomly around – such is fundamentally flawed as it contradicts thermodynamics.

    If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
    --Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)


    So how then does the Van der Waals (VdW) force let the gecko dangle from the ceiling? Well, the charge fluctuations are already quantum – i.e. the electrons are not actually jumping forth and back as if they have some temperature. Their position is undetermined and this fundamental quantum indeterminacy is what renders the exact charge distribution (which we classically think should obtain) also somewhat undetermined, or better, there is no such exact distribution.


    The many worlds interpretation is one of the most advanced and natural interpretations of quantum mechanics (because its basic "assumption" is tautologically true). (Bohm's interpretation is a defending of a mechanistic physicality only marginally elevated over pseudoscience.) In terms of many worlds, loosely speaking with much poetic license: The molecules' classical possibilities of having their electrons found in complementary positions along the two molecules (so that they attract) interfere constructively and are therefore more likely than those that repel. Nevertheless, they are all there together in superposition and so nothing is radiated - this is much the same reason for why the hydrogen atom's electron does not fall into the nucleus.

    This is what we call the VdW force if the overall effect is for example that two Neon atoms are stuck together. There is no force between them but the VdW one from quantum fluctuations, but there is no energy loss due to charge fluctuations radiating electromagnetic fields. This is why Noble gasses can condense and become liquids at low temperatures.


    The gecko could not hang from the ceiling in a classical world. It is the entanglement of potential worlds that at the gecko's feet lead to the VdW force. And in this sense it is that the gecko does not so much grasp the ceiling, but his foot grasps the feet of all the parallel geckos that hang there in all the parallel worlds. Without them, if you disturb that interference, the gecko would fall. They walk together, and while classically they would all fall together just like classical matter would collapse, it is the self-consistency of the quantum world that keeps the dream dreaming itself. Apparently, the dream is consistent with beautifully creepy things walking upside down along the ceiling - go figure.


    --------------------------------------------

    [1] K. Autumn, M. Sitti, Y. Liang, A.Peattie, W. Hansen, S. Sponberg, T. Kenny, R. Fearing, J. Israelachvili, R.J.Full.: “Evidence for van der Waals adhesion in gecko setae.” Proceedings of the National Academy of Sciences (2002)

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    Comments

    Very nice! Can you also explain your teaser; the relativistic effects manifest in magnetism?

    vongehr
    What we call "magnetic force" is due to relativistic time dilation and Lorentz contraction with moving electrical charges. Two wires with parallel currents next to each other attract because the moving electrons' mutual distance is contracted (relative to the stationary positive charges in the other wire) and are therefore seen with a higher charge density than the positive nuclei. This excess electrical charge density is what gives the force. In a world where the velocity of light were much much larger still, we would not have discovered magnetism.
    Assuming charge to be invariant.
     
    I dislike the strange semantics games you always play in your articles. I think they are in many cases more misleading than informative. Often you walk this line where it is difficult to tell if you are actually misunderstanding the physics or just presenting it in a horribly distorted form to try to make it more sensationalist for readers (I see you change the title of your incestuous pedophile rapist murderer article ... so you at least backed off on some of the sensationalism when pushed).

    In this case I think it is fairly clear that you are just not understanding the physics.
    So let me give a more reasonable introduction for students.

    You wrote:
    "that they keep fluctuating makes the force so dependent on the distance according to a F ~ 1/R^6 law - if they were dipoles that just induce each other and then stay as they are, it would be 1/R^4"

    It is the _energy_ not the force that goes like 1/R^6. And an induced dipoles give exactly this (not 1/R^4) which is exactly the reason many people use that classical image to introduce the topic. So for any students reading this, consider the following: two neutral helium atoms. If we consider an electronic configuration on one atom that gave it a small dipole, the electric field strength would go like 1/r^3. For small electric fields a neutral atom will be polarized giving it a dipole proportional to the electric field ... so p ~ 1/r^3. So the energy goes like p.E which gives 1/r^6.

    So the neutral helium atoms can have a Van der Waals attraction.
    I don't know what the biochemist actually said since Sascha appears to be paraphrasing him, but I would agree that describing this as classical random (albeit correlated) fluctuating dipoles on the atoms leads to misleading ideas. In particular radiation. However Sascha embraces this idea of continual fluctuation but just qualifies that it is quantum fluctuations in a ground state and so can't radiate. That is very much missing the point.

    The ground state of two helium atoms held some distance r away from from each other does not have "these fluctuations are actually of quantum nature and never calm down." No, the ground state is stationary. The phase of the overall wave-function changes but the probability density is constant. If it fluctuated, it would couple to radiation even in quantum mechanics, so his picture of forever fluctuating atoms is wrong.

