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

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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.

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[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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