New experimental limit on the Pauli exclusion principle violation by electrons from the VIP experiment

The Pauli Exclusion Principle (PEP) represents one of the fundamental principles of the modern physics and is at the very basis of our understanding of matter: thus it is of foremost importance to test the limits of its validity. The PEP is a manifestation of the Spin-Statistics relation: the half-integer spin particles (fermions) follow Fermi statistics, while the integer-spin particles (bosons) the Bose –Einstein one, and is intimately related with the notion of “identity” of particles. In its original form the PEP was an adjunct to Bohr’s old quantum theory, which stated that an electron in an atom could only move to one of a discrete set of orbits; on the basis of experimental findings (X-ray atomic spectra for example) Pauli added the postulate that only one electron in the atom can fill each of the allowed orbits (including the spin in the orbit’s definition). When Bohr’s theory gave way to modern quantum mechanics, in which the traditional planet-like orbits of electrons in atoms are replaced by the more abstract notion of the electron states, the PEP survived as the statement that no two electrons could be in the same state (i.e. they cannot have the same quantum numbers). More generally, there is a strong connection between spin and symmetry class, as Pauli stressed in his Nobel Lecture “…we want to stress here a law of Nature which is generally valid, namely, the connection between spin and symmetry class. A half-integer value of the spin quantum number is always connected with antisymmetrical states (exclusion principle), an integer spin with symmetrical states”. In the same Nobel lecture however, Pauli himself says “Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from more general assumption. I had the feeling and I still have it today, that this is a deficiency. The impression that the shadow of some incompleteness fell here on the bright light of success of the new quantum mechanics seems to me unavoidable”. This statement, more than 60 years after Pauli formulated it, can be repeated practically unchanged – not much progress has been achieved in the deep understanding of the physical origin of the spin-statistics relation. As a consequence, even if today there are no compelling reasons to doubt the validity of the Pauli Exclusion Principle, it still spurs a lively debate on its limits, as testified by the abundant contributions found in the literature and in topical conferences. Here I describe a method to observe possible small violations of the PEP for electrons, through the search for anomalous X-ray transitions in copper atoms, produced by new electrons in a copper block (introduced by a circulating current), which can be captured in a Pauli-forbidden transition to the 1S level, already occupied by two electrons. In 1990, an upper limit on the PEP violation was found using this method by Ramberg and Snow (RS) with a dedicated experiment. The search method is implemented in the VIP (Violation of the Pauli Exclusion Principle) experiment, an international collaboration among 6 Institutions from 4 countries, that has the scientific goal to improve by three-four orders of magnitude the RS’s limit on the probability of PEP violation for electrons, bringing it into the 10^-29–10^-30 region, which may be of particular interest for all those theories related to possible PEP violations, and that would come from new physics. Reaching such limits opens up some very interesting scenarios, as stressed by Duck and Sudarshan: “… recently… membrane theorists have been speculating on a large compactification radius for one of their eleven dimensions, which could give a ratio (for PEP violation) of 10^-30”. VIP has performed the most precise measurement on the validity of PEP for electrons, establishing the limit on the probability of its violation at 5.7 x 10^-29. This result, presented here for the first time, improves on RS measurement by almost three orders of magnitude, and represents the reference value for all those theories that deal with possible violations of spin-statistics relation.

Il Principio di Esclusione di Pauli (PEP) rappresenta uno dei principi fondamentali della fisica moderna ed è alla base della nostra comprensione della materia. Il PEP è una manifestazione della relazione Spin-Statistica ed è intimamente correlato alla nozione di “identità” delle particelle. Nella sua forma originale il PEP fu una conseguenza della vecchia teoria quantistica di Bohr, secondo la quale un elettrone in un atomo avrebbe potuto muoversi solo attraverso un set discreto di orbite. Sulla base di osservazioni sperimentali (ad esempio i raggi-X negli spettri atomici) Pauli aggiunse il postulato secondo cui in un atomo un solo elettrone può occupare ciascuna delle orbite consentite (includendo la definizione di Spin). Quando la teoria di Bohr cedette il posto alla meccanica quantistica moderna, in cui le tradizionali orbite tipo-pianeta degli elettroni nell’atomo vennero sostituite dalla più astratta nozione di stati elettronici, il PEP si tradusse nel fatto che due elettroni non avrebbero potuto trovarsi nello stesso stato (cioè i due non avrebbero potuto avere gli stessi numeri quantici). Tale stato di cose è rimasto invariato dopo oltre 60 anni dalla formulazione di Pauli. Di conseguenza, sebbene non ci siano motivi di dubitare la validità del Principio di Esclusione, oggi si dibatte sui suoi limiti. In questa tesi descriverò il metodo per osservare possibili piccole violazioni del PEP per gli elettroni, attraverso la ricerca di raggi-X provenienti da transizioni anomale in atomi di rame. Tali transizioni sarebbero prodotte da elettroni “nuovi” introdotti attraverso un flusso di corrente in una lamina di rame, che potrebbero essere catturati e compiere transizioni (che violano il PEP) verso un livello 1S già occupato da due elettroni con spin opposto. Nel 1990, un limite superiore alla probabilità di violazione del PEP fu trovato, sfruttando tale metodo, da Ramberg and Snow (RS). L’esperimento VIP (Violation of the Pauli Exclusion Principle) ha effettuato le misure più precise sulla validità del PEP per elettroni, fissando il limite della probabilità sulla sua violazione a 5.7 x 10-29. Questo risultato, presentato qui per la prima volta, ha migliorato le misure di RS per almeno tre ordini di grandezza e rappresenta il valore di riferimento per tutte quelle teorie che sono correlate ad una possibile violazione della relazione spin-statistica.