Galileo's Sky

這是 study GMR 時, 順便看到的, 好熟悉的名詞, 但是都忘光了,
只大約記得 兩電子(其實是相同的 fermions) 不能同時俱有相同的 quantum state.
沒想到這定理解釋了一些很重要的日常生活現象!

it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same time allowing light and radiation to pass.

...

The Pauli exclusion principle helps explain a wide variety of physical phenomena. One such phenomenon is the "rigidity" or "stiffness" of ordinary matter (fermions): the principle states that identical fermions cannot be squeezed into each other (cf. Young and bulk moduli of solids), hence our everyday observations in the macroscopic world that material objects collide rather than passing straight through each other, and that we are able to stand on the ground without sinking through it.



以下是節錄 Wikipedia 的內容:
純粹是好奇, 沒看懂就算了!



fermions are particles with half-integer spin, such as protons and electrons. They are named after Enrico Fermi.


The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. This principle is significant, because it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same time allowing light and radiation to pass. It states that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that, for two identical fermions, the total wave function is anti-symmetric. For electrons in a single atom, it states that no two electrons can have the same four quantum numbers, that is, if n, l, and m_l are the same, m_s must be different such that the electrons have opposite spins.


The Pauli exclusion principle is one of the most important principles in physics, primarily because the three types of particles from which ordinary matter is made—electrons, protons, and neutrons—are all subject to it; consequently, all material particles exhibit space-occupying behavior. The Pauli exclusion principle underpins many of the characteristic properties of matter from the large-scale stability of matter to the existence of the periodic table of the elements.

Particles with antisymmetric wave functions are called fermions—and obey the Pauli exclusion principle. Apart from the familiar electron, proton and neutron, these include neutrinos and quarks (from which protons and neutrons are made), as well as some atoms like helium-3. All fermions possess "half-integer spin", meaning that they possess an intrinsic angular momentum whose value is (Planck's constant divided by 2π) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by "antisymmetric states", which are explained in greater detail in the article on identical particles.

Particles with integer spin have a symmetric wave function and are called bosons; in contrast to fermions, they may share the same quantum states. Examples of bosons include the photon and the W and Z bosons.



The Pauli exclusion principle helps explain a wide variety of physical phenomena. One such phenomenon is the "rigidity" or "stiffness" of ordinary matter (fermions): the principle states that identical fermions cannot be squeezed into each other (cf. Young and bulk moduli of solids), hence our everyday observations in the macroscopic world that material objects collide rather than passing straight through each other, and that we are able to stand on the ground without sinking through it. Another consequence of the principle is the elaborate electron shell structure of atoms and of the way atoms share electron(s) - thus variety of chemical elements and of their combinations (chemistry). (An electrically neutral atom contains bound electrons equal in number to the protons in the nucleus. Since electrons are fermions, the Pauli exclusion principle forbids them from occupying the same quantum state, so electrons have to "pile on top of each other" within an atom).

For example, consider a neutral helium atom, which has two bound electrons. Both of these electrons can occupy the lowest-energy (1s) states by acquiring opposite spin. This does not violate the Pauli principle because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states. However, the spin can take only two different values (or eigenvalues). In a lithium atom, which contains three bound electrons, the third electron cannot fit into a 1s state, and has to occupy one of the higher-energy 2s states instead. Similarly, successive elements produce successively higher-energy shells. The chemical properties of an element largely depend on the number of electrons in the outermost shell, which gives rise to the periodic table of the elements.


Astronomy provides another spectacular demonstration of this effect, in the form of white dwarf stars and neutron stars. For both such bodies, their usual atomic structure is disrupted by large gravitational forces, leaving the constituents supported by "degeneracy pressure" alone. This exotic form of matter is known as degenerate matter.
In white dwarfs, the atoms are held apart by the degeneracy pressure of the electrons.
In neutron stars, which exhibit even larger gravitational forces, the electrons have merged with the protons to form neutrons, which produce a larger degeneracy pressure. Neutrons are the most "rigid" objects known - their Young modulus (or more accurately, bulk modulus) is 20 orders of magnitude larger than that of diamond.

According to general relativity, in the centers of black holes the gravitational forces would become so intense that everything would break down into fundamental particles, which are supposedly point-like with no internal structure. All of these particles could then pile up at one zero-dimensional point because the gravitational forces would be greater than the degeneracy pressure . This would seem to violate the Pauli exclusion principle, but since the interiors of black holes are beyond the event horizon, and thus inaccessible to experimental verification, this hypothesis remains untested.