The quantum attraction I will talk about today has nothing to do with
people being attracted to each other because of some quantum phenomenon.
Although, it will enter in some living creature's life, which is the gecko sticking up glass walls.
It's an incredible feature that the gecko has and it's based upon a true attractive force
which is of quantum mechanical origin.
It's called the Van Del Waals force and I will try to explain to you in brief, where it comes from.
Let me get back to the really simple basics of attractive forces.
Everybody knows that if you take a positively charged particle and a negatively charged particle,
they attract each other. Opposite charges attract.
This is called the Coulomb Force, everyone knows that.
The next level of sophistication is to take dipoles.
A dipole is two charges of opposite sign held at some distance from each other.
So you can imagine that if you have two dipoles
they will attract each other if they are oriented in the right direction.
So in this case, there will be an attractive force between the positive and the negative here,
that is stronger than the attractive force between these ones because they are
further away so the two dipoles would like to click together along this axis.
A real life example of an electric dipole is water.
Water is H2O, it's made of an oxygen atom and two hydrogen atoms.
The thing that keeps the water molecule together is a covalent chemical bond
where electrons are shared between the hydrogen and the oxygen but in fact
there is a little bit more electron density on the oxygen side than there is on the hydrogen side.
So the water is like a negative charge on the side of the oxygen and a positive charge
on the side of the hydrogen. So the reason why water is liquid at room temperature is
because water molecules like to be together, they attract each other through this force
and when you go below zero degrees centigrade, it actually freezes and forms a solid
because of this attractive forces between dipoles.
Now let's go to yet the next level.
Let's try and find out what is the force between neutral particles and the simplest example
of that is a hydrogen atom. A hydrogen atom is one positive charge, a proton, and the
negative charge, an electron, orbiting around the proton. In fact, it doesn't quite orbit
around the proton like the moon around the Earth, but it's spread out in a wave of probability
around the proton and this wave of probability is spherically symmetric; it's the same in every direction.
Now let's imagine you take another hydrogen atom nearby and you ask yourself,
"Is there any force between these two hydrogen atoms?"
Well, you would be tempted to say that there isn't because this atom is overall charged neutral.
There's a positive and a negative charge cancelling each other and the same for this one.
You would say, "Well, but this proton attracts to that electron",
yes, but it also repels equally strongly with this other proton.
So if this was the end of the story, there would be no force between two neutral hydrogen atoms.
In fact, things are a bit more subtle than that.
This wave of probability of the electron around the proton has quantum fluctuations.
So the actual position of the electron around the proton fluctuates in time.
So you can well imagine that at some point in time, the first proton could have
an electron cloud around it that is a little bit skewed towards the right.
And if the same happens at the same time with the hydrogen on the right hand side
then what you have is two dipoles.
Because this is a essentially like a dipole that is positive on the left and negative on the right and the same on this one.
So these two dipoles now are attract each other.
But these fluctuations of the electron cloud are random.
So on average, the electron is around the middle.
So there could be some time where these two hydrogen atoms attract each other but then there could be another time
where the cloud of the electron on the right hand side hydrogen is on skewed to the left and so they actually repel.
So on average, you would think they still don't have any force between each other.
The interesting thing is that when you put them really close together,
you get some form of correlation between the quantum fluctuations of the two electron charges.
So in other words, if you calculate the average position
let's say along the X axis, the horizontal axis of these electron, the average value is zero.
And the same for this one.
But if you calculate the product of the position of electron number one and the position of electron number two,
so X1 times X2
on average is non-zero when the fluctuations are correlated
meaning that the fluctuation of one electron cloud
essentially induces the fluctuation of the other electron cloud so they go together.
And when they do so, there is a net attractive force between these atoms that are otherwise charged neutral.
This is a very important, very fundamental microscopic force of pure quantum-mechanical origin
and the amazing thing is that there are large living creatures that use it.
The geckos are capable of climbing on glass walls.
They stick to the glass with an incredible force and what they use is precisely a microscopic version
of this quantum-mechanical force.
And nowadays there are people who are trying to build robots that artificially exploit this force
to climb for example, on glass walls.