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If the two bosons are different particles there can be no interference between them. So the probability that a detector picks up the two ricocheting particles is simply the square of the height of the first wave plus the square of the height of the second wave, since the probability of anything happening in the microscopic world is always the square of the height of the wave associated with it. Well, it turns out—and this will have to be taken on trust—that the two probabilities are roughly the same. So the overall probability simply is twice the probability of each event happening individually.

Say the waves have a height of 1 for both processes. This would mean that if they were squared and added to get the probability for both processes, it would be (1 × 1) + (1 × 1) = 2. Now a probability of 1 corresponds to 100 per cent, so a probability of 2 is clearly ridiculous! But bear with this. It is still possible to make a comparison of probabilities, which is where all this is leading.

Now, say the two bosons are identical particles. In this case, the two possibilities—A going in direction 1 and B in direction 2, and A going in direction 2 and B in direction 1—are indistinguishable. And because they are indistinguishable, the waves associated with them can interfere with each other. Their combined height is 1 + 1. The probability for both processes is therefore (1 + 1) × (1 + 1) = 4.

This is twice as big as when the bosons were not identical. In other words, if two bosons are identical, they are twice as likely to ricochet in the same direction as if they were different. Or to put it another way, a boson is twice as likely to ricochet in a particular direction if another boson ricochets in that direction too.

The more bosons there are the more significant the effect. If n bosons are present, the probability that one more particle will ricochet in the same direction is n + 1 times bigger than if no other bosons are present. Talk about herd behaviour! The mere presence of other bosons doing something greatly increases the probability that one more will do the same thing.

This gregariousness turns out to have important practical applications—for instance, in the propagation of light.

LASERS AND LIQUIDS THAT RUN UPHILL

All the processes so far considered have involved particles colliding and ricocheting in a particular direction. But that is not essential. The arguments used could apply equally well to the creation of particles—for instance, the “creation” of photons by atoms that emit light.

Photons are bosons, so the probability that an atom will emit a photon in a particular direction with a particular energy is increased by a factor of n + 1 if there are already n photons flying in that direction with that energy. Each new photon emitted increases the chance of another photon being emitted. Once there are thousands, even millions, flying through space together, the probability of new photons being emitted is enormously enhanced.

The consequences are dramatic. Whereas a normal light source like the Sun produces a chaotic mixture of photons of all different energies, a laser generates an unstoppable tide of photons that surge through space in perfect lockstep. Lasers, however, are far from the only consequence of the gregariousness of bosons. Take liquid helium, which is composed of atoms that are bosons.

Helium-4, the second most common atom in the Universe, is one of nature’s most peculiar substances.

4

It was the only element to have been discovered on the Sun before it was discovered on Earth, and it has the lowest boiling point of any liquid, –269 degrees Celsius. In fact, it is the only liquid that never freezes to become a solid, at least not at normal atmospheric pressure. All these things, however, pale into insignificance beside the behaviour of helium below about –271 degrees Celsius. Below this “lambda point,” it becomes a superfluid.

Usually, a liquid resists any attempt to move one part relative to another. For instance, treacle resists when you stir it with a spoon and water resists when you