The Casimir force is a peculiar force that acts between small metallic objects placed
very very close to each other.
And it's becoming of important technological interest because people are trying to make
very small, miniaturised electronic circuits and in particular, switches, that are metal
plates that face each other and so this force has the effect of making small switches actually
stick together.
But like is often the case, when you look at the microscopic origin of the forces of
nature, also a Casimir force has a very deep quantum mechanical origin.
In fact, it is a microscopic manifestation of what's known as the quantum fluctuations
of the vacuum.
Before I get into the quantum mechanics of it, it's interesting to give a classical sailing
analogy of the Casimir force which is not completely correct.
There are people that debate whether the classical analogy really exists but I'm not a sailor
myself, so I cannot say very much about it.
But I'll tell you what the story is behind this.
In the mid 19th century, there was a book written by sailing instructor who spoke about
this mysterious force that makes ships stick together in a rough sea.
So what happens is this.
Imagine you take ship and you moor it in the sea and the sea is rough.
So there's a lot of waves hitting the ship from the left and from the right.
These waves could be high, could be low, could be very long wavelengths, short wavelengths,
but on average, they will hit the ship equally from the left and from the right.
So even though the ship might move left and right, on average, it will stay centred.
Now imagine you moor another ship next to the first one.
Now, in between the two ships, you can't just have any kind of waves.
Normally the sea would have to be calm in between the two ships or you could have waves,
provided that the wavelength of the waves matches the distance between the two ships
so you could have a wave that has half a period between the two ships, or an entire period,
or one and a half and so on but not just any wave.
So the net result is that there are more possible waves coming from outside the ships, than
from inside the ships and so as a result of that, the ships might be pushed together and
bang against each other.
There is an equivalent phenomenon taking place with electromagnetic waves treated quantum
mechanically.
So if instead of the ships, you now take two metal plates, and you place them facing each
other, in between the two metal plates that are essentially mirrors, you cannot have just
any wavelength of electro magnetic fields.
The electro magnetic field that quantum mechanic will allow you to have in between the two
plates, must have an integer multiple of the half wavelength of the electro magnetic field
in between the two plates.
Whereas from the outside, any wave could be allowed.
And so the net result is that there is a force which is called the Casimir force that tends
to push the two plates together.
So this is a microscopic manifestation of the quantisation of the field between two
reflective metal plates.
The interesting thing about this force is that it's very strongly dependent on the distance.
It's proportionate to the area of the metal plates, but it's inversely proportional to
the fourth power of the distance.
So when you make some very small metal plates and you put them very close to each other,
actually, this force can be substantial.
So this is bothering people who are trying to make what's called micro electron mechanical
switches, these are very small switches that are being used in micro electronic circuits,
particularly at high frequency.
Whereas actually what you're trying to do, is to take some metal switch that you can
pull up and down and it's facing some other metal plate.
So ideally, what you're trying to do is to pull this switch opened or closed.
But now, in between this lever and the back plate, there is this Casimir force due to
the quantisation of the electro magnetic field between them.
And so sometimes, these switches actually stick together so this fundamental quantum
mechanical force is nowadays posing a limitation to how you can miniaturise very small switches.