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Generalized Uncertainty Principle in Astrophysics from Fermi Statistical Physics Arguments
International Journal of Theoretical Physics ( IF 1.4 ) Pub Date : 2020-06-17 , DOI: 10.1007/s10773-020-04480-7
Rami Ahmad El-Nabulsi

The Heisenberg’s uncertainty principle is one of the most important concepts in quantum mechanics. One of its important outcomes is that enormously high momentum is required to look at extremely small length-scales. Nevertheless, quantum gravity and Grand Unified models taught us that a minimal observable length cutoff which is of the order of the Planck length is required. Such an important feature suggests that the conventional uncertainty principle must be generalized and accordingly the Heisenberg’s uncertainty principle is replaced by a generalized uncertainty relation. Although the effects of the generalized uncertainty relation can only be found in the context of extremely high energies/short distances and not at any scale currently probed in the laboratory, we discuss in this study its impacts on white dwarfs using the quantum mechanical statistical properties of a degenerate Fermi gas in D -spatial dimensions. Both the non-relativistic and extreme relativistic cases were discussed. It was observed that the effect of the generalized uncertainty relation is to shrink the radius of proton, a phenomenon which was observed recently using high precision laser spectroscopy of atomic hydrogen. Several points were discussed and a number of quantum statistical properties were derived.

中文翻译:

从费米统计物理论证看天体物理学中的广义不确定性原理

海森堡测不准原理是量子力学中最重要的概念之一。其重要结果之一是需要极大的动量才能观察极小的长度尺度。然而,量子引力和大统一模型告诉我们需要一个最小的可观察长度截止,它是普朗克长度的数量级。如此重要的特征表明,传统的不确定性原理必须被推广,因此海森堡的不确定性原理被广义的不确定性关系取代。虽然广义不确定性关系的影响只能在极高能量/短距离的背景下发现,而不是在实验室目前探测的任何尺度上,我们在这项研究中使用 D 空间维度中简并费米气体的量子力学统计特性讨论了它对白矮星的影响。讨论了非相对论和极端相对论的情况。据观察,广义不确定性关系的影响是缩小质子的半径,这是最近使用原子氢的高精度激光光谱观察到的现象。讨论了几个要点,并推导出了许多量子统计特性。最近使用原子氢的高精度激光光谱观察到的现象。讨论了几个要点,并推导出了许多量子统计特性。最近使用原子氢的高精度激光光谱观察到的现象。讨论了几个要点,并推导出了许多量子统计特性。
更新日期:2020-06-17
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