引力透镜干涉测量中的量子不确定性
Quantum Uncertainty Considerations for Gravitational Lens Interferometry
摘要：
到目前为止，光路之间的引力透镜延迟时间的测量依赖于具有足够可变性的源，以允许比较来自每个路径的光度变化。然而，许多引力透镜的延迟时间无法测量，因为内禀源振幅变化太小而无法检测。在基本量子力学水平上，这种光度时间戳允许哪条路径的知识，消除了获得干涉图案的能力。然而，如果两个路径可以相等（零时间延迟），则可能发生干扰。我们描述了一种干涉测量引力透镜延迟时间的方法，使用量子擦除器/恢复器的方法，从而沿两条路径的时间旅行可以呈现可测量的相等。能量和时间是不可交换的可观测量，在能量-时间不确定原理中，通过调整无线电带通的宽度，对光子能量的约束决定了时间延迟的不确定性，从而决定了沿着一个或另一个引力透镜测地线的路径是否是可知的。例如，如果从干涉开始，当带通被加宽（对能量的约束被放松）到这样一个点时，哪条路径的信息返回，在这个点上，不确定原理允许对到达时间的了解比引力透镜延迟时间本身更好，在这个点上，干涉将消失。我们讨论了近期的可行性，根据目前的窄带无线电探测器和已知的短时间延迟引力透镜的测量。
英文摘要：
The measurement of the gravitational lens delay time between light paths has relied, to date, on the source having sufficient variability to allow photometric variations from each path to be compared. However, the delay times of many gravitational lenses cannot be measured because the intrinsic source amplitude variations are too small to be detectable. At the fundamental quantum mechanical level, such photometric time stamps allow which-path knowledge, removing the ability to obtain an interference pattern. However, if the two paths can be made equal (zero time delay) then interference can occur. We describe an interferometric approach to measuring gravitational lens delay times using a quantum-eraser/restorer approach, whereby the time travel along the two paths may be rendered measurably equal. Energy and time being non-commuting observables, constraints on the photon energy in the energy-time uncertainty principle, via adjustments of the width of the radio bandpass, dictate the uncertainty of the time delay and therefore whether the path taken along one or the other gravitational lens geodesic is knowable. If one starts with interference, for example, which-path information returns when the bandpass is broadened (constraints on the energy are relaxed) to the point where the uncertainty principle allows a knowledge of the arrival time to better than the gravitational lens delay time itself, at which point the interference will disappear. We discuss the near-term feasibility of such measurements in light of current narrow-band radio detectors and known short time-delay gravitational lenses.
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