# Experimental evidence of Pauli's exclusion principle

A fermion is described by a set of quantum numbers, this set of numbers lead us to a unique wave function. If two fermions are described by the same wave function (violating the Pauli's exclusion principle), how can we differentiate this fermions if experimentally it produces the same result?

• – Phyllipe Oct 5 '13 at 22:14
• I'm getting the feeling this could be a semi-list kind of question, but I'll add this anyway: Bose-Einstein condensation (BEC) is a physical phenomenon which cannot occur in fermions mainly due to the exclusion principle. So the nonexistence of fermionic BEC's sort of corroborates the exclusion principle. – Wouter Oct 5 '13 at 22:36
• The answers below give the corroborative evidence which validate the Pauli exclusion principle for fermions. Note "validate" . It means that all measurements up to now are consistent with this principle. A principle or a theory dependent on a principle can never be proven correct by experiment in the sense of the QED at the end of mathematical proofs. They can only be falsified. There does not exist a measurement falsifying the principle, and there are thousands upon millions of measurements. – anna v Oct 6 '13 at 6:55

I think the atomic configuration is the strongest evidence to Pauli's Exclusion Principle. You simply have atoms that have energy levels sorted in a way that agrees with the pauli's principle.

Besides, the Zeeman effect shows the separation between different spins, which raises the degeneracy between the levels that agree in all quantum numbers but not the spin.

Actually, there is experimental work in progress to test the Pauli principle with higher accuracy ( http://iopscience.iop.org/1742-6596/447/1/012070/pdf/1742-6596_447_1_012070.pdf ): "The experiment VIP at the Gran Sasso underground laboratory is searching for possible small violations of the Pauli Exclusion Principle for electrons leading to forbidden X-ray transitions in copper atoms. VIP is aiming at a test of the Pauli Exclusion Principle for electrons with high accuracy, down to the level of $10^{-29}$-$10^{-30}$, thus improving the previous limit by 3-4 orders of magnitude."

Leaving aside the explanation of the valence structure of the atoms, the Pauli principle also explains some of the properties of the nuclei.

Moreover, exclusion leads to the prediction of degenerate gasses, which can be observed directly in a condense-matter context.

How can we know from the experiment that the Pauli's exclusion principle is ok?

This question seems to put the cart before the horse. The Pauli exclusion principle was formulated to help explain certain experimental results.

From Wiki:

Pauli looked for an explanation for these numbers, which were at first only empirical. At the same time he was trying to explain experimental results in the Zeeman effect in atomic spectroscopy and in ferromagnetism.

...

The Pauli exclusion principle helps explain a wide variety of physical phenomena. One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.

Pauli exclusion principle, assertion that no two electrons in an atom can be at the same time in the same state or configuration, proposed (1925) by the Austrian physicist Wolfgang Pauli to account for the observed patterns of light emission from atoms. The exclusion principle subsequently has been generalized to include a whole class of particles of which the electron is only one member.

etc.

• Of course the really interesting part is the extensions to other systems. Until then it was just another one of many quantum related ad hoceries. – dmckee --- ex-moderator kitten Oct 6 '13 at 0:49
• @dmckee, right, so, the proper question is not if there is experimental proof but if there are experimental results at odds with the (extended) principle. – Alfred Centauri Oct 6 '13 at 0:56
• @AlfredCentauri, many world's theory explains quantum measurement, but we cannot take it as truth because there is no way to experimentally demonstrate it apart from by saying it explains quantum measurement. So to demonstrate a theory experimentally, I would think you would need to have it demonstrate something other than the initial thing it was trying to explain in the first place. – Kenshin Oct 6 '13 at 3:42
• @Chris, a principle is not a theory. – Alfred Centauri Oct 6 '13 at 3:44
• @AlfredCentauri, what is the difference between a principle and a theory? Are principles assumed true until a counter example is shown, but theories are not assumed true until their predictions can be tested? What would happen if two principles predict the same thing? – Kenshin Oct 6 '13 at 3:49