Fermion and Boson classifications are not entirely set in stone. While individual particles are either one or the other, systems of particles can cause the laws to fail.

The differences between bosons (ghost-like particles such as photons, which possess whole-integer spin) and fermions (“normal” particles such as electrons, protons and neutrons with ½ integer spin) sounds simple enough, but it’s truly not. While the line between Bosons and Fermions seems both clear and definite – like the distinction between fire and water – there are some pretty strange exceptions to the rule.

Spin Addition

Individual electrons, protons and neutrons – those most basic elements of every atom, are all fermions, unquestionably so. However, if the true test of whether a particle is a fermion or boson lies in its spin number, then at those certain times when an even number of fermions get together to form a system, one must conclude that the sum total of their spin states creates a bosonic system, as two ½ integers added together always equal a whole number.

As a result, one should expect to see properties of bosons being displayed in certain types of atoms. Conversely when an odd number of fermions come together the fermionic properties remain. Using these same principles, no matter how many bosons may form together into a quantum system, the sum total, by way of simple arithmetic, will always remain a boson (though bosons don’t exactly interact with each other, so this point is rendered moot).

As strange as this may seem, it truly is the case, though most of the time when larger systems undergo this transition from fermion to boson, the effect is not noticeable, as the system (such as an atom or molecule) will generally continue to behave according to its own molecular properties. In rare cases, however, this is not always true.

Take helium as a classic example.

Superfluid Helium

While most isotopes of helium are indeed fermions as one would expect (the structure of individual atoms, by design, are fermionic in nature), atoms of helium with two protons and two neutrons (known as Helium-4) are considered bosonic due to the total spin of the system adding up to a whole integer. No, it’s not very interesting on the surface.

What makes this particular case remarkable, however, is the fact that in the case of helium, “quantum” features of the substance actually can become visible in a macroscopic sense.

When super-cooled (that is, cooled down to a temperature known as the “lambda point”, which in this case is somewhere around 2.17 kelvins, or -271 degrees Celsius, which makes it very difficult to duplicate in home freezers) Helium-4 transforms into a wonderful state known as superfluidity. It is here that the bosonic characteristics become visible, and it becomes an incredibly strange substance indeed – a substance which has become a wonderfully baffling puzzle for physicists for many years.

This superfluid helium possesses almost zero viscosity (viscosity is the measure of a liquid’s submission to friction, though it also relates to the overall “thickness” of the liquid – those with very high viscosity, such as syrup, are very thick and slow moving, while liquids with a low viscosity, like water, tend to be very thin and quick). In addition, this liquid seems to deny the most basic laws of thermodynamics by possessing zero entropy and almost infinite electrical conductivity (if electrical wires could be made out of superfluid helium, the cost of electricity would decrease dramatically). These features lead to some startling experimental results:

If placed into a container with an open top, superfluid helium is prone to completely disregard the effects of gravity, creeping its way up the sides and out of the container, and will continue to do so until its level is even on both sides of the container.

In addition (and even stranger), super-fluid helium appears to possess quantized rotational speed.

To picture this, it might help to imagine a bucket of water being spun around. As the bucket rotates faster, the water also begins to rotate with it, eventually forming a whirlpool. Very simple classical physics are involved in this. Superfluid helium, on the other hand, possesses what are called quantized vortices. This means that even its speed of rotation in a spinning container obeys quantum rules. As its container spins, the liquid helium remains motionless. When the container reaches a certain speed (known as the first critical velocity), the helium finally begins to rotate very quickly, skipping all in-between speeds (sound familiar? Think of an electron’s quantum leaps within an atom). For some very odd bosonic reasons, superfluid helium cannot possibly spin at any other speed than these particular, quantized velocities.

It is fairly obvious why this substance has become such an interest to quantum physicists, as it finally enables them to see certain quantum effects with their eyes, rather than simply on paper as mathematics. It is no wonder that a great physicist like Richard Feynman would have spent a great deal of his time studying this very subject.

And this is all do to the bosonic nature of certain particles.

References:

Weinberg, S. (1992). Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature. New York, NY: Vintage Books.

Oerter, R. (2006). The Theory of Almost Everything. New York, NY: Plume Printing.

Kl-Khalili, J. (2003). Quantum: A Guide for the Perplexed. New York, NY: Weidenfield & Nicolson.