全息不确定性、不确定性和噪声
Holographic Indeterminacy, Uncertainty and Noise
摘要：
发展了一种理论来描述时空量子化对横向于宏观分离的位置测量的非局域效应。接近于经典零轨线的时空量子态近似于普朗克波长（l_P）参考光束的平面波函数，这些波函数用于连接宏观分离事件的横向位置算子。具有零时空分离但被宏观空间距离$L$分开的事件的横向位置被证明是量子共轭观测量，导致全息不确定性和一个新的不确定原理，相对横向位置的标准偏差的下限Δx_ \perp > \sqrt{l_PL}或角取向的下限Δθ> \sqrt{l_P/L}。由此产生的独立自由度的数量限制同意从黑洞物理学和弦理论的全息协变熵界定量。该理论预言了时空的普遍"全息噪声“，表现为剪切扰动，其功率谱密度与频率无关S_H=l_P/c，或以等效的度规扰动单位h_{H,rms} \sqrt{l_P/c} = 2.3 \times 10^{-22} / \sqrt{Hz}表示。如果这种全息现象学的描述是正确的，那么现有技术的干涉仪就可以对量子引力进行直接的定量研究。
英文摘要：
A theory is developed to describe the nonlocal effect of spacetime quantization on position measurements transverse to macroscopic separations. Spacetime quantum states close to a classical null trajectory are approximated by plane wavefunctions of Planck wavelength (l_P) reference beams; these are used to connect transverse position operators at macroscopically separated events. Transverse positions of events with null spacetime separation, but separated by macroscopic spatial distance $L$, are shown to be quantum conjugate observables, leading to holographic indeterminacy and a new uncertainty principle, a lower bound on the standard deviation of relative transverse position Δx_\perp > \sqrt{l_PL} or angular orientation Δθ> \sqrt{l_P/L}. The resulting limit on the number of independent degrees of freedom is shown to agree quantitatively with holographic covariant entropy bounds derived from black hole physics and string theory. The theory predicts a universal ``holographic noise'' of spacetime, appearing as shear perturbations with a frequency-independent power spectral density S_H=l_P/c, or in equivalent metric perturbation units, h_{H,rms} \sqrt{l_P/c} = 2.3 \times 10^{-22} /\sqrt{Hz}. If this description of holographic phenomenology is valid, interferometers with current technology could undertake direct quantitative studies of quantum gravity.
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