Why are there unstable particles? What is the mean-life?

A muon from cosmic rays travels towards the Earth's surface and at a given moment, it disappears, with an electron and a neutrino appearing in its place. As a child might ask: why do muons get tired of living?

There are stable particles, such as electrons, which last forever unless they are absorbed. Others, however, are unstable: after a while they spontaneously decay into different, lighter particles. This is the case, for example, with muons, which are said to have a mean-life of 2.2 millionths of a second (or microseconds: 2,2·10^-6 s). It must be said that these particles have never existed "inside" the decaying particles...

The mean-life of a particle is a probabilistic concept: it is impossible to predict when any given muon will decay. If we observe a big population of particles at rest, their mean-life is the average lifetime of those particles before decaying and it is a constant across different experiments: a characteristic of each kind of particle. Besides, the mean-life is the average time in which a very large population of identical particles is reduced to a fraction 1/e of the initial one, i.e. about 37% (“e” is approximately 2,718).

For example, if we start with 100 000 000 000 muons, after 2.2 microseconds an average of 37 000 000 will be left, and after twice that time only 13 000 000. In about 18 half-lives there should be only one particle left out of the initial 100 000 000 000 000!

But we haven't answered the question of why they are unstable. It just so happens...?

Actually, for many physicists, the elementary particles (1) - which we mistakenly imagine as little balls - are not the "basic building blocks" from which everything is made. The basic ingredients would be quantum fields, which are extended like fluids, not localised like particles. So for example, the muonic field would be "something" that fills the universe and under certain circumstances can condense as a localised wave that travels and carries energy, i.e. behaves like a particle.

These localised waves, like all the vibrations we know, dissipate spontaneously - for example, the strings of a guitar stop vibrating if we don't give them energy, just like the waves we make in a swimming pool, etc. - what happens is that in the quantum world, the particles do not dissipate little by little, but they do so instantaneously, transforming themselves into other particles.

And why are there stable particles? Suffice it to say here that the Universe seems to obey strictly a set of very fundamental laws: “conservation laws". For example, the electric charge or the total energy cannot vary in any physical process. So, for example, an electron is stable because there are no lighter – so that energy is conserved - charged particles to disintegrate into. Heavier charged particles are all unstable because in the quantum world, our world, everything that is not forbidden happens.

_{(1) More information about elementary particles at https://particleadventure.org/ or, only in Spanish, in the Experimenta booklet "Cosmic rays": http://www.muncyt.es/stfls/MUNCYT/Publicaciones/rayos_cosmicos_muncyt.pdf}