    All that is happenning is that the electron positions around the two atoms are correlated in the ground state. The correlation is much what one would intuitively expect from the classical picture: the correlation in the wave-function shows that if you disturbed the system by measuring the position of multiple electrons, you'd find a correlation between the resulting atom dipoles. But that does not mean the quantum system in its ground state is fluctuating between all these different possible position measurement outcomes as described by the ground state wave-function. The ground state is a stationary state.

    vongehr
    I dislike the strange semantics games you always play
    Careful terminology is very important if one does not want to talk pseudo issues.
    you change the title of your incestuous pedophile rapist murderer article ...
    Because its length made problems with the software - it could not properly link. Here on alpha meme, if a theory tells us that you rape your mama in a parallel world, we gona call a spade a spade. If you like people only telling you half the truth, there are plenty of cheerleaders for establishment naive scientism out there who can give you that diet. Here I look straight at the issues in order to fight the credibility crisis that science is in.
    It is the _energy_ not the force that goes like 1/R^6.
    Thank you for pointing this out. Finally you have something marginally useful to say. ;-) Yes, spatially fixed dipoles have E ~ 1/R3, Boltzmann averaged (~ ongoing fluctuation) have 1/R6. Let me fix this in the article and tell me if it is better now.
    I would agree that describing this as classical random (albeit correlated) fluctuating dipoles on the atoms leads to misleading ideas. In particular radiation.
    Thank you, yes this is the main point, namely guarding against the widespread misconception that QM is just some random jumping about of the little stuff. Such is heat and is very very different from true quantum physics.
    Sascha embraces this idea of continual fluctuation but just qualifies that it is quantum fluctuations in a ground state and so can't radiate. That is very much missing the point.
    Well, unobserved quantum fluctuations are a difficult issue. I do not "embrace" them - I simply have to deal with that picture since it is the one that is widely presented in relation to VdW. Again, QM is not there actually being fluctuating small stuff. Such is indeed missing the point, as I have stressed in many articles. Sorry if in this article it perhaps comes across as if I somehow embrace such a picture via the many world interpretation. I do not.
    "these fluctuations are actually of quantum nature and never calm down." No, the ground state is stationary. ... ALL THE REST
    Yes, to the outside observer, but the molecules observe each other, and in that perspective it is that the quantum fluctuations come in. The universe is in a stationary state and never changes at all, but that does not mean that sub systems (you and me) do not see time going on. Fluctuations/particles are observer dependent. It is like if you fall into a black hole and the Hawking radiation between you and the black hole is not there anymore (neglecting grey body factors, Hawking radiation is Unruh temperature seen by accelerated observers, i.e. if you fall freely, there is none). Hawking radiation is QM fluctuation, this means whether it is there or not depends on who looks.

    For those who want to look into the intricacies of the London Dispersion Force, there is an interesting section on the linked Wiki page that one can start from:
    Note that this final London equation does not contain instantaneous dipoles (see molecular dipoles). The "explanation" of the dispersion force as the interaction between two such dipoles was invented after London gave the proper quantum mechanical theory. See the authoritative work[5] for a criticism of the instantaneous dipole model and[6] for a modern and thorough exposition of the theory of intermolecular forces. 
    The universe is in a stationary state and never changes at all, but that does not mean that sub systems (you and me) do not see time going on.

    Sorry about the lack of formatting, I can't log in.

    Okay, "The universe is in a stationary state"... How can we possibly know that? Surely if all evolving states are possible and therefore non-zero in the wavefunction it would be very unlikely for the superposition to be stationary?

    I may very well be missing something but please explain why the universe would be different in this respect from any system where we take account of observer, decoherence and entanglements. Thanks.

    Please ignore. I've realized what you mean by the universe being unchanging but I can't delete it. because of the login problem. Cheers.

    vongehr
    Well, lets not delete it, since perhaps others still do have the same question. The point is that under the assumption of a wave function of the universe, the state of it must be stationary (e.g. the energy uncertainty is zero, thus time uncertainty is infinite). This has been explained for example by the following paper I believe to remember correctly:
    Page, DN and Wootters, WK (1983) Evolution without evolution: Dynamics
    described by stationary observables. Physical Review D27, 2885
    Thank you. I like , no I learn from you physics explanation. I will have to back track through your links to understand, e.g. Tautology, Susskind,many worlds, etc, but I will.

    What I appreciate is that you are trying to explain the difficult physics that is even , perhaps, misunderstood my many excellent physicist. Hence you give me the courtesy of trying to explain what is difficult and not yet settled, I.e. many worlds, but that is an advanced interpretation.

    So I will be reading to understand. And will follow links etc to understand. And when I understand enough to comment or ask a question I will.

    "if they were dipoles that just induce each other and then stay as they are, it would be 1/R^3"

    Can you explain this in more depth? LagrangianForBreakfast's explanation seems pretty straightforward and makes sense. The field of the dipole goes as 1/r^3, and induced dipole is proportional to the field so is on the order 1/r^3 and the energy is on the order p . E so all together gives 1/r^6. What is wrong in that logic?

