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arXiv 0710.4153gr-qcastro-phhep-th
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涌现时空的量子不确定性

Quantum Indeterminacy of Emergent Spacetime

Craig J. Hogan

摘要:

结果表明,从2+ 1维的对偶量子场论中产生的近似平坦的3+ 1维时空在宏观尺度上表现出经典欧几里得几何的量子涨落。假设一个协变全息映射,其中二维表面上波矢为k的平面波态以相对于表面元法线的角度θ= lP k映射到出射的第三维经典零轨线上,其中lP表示普朗克长度. 3+1D世界中的轨道则显示出角取向的量子不确定性,在给定帧中纵向传播距离z的标准偏差Δθ= \sqrt{l_P/z}。在宏观上分离的事件沿零轨迹的横向位置的量子互补性对应于一个几何形状,这是不完全经典的,但显示可观察到的全息量子噪声。本文给出了一个简单的思想实验的欧氏行为波动的统计估计。由于这种理论的自由度有限,这种效应可以被视为采样噪声,与熵的协变界限一致。

英文摘要:

It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane wave states with wavevector k on a 2D surface map onto classical null trajectories in the emergent third dimension at an angle θ=l_P k relative to the surface element normal, where l_P denotes the Planck length. Null trajectories in the 3+1D world then display quantum uncertainty of angular orientation, with standard deviation Δθ=\sqrt{l_P/z} for longitudinal propagation distance z in a given frame. The quantum complementarity of transverse position at macroscopically separated events along null trajectories corresponds to a geometry that is not completely classical, but displays observable holographic quantum noise. A statistical estimator of the fluctuations from Euclidean behavior is given for a simple thought experiment based on measured sides of triangles. The effect can be viewed as sampling noise due to the limited degrees of freedom of such a theory, consistent with covariant bounds on entropy.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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