时空泡沫的极限
Limits on Spacetime Foam
摘要：
由于量子涨落，时空在小距离尺度上可能是“泡沫”的。我们详细阐述了通过在遥远的类星体和活动星系核的图像中寻找可见盘来探测时空泡沫的建议。这是一个零测试的意义上，继续存在的未解决的“点”源在毫弧秒水平的样本遥远的紧凑源提出了严格的限制量子化的时空泡沫理论在普朗克水平。我们讨论了泡沫时空的几何形状，以及计算预期角展宽的适当距离测度。然后，我们处理最近的数据和限制，他们把时空泡沫模型。虽然从遥远的脉冲源，如伽玛射线暴的时间滞后已被假定为一个可能的测试时空泡沫模型，我们证明，时间滞后的影响是相当小的，而不是已经计算，由于在这样的模型固有的光的速度的正负波动的概率相等。到目前为止，来自哈勃超深空（UDF）的高红移类星体的图像提供了对时空泡沫理论最严格的检验。虽然随机游走模型（$α= 1/2$）已经被排除，但全息（$α=2/3$）模型仍然可行。这里$α\sim 1$参数化了不同的时空泡沫模型，根据这些模型，距离$l$的波动由$\sim l^{1 - α} l_P^α$给出，其中$l_P$是普朗克长度。事实上，我们在本研究选择的UDF图像中看到了轻微的波长相关模糊。使用{ \it Hubble Space Telescope（HST）}存档中的现有数据，我们发现不可能排除$α=2/3$模型，但排除所有具有$α<0.65$的模型。相比之下，目前的伽玛暴时间滞后观测只排除了具有$α<0.3$的模型。
英文摘要：
Plausibly spacetime is "foamy" on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and AGNs. This is a null test in the sense that the continued presence of unresolved "point" sources at the milli-arc second level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as GRBs have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble Ultra-Deep Field (UDF) provide the most stringent test of spacetime foam theories. While random walk models ($α= 1/2$) have already been ruled out, the holographic ($α=2/3$) model remains viable. Here $α\sim 1$ parametrizes the different spacetime foam models according to which the fluctuation of a distance $l$ is given by $\sim l^{1 - α} l_P^α$ with $l_P$ being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the UDF images selected for this study. Using existing data in the {\it Hubble Space Telescope (HST)} archive we find it is impossible to rule out the $α=2/3$ model, but exclude all models with $α<0.65$. By comparison, current GRB time lag observations only exclude models with $α<0.3$.
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