论文标题
在缺乏光子色散的情况下调和量子重力最小长度
Reconciling a quantum gravity minimal length with lack of photon dispersion
论文作者
论文摘要
通用论点导致量子重力的长度尺度最小。这种最小长度尺度的可能的观察信号是光子应表现出分散。在2009年，对短伽玛射线爆发的观察似乎将最小的长度尺度绑定到小于普朗克长度的距离，这意味着时空似乎连续到低于普朗克长度的距离。这对此类最小距离模型构成了挑战。在这里，我们提出了对位置和动量运营商的修改，$ {\ hat x} $和$ {\ hat p} $，它导致长度最小的比例，但保留了光子能量摩托车关系$ e = p c $。这样，没有具有不同能量的光子的分散。可以在不修改换向关系$ [{\ hat x}，{\ hat p}] = i \ hbar $的情况下实现这一目标。
Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009 the observation of a short gamma ray burst seemed to bound the minimal length scale to distances smaller than the Planck length, implying that spacetime appeared continuous to distances below the Planck length. This poses a challenge for such minimal distance models. Here we propose a modification of the position and momentum operators, ${\hat x}$ and ${\hat p}$, which lead to a minimal length scale, but preserve the photon energy-momentum relationship $E = p c$. In this way there is no dispersion of photons with different energies. This can be accomplished without modifying the commutation relationship $[{\hat x}, {\hat p}] = i \hbar$.
