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

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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.