## lördag 10 maj 2014

### Strange Laws by Strangest Man: Dirac

Paul Dirac, The Strangest Man, who conjured (strange) laws of nature from pure thought.

Paul Dirac coined in 1926 the name fermion after Enrico Fermi as an elementary particle with antisymmetric wave-function $\psi (x_1,…,x_N)$ as a function of $N$ three-dimensional space variables $x_1,…,x_N$, and a boson after Satyendra Nath Bose to have a symmetric wave-function.

Dirac conjectured that Nature is so constructed that only wave-functions which are either anti-symmetric or symmetric can occur, but could not give a reason other than mathematical beauty. Dirac was encouraged by the property of an antisymmetric wave function to change sign under permutation of two particles, which forbids two particles to be at the same spot (assuming the same spin), which he happily recognized as Pauli's exclusion principle.

Since then it has become an incontrovertible fact impossible to question that Nature only accepts either anti-symmetric or symmetric wave-functions, but no underlying reason has ever been presented, other than mathematical beauty (for people who rightly can admire such a thing).

But if there it has no physical reason, Dirac's conjecture may be wrong. The first evidence to this effect is that the wave-function for Helium appears to be neither symmetric nor anti-symmetric as representing a configuration with the two electrons separated into two opposite half spheres.  If Dirac's conjecture is wrong for $N=2$, it may well be wrong also for $N>2$ and then standard quantum mechanics collapses…