Galileo's Sky

Degenerate matter (退化物質)

一種很有趣的現象,
因為 包利不相容原理, 使得一些粒子(fermions)無法在同時處在同一量子態,
所以當一物質的密度高到一定程度, 也就是構成粒子靠得非常緊密時,
任何要使得此物質靠得更緊密(密度升高)的力量, 將使得此物質只能提升到更高的能態,
因此需要很大的力量, 這也就是外界所感受到的阻力.
此時支撐此物體的力量稱為 degeneracy pressure, 而這種物質就稱為 degenerate matter.

當恆星演進至生命末期時, 因為氫氣已經燃燒殆盡, 此時重力主導一切,
因此恆星開始收縮, 使得核心密度急劇升高, 此時會產生更多的熱,
接著又有一連串的反應和變化, 若重力仍然主導一切,
會進一步收縮, 直到 degeneracy pressure 與之抗衡, 此時就是 白矮星(white drawf)了.
若此時分子運動速度已接近光速(因為 Heisenburg uncertainty principle 的關係),
degeneracy pressure 也撐不住了, 重力再度戰勝, 恆星核內的原子結構開始崩解,
若 degeneracy pressure 還是無能為力, 連原子核也撐不住了,
電子開始與原子核內的質子開始結合, 於是焉, 中子星 (neutron star) 誕生了!
中子星的支撐力量還是 包利不相容原理 的 degeneracy pressure!

故事先說到這裡.

degeneracy pressure 和 gravity,
基本粒子的量子力學 和 恆星生老演化 直接連線,
從小尺度的微觀世界現象, 直接影響大尺度的巨觀世界行為,
這真的是太神奇了!!





Wikipedia:

Degenerate matter is matter which has sufficiently high density that the dominant contribution to its pressure arises from the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle forbids the constituent particles to occupy identical quantum states. Any attempt to force them close enough together that they are not clearly separated by position must place them in different energy levels. Therefore, reducing the volume requires forcing many of the particles into higher-energy quantum states. This requires additional compression force, and so is felt as a resisting pressure. The species of fermion are sometimes identified, so that we may speak of electron degeneracy pressure, neutron degeneracy pressure, and so forth.

Imagine that there is a plasma, and it is cooled and compressed repeatedly. Eventually, we will not be able to compress the plasma any further, because the Exclusion Principle states that two particles cannot be in the exact same place at the exact same time. When in this state, since there is no extra space for any particles, we can also say that a particle's location is extremely defined. Therefore, since (according to the Heisenberg Uncertainty Principle) uncertainty in momentum × uncertainty in space = Planck's Constant/4π, then we must say that their momentum is extremely uncertain since the molecules are located in a very confined space. Therefore, even though the plasma is cold, the molecules must be moving very fast on average. This leads to the conclusion that if you want to compress an object into a very small space, you must use tremendous force to control its particles' momentum.

Unlike a classical ideal gas, whose pressure is proportional to its temperature (PV = NkT, where P is pressure, V is the volume, N is the number of particles (typically atoms or molecules), k is Boltzmann's constant, and T is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas is given by P = Kn^{5 / 3}, where K depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by P = K'n^{4 / 3}, where K' again depends on the properties of the particles making up the gas.

Degenerate matter still has normal thermal pressure, but at high densities the degeneracy pressure dominates. Thus, increasing the temperature of degenerate matter has a minor effect on total pressure until the temperature rises so high that thermal pressure again dominates total pressure.

Exotic examples of degenerate matter include neutronium, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter as a significant contribution to their pressure is provided by the interplay between the electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons allocated among the quantum states determined by the nuclear electrical potentials. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with the case of the degenerate matter that forms the body of a white dwarf where all the electrons would be treated as occupying free particle momentum states.

At the end of a star's life, gravity has an enormous grip on the star's core, and compresses it to where it can go no further because of degeneracy pressure. However, as the molecules' average speed approaches (within quantum uncertainty) the speed of light to make up for gravity, then degeneracy pressure can do no more, because nothing can move faster than the speed of light. If degeneracy pressure fails in this way, then the atoms crush into atomic nuclei in a degenerate electron gas, and if degeneracy pressure fails again, then the electrons will crush into the nuclei and combine with protons to become neutrons.