Editing Pauli exclusion principle (section)

=== Stability of matter ===

{{further|Stability of matter}}

The stability of each electron state in an atom is described by the quantum theory of the atom, which shows that close approach of an electron to the nucleus necessarily increases the electron's kinetic energy, an application of the [[uncertainty principle]] of Heisenberg.<ref name=Lieb>{{Cite arXiv |eprint = math-ph/0209034|last1 = Lieb|first1 = Elliott H.|title = The Stability of Matter and Quantum Electrodynamics|year = 2002}}</ref> However, stability of large systems with many electrons and many [[nucleons]] is a different question, and requires the Pauli exclusion principle.<ref name=Lieb2>This realization is attributed by {{cite arXiv |eprint = math-ph/0209034|last1 = Lieb|first1 = Elliott H.|title = The Stability of Matter and Quantum Electrodynamics|year = 2002}} and by {{cite book |author=G. L. Sewell |title=Quantum Mechanics and Its Emergent Macrophysics |isbn=0-691-05832-6 |year=2002|publisher=Princeton University Press}} to F. J. Dyson and A. Lenard: ''Stability of Matter, Parts I and II'' (''J. Math. Phys.'', '''8''', 423–434 (1967); ''J. Math. Phys.'', '''9''', 698–711 (1968) ).</ref>

It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume. This suggestion was first made in 1931 by [[Paul Ehrenfest]], who pointed out that the electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells. Atoms, therefore, occupy a volume and cannot be squeezed too closely together.<ref>As described by F. J. Dyson (J.Math.Phys. '''8''', 1538–1545 (1967)), Ehrenfest made this suggestion in his address on the occasion of the award of the [[Lorentz Medal]] to Pauli.</ref>

The first rigorous proof was provided in 1967 by [[Freeman Dyson]] and Andrew Lenard ([[:de:Andrew Lenard|de]]), who considered the balance of attractive (electron–nuclear) and repulsive (electron–electron and nuclear–nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle.<ref>F. J. Dyson and A. Lenard: ''Stability of Matter, Parts I and II'' (''J. Math. Phys.'', '''8''', 423–434 (1967); ''J. Math. Phys.'', '''9''', 698–711 (1968) )</ref><ref name=Dyson1967a>
{{cite journal
 | last =Dyson
 | first =Freeman
 | title =Ground-State Energy of a Finite System of Charged Particles
 | journal =J. Math. Phys.
 | volume =8
 | issue =8
 | pages =1538–1545
 | year =1967
 | doi =10.1063/1.1705389
 |bibcode = 1967JMP.....8.1538D
}}</ref>
A much simpler proof was found later by [[Elliott H. Lieb]] and [[Walter Thirring]] in 1975. They provided a lower bound on the quantum energy in terms of  the [[Thomas-Fermi model]], which is stable due to a [[Density functional theory#Thomas–Fermi model|theorem of Teller]]. The proof used a lower bound on  the kinetic energy which is now called the [[Lieb–Thirring inequality]].

The consequence of the Pauli principle here is that electrons of the same spin are kept apart by a repulsive [[exchange interaction]], which is a short-range effect, acting simultaneously with the long-range electrostatic or [[Coulombic force]]. This effect is partly responsible for the everyday observation in the macroscopic world that two solid objects cannot be in the same place at the same time.