Renaming the Pauli principle

The feature “Putting the Pauli exclusion principle on trial” (CERN Courier March 2018 p35) was extremely interesting, describing highly accurate experiments that have put severe limits on the possible violation of the Pauli principle. Testing this sacrosanct principle reminds me that, at CERN, we test charge-parity-time (CPT) invariance with antinuclei and antiatoms.

Two points struck me from the article. First, the authors say, rightly, that 50 years ago Freeman Dyson and Andrew Lenard proved that the “stability of matter” follows from the Pauli Principle. However, this proof was very complex and, in 1975, Elliott Lieb and Walter Thirring produced a much simpler proof that also gave almost realistic numbers for the binding energy and the minimum volume occupied by a neutral assembly of charged particles (Phys. Rev Lett. 36 687). I am slightly astonished that the authors do not quote this paper, especially since one of the authors is from Vienna and I believed that Thirring was well known in this city.

The second point is historical and concerns the “modern form” of the Pauli principle expressed via the asymmetry of the wave function, as described by the authors. When Pauli proposed the exclusion principle in 1925, the Schrödinger equation did not exist; Pauli was thinking in terms of an independent particle model where particles could be given definite quantum numbers. My late friend, the great theoretician Vladimir Glaser, told me that it was in fact Heisenberg who at the same time understood the usefulness of generalising the Schrödinger equation to N particles and replaced the Pauli principle by the requirement of the asymmetry of the wave function with respect to the exchange of electrons (including spin). We all know how important the generalisation of the Schrödinger equation was to N particles since it allows one to calculate the binding energy of any atomic or molecular system, given enough computing power. The Schrödinger equation has even been used to calculate the masses of hadrons considered as systems of quarks, its only defect being that it is nonrelativistic.

These facts are confirmed in the book called Out the Crystal Maze (Oxford University Press, 1997), which gives references to three fundamental papers of Heisenberg: two on the many-body problem in quantum mechanics (Z. für Physik 38 411 and Z. für Physik 41 239) and one on ions with two electrons (Z für Physik 39 1926). Frankly, it is too late, but I think that one should rename the Pauli principle as the Pauli–Heisenberg principle.

  • André Martin, formerly CERN.