实验室测试量子引力的一个建议
A proposal for testing Quantum Gravity in the lab
摘要：
试图建立量子引力理论的尝试统称为{ \it量子引力}。各种量子引力的方法，如弦论和圈量子引力，以及黑洞物理学和双狭义相对论预测了最小可测量长度，或最大可观测动量，以及海森堡不确定原理的相关修正，即所谓的广义不确定原理（GUP）。我们已经提出了一个GUP与弦论，黑洞物理学和双狭义相对论理论一致，并已表明，这修改了所有的量子力学哈密顿量。当应用于一个基本粒子时，它意味着限制它的空间必须是量子化的，事实上，所有可测量的长度都以基本长度（可以是普朗克长度）为单位量子化。一方面，这可能标志着时空连续体图像在该尺度附近的崩溃，另一方面，它可以根据当前的观测结果预测GUP中量子引力参数的上限。此外，这种基本的空间离散性可能会在比普朗克尺度大得多的尺度上产生可观察到的后果。因为这以一种普遍的方式影响所有的量子哈密顿量，它预言了各种量子现象的量子引力修正。因此，在目前的工作中，我们计算这些修正兰姆位移，简谐振子，朗道能级，和隧道电流在扫描隧道显微镜。
英文摘要：
Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.
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