Collaborative Research: Measuring G with a Microsphere in a Magneto-Gravitational Trap

在牛顿和爱因斯坦的引力理论中，宇宙的引力常数“G”决定了引力的强度。但是，尽管它对我们理解引力至关重要，但在过去20年的实验中，G的测量结果与报道的误差大相径庭。这些差异是非恒定G的证据，反映了爱因斯坦之外的一些新的引力理论，还是仅仅是由于对实验错误的误解？为了解决这个问题，我们正在努力设计一种全新的实验来测量G，其中包括一个悬浮在磁阱中来回摆动的微米直径球体。由于在振荡球体附近引入了精心加工的质量，振荡频率将发生变化，我们预计我们对这种频率变化的测量将确定G到百万分之十——与其他最先进的实验相当，但在很大程度上是独立的，希望能更好地理解误差来源。我们建议使用一种新的实验装置来测量牛顿引力常数G。测量方法是基于摆动时间法，其中一对场质量改变弹簧常数，从而改变简谐振子的振荡频率。该方法的独特之处在于，简谐振子由悬浮在超高真空磁阱中的微球组成。该系统具有几个独特的特点，使其适合精密测量，包括低振荡频率，超高质量因子(Q)，以及补偿振荡频率漂移的多个自由度。实验设计中的关键挑战之一是稳定或补偿振荡频率，以便能够很好地解决频率移，以测量G到10ppm。因此，第一年将致力于为此优化实验设计，目的是为这种新方法提供原理证明，并为执行最先进的g测量提供途径。所提出的策略也被选择来最小化困扰其他g测量的系统误差。首先，摆动时间方法易于分析，对偏差的一阶灵敏度为零。其次，大部分记录的数据将以精确的粒子时间戳图像的形式进行，这些图像可以根据需要进行分析和重新分析。第三，所有数据将免费提供给其他团体进行研究、分析，并与我们报告的结果进行比较。这将确保在新的测量有信心，尽管在过去的测量G。

The gravitational constant of the universe "G" sets the strength of gravity both in Newton's and Einstein's theories of gravity. But despite its central importance to our understanding of gravity, experiments over the past 20 years have led to measurements of G that disagree enormously beyond the reported errors. Are these discrepancies evidence of a non-constant G, reflective of some new gravitational theory beyond Einstein, or are they simply due to misunderstandings of experimental errors? To tackle this question, we are undertaking an effort toward a fundamentally new experimental design for measuring G, which involves a magnetically-suspended, micron-diameter sphere that oscillates back and forth in a magnetic trap. The oscillation frequency will shift due to the introduction of carefully-machined masses placed near the oscillating sphere, and we expect our measure of this frequency shift will determine G to about ten parts in a million--on par with other state-of-the-art experiments, but with largely independent, and hopefully better-understood sources of error.We propose measuring G, the Newtonian gravitational constant, using a novel experimental setup. The measurement approach is based on the time-of-swing method, where a pair of field masses modifies the spring constant, and thus the oscillation frequency, of a simple harmonic oscillator. The unique feature of the proposed approach is that the simple harmonic oscillator consists of a microsphere levitated in a magnetic trap in ultra-high vacuum. This system has several features that make it uniquely suited to precision measurements, including a low oscillation frequency, ultra-high quality factor (Q), and multiple degrees of freedom for compensation of drift in the oscillation frequency. One of the key challenges in the experimental design is stabilizing or compensating the oscillation frequencies so frequency shifts can be resolved well enough to measure G to 10 ppm. Thus, the first year will be dedicated to optimizing the experimental design to this end, with a goal of presenting a proof of principle for this novel approach, as well as a path forward to performing the state-of-the-art measurement of G. The proposed strategy has also been chosen to minimize the systematic errors that have plagued other measurements of G. First, the time-of-swing method is simple to analyze, with zero first-order sensitivity to misalignment. Second, most of the recorded data will be taken in the form of precisely time-stamped images of the particle, which can be analyzed and reanalyzed as needed. Third, all data will be made freely available for other groups to study, analyze, and compare with our reported results. This will ensure that there is confidence in the new measurement despite disagreement among past measurements of G.