    "1/R^6 energy dependence is just like two very hot and thus randomly rotating electric dipoles"

    It doesn't matter if the dipole rotates. There is an angle dependence, but the dependence on the order of r remains the same.

    "** QM fluctuations are observer dependent - they "exist" when you describe the situation as one molecule observing the other."

    I didn't see what you wrote before you corrected it, so maybe I'm missing something, but it is not clear to me what you are saying about the fluctuations. So an isolated atom has spherical symmetry in the charge distribution, and then another atom comes along and "observers" it and so partially collapses the electron wavefunction in the position basis? And therefore splits all these possibilities of what it measured (what dipole it sees) into different parallel worlds? But then would each and every one of those parallel worlds see one definite dipole moment due to the measurement? That doesn't sound right at all to me. I don't think I understand what you are saying about the fluctuations and many worlds.

    vongehr
    Can you explain this in more depth? LagrangianForBreakfast's explanation seems pretty straightforward and makes sense.
    LFB's explanation is fine but does not bother to use the different dependencies (according to whether there are or are not fluctuations) in order to criticize the wrong but common explanation for VdW; the latter being my point.
    It doesn't matter if the dipole rotates. There is an angle dependence, but the dependence on the order of r remains the same.
    No - if the dipoles consistently rotate randomly inside a thermal bath, the classical dependence is 1/R6 due to the average interaction - the same as the quantum VdW-London dispersion. The quantum fluctuations and the classical ones work quite similar, which is perhaps what lead to the misconception. But the quantum fluctuations cannot be observed outside of the compound system (they do not radiate, neither do they need the thermal bath - their "temperature" is the Heisenberg constant).
    I didn't see what you wrote before you corrected it, so maybe I'm missing something,
    I only took out the misleading "F" and did not remove much else. Just added some stuff.
    But then would each and every one of those parallel worlds see one definite dipole moment due to the measurement? That doesn't sound right at all to me.
    It is somewhat like the alive Schroedinger cat looking at the intact vial while the other cat is dying and sees the broken flask. They still are in a superposition to the outside observer. The difference is that the dead cat stays dead while an atom forgets everything with every new interaction - i.e. those parallel worlds are consistently re-merging.
    rholley



    Not just Geckos.  How about these ...




    War Goethe ein größeres Wunder
    Als eine kleine Fliege?
    Das ist hier die Frage.
    Sieh, wie sie so
    An der glatten Wand entlangwandelt ...

           Heinz Erhardt
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Actually, I think flies excrete a tiny amount of liquid as a binding agent and take advantage of their extremely light weight, as opposed to spiders and geckos which use van der waals.

    http://www.livescience.com/10536-flies-walk-ceilings.html

    rholley
    According to a recent BBC programme, certain beetles* also stick by the gecko method.

    Based on these, here is an interesting development at the University of Kiel, which the programme stated were definitely not due to an adhesive liquid layer:

    Insect-o-stick... the adhesive tape that borrows nature's tricks


    This is coming from the same researcher that found the fly secretions.




    *not this kind of Beetle, though:


    Robert H. Olley / Quondam Physics Department / University of Reading / England
    blue-green

    This is too important to leave to a hand waving “calculation”.

    Time for some magical math, just as Einstein had to do on the bending of starlight to get people to think out of the box.

    I fully subscribe to Sasha's think before you calculate touchstone. As John Wheeler emphasized in his Special Relativity primer fifty years ago: Spacetime Physics page 60:

    WHEELER'S FIRST MORAL PRINCIPLE. Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun! 
    [end quote]


    There is an alternative to the Many Worlds Interpretation that Wheeler published in German and English in the late 1960s and early 1970s. It is worth noting that Wheeler was the thesis adviser for both Feynman's Path Integral approach and also Hugh Everett's relative-state theory, so he was at the incubation state of all later MWIs …. and he had his reservations about all them, even his own work.

    Wheeler's approach involved a “Superspace” in which each point represents a “3-geometry” shaped by matter. The basic idea was that quantum fluctuations or even gravitational collapse at 10^-33 cm Plank scales causes the sheer number and variety of viable and significantly probable 3-geometries to burst out of what can be stuffed into any single 4D spacetime, no matter how you slice it into  space-like slices of wavy pastrami and grits.

    As long as no one actually does the hard calculations as Einstein did ~ the magical maths ~ we will never know what sort of full theory is needed to explain the Geckos tap dancing on the ceiling of a Thai kitchen. There are too many “versions” of string theory, MWI, Superspace and good-old-fashioned Van der Waals for the hand-waiving to cut to the chase. After applying Wheeler's First Moral Principle, it is time to get to the second one.