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，但过去20年的实验已经导致G的测量结果存在巨大的差异，超出了报告的误差。这些差异是否证明了G是非常数的，反映了超越爱因斯坦的一些新的引力理论，或者它们仅仅是由于对实验误差的误解？为了解决这个问题，我们正在努力实现一种全新的测量G的实验设计，该设计涉及一个磁悬浮的微米直径球体，该球体在磁阱中来回振荡。振荡频率将转移，由于引入精心加工的质量放置在振荡球附近，我们希望我们的这种频率偏移的测量将确定G约为百万分之十-与其他国家的最先进的实验，但在很大程度上是独立的，并希望更好地理解的误差来源。的测量方法是基于时间的摆动方法，其中一对场质量修改弹簧常数，从而振荡频率，一个简单的谐振子。所提出的方法的独特之处在于，简谐振子由悬浮在超高真空中的磁阱中的微球组成。该系统具有多个特性，使其特别适合精密测量，包括低振荡频率、超高品质因数（Q）和多个自由度，用于补偿振荡频率的漂移。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偏移，以测量G至10 ppm。因此，第一年将致力于为此优化实验设计，目标是为这种新方法提供原理证明，以及执行最先进的G测量的路径。所提出的策略也被选择来最小化困扰G的其他测量的系统误差。首先，摆动时间法分析简单，对未对准的一阶灵敏度为零。其次，大多数记录的数据将以精确的时间戳颗粒图像的形式获取，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小组研究、分析，并与我们报告的结果进行比较。这将确保在新的测量中有信心，尽管在G的过去测量中存在分歧。

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.