News

Electrons, the ubiquitous constituents of matter, are very interesting objects of study. The electron was the first elementary particle to be discovered (by J.J. Thomson in 1897)  and today it belongs to the rather exclusive group of the fundamental particles of the Standard Model.

In 1927 Paul Dirac discovered the equation that describes the propagation (in space and time) of electrons. This was a great achievement: his equation incorporated Einstein’s theory of relativity and the principles of quantum mechanics (Bohr, Heisenberg, Schrödinger) at the same time. The Dirac equation had a very remarkable feature. It predicted, in fact it required, that if electrons exist, which is obviously the case, also the anti-particle of the electron should exist, but no such particle was known. Initially this was a problem for Dirac but when the positron was discovered (Anderson, 1933) this problem was solved.

The electron and the positron are distinctly different particles as they have opposite charge. Neutrinos are fundamental particles in many respects similar to electrons and positrons, with one distinct difference: they carry no electrical charge, they are neutral. And this opens the possibility that neutrinos and their

anti-particles, the anti-neutrino’s, are in fact the same particles. This possibility was suggested by Majorana (in a publication of 1937).  In somewhat technical terms, Majorana found a representation of the Dirac equation with real (as opposed to complex) wave functions as a solution. For a particle described by a real wave function the distinction between particle and anti-particle vanishes.

Both electrons and neutrinos carry a quantity called ‘spin’, angular momentum. They carry a spin of ½ unit. Such particles are called fermions. (All fundamental constituents of matter are fermions.) Their quantum-mechanical properties are very different from particles with ‘integer’ spin (bosons). This difference is expressed by the Pauli exclusion principle, it leads for example to electron orbits in atoms and explains the structure and stability of matter.

Whether neutrinos are ‘Dirac particles’ or ‘Majorana particles’ is a valid physics question that has not been answered to date. It is experimentally very difficult to answer this question, but experiments are ongoing. If neutrinos are Majorana particles this has profound consequences for our understanding of the nature of fundamental particles as encoded in the Standard Model.

Whether Majorana particles exist or not in nature remains an open question. Apart from neutrinos, so called neutralinos are candidates as well. Neutralinos appear in extensions of the Standard Model (invoking ‘super symmetry’ between fermions and bosons) but whether Supersymmetry is realized in nature is not at all sure. This is one of the questions the Large Hadron Collider at CERN is trying to answer.

Nature News of February 28, 2012 announces:  ‘Quest for quirky quantum particles may have struck gold’ , Evidence for elusive Majorana fermions raises possibilities for quantum computers. The scientific quality of this news article is rather poor. Although it is published by Nature. But it is a news article. Sensational, that sells. The achievement it describes is impressive, however. Leo Kouwenhoven and his group of Delft University have created a setup to demonstrate, for the first time, the existence of quantum states in a nano-device that are mathematically equivalent to Majorana ferminos as described above. Moreover such devices may be used as ‘quantum bits’ of futuristic quantum computers. Leo Kouwenhoven has produced a scientific result that ranks in a rare category: that of breakthroughs. We will hear more from him!

The question whether neutrinos are Majorana particles or Dirac particles continues to need an answer. Elementary particle physicists will have to continue their experiments to find out. The question whether neutralinos are realized in nature: high energy physics experiments will have to tell.

Meanwhile I will find out more about Majorana states in condensed matter and as soon as Kouwenhoven’s results are available in the Open Access literature I will read more about them with great interest!

Jos Engelen
March 2, 2012