Search for Deviations from Newtonian Gravity at Micron Scale (A Continuation Proposal)

现代理论试图弥合粒子物理学中公认的模型（“标准模型”）与引力变得与自然界中所有其他力一样强（比原子大小小23个数量级）之间的差距，预测牛顿定律在更长的长度尺度上的修正，最高可达1毫米。最近，有几个实验旨在检测或约束在宏观长度尺度上对牛顿定律的偏离。在斯坦福大学，我们已经建立了一个这样的实验，基于一个低温探头来测量被20微米左右的距离分开的质量之间低至一牛顿的力。在我们的实验中，使用低温氦气轴承在安装在微机械悬臂上的小测试质量下旋转包含交替密度驱动质量模式的圆盘。两者之间的任何与质量相关的力都会对测试质量产生时变力，从而产生悬臂梁的时变位移。理论物理学的圣杯是提供一种简洁而优雅的理论来统一自然界的所有力。虽然电磁力（带电粒子之间的力）、强磁力（使原子核结合在一起的力）和弱磁力（与原子核的某些衰变有关的力）都被很好地理解，但人类可能经历的第一种力——引力，却知之甚少，而且将它与其他力统一起来构成了一个巨大的智力挑战。这一领域的新理论见解为研究人员提供了一个机会，通过精确的“桌面”实验，尝试为这一领域的研究做出贡献。在斯坦福大学，我们利用物理、化学、材料科学和工程领域的先进技术，建造了一种仪器，可以测量比普通尺度小20多个数量级的力。设计、建造、测试和在实际实验中使用这样的设备的挑战迫使我们想出许多优雅的解决工程问题的办法。这不仅使从事该项目的学生受益，也使其他在不同领域工作的研究人员受益。例如，我们为这个项目开发的微型悬臂现在被用作扭矩磁力计，用于测量纳米样品的磁性。在另一个例子中，我们在实验中找到的控制旋转转子速度的解决方案与辐射施加压力的基本物理定律有关。

Modern theories attempt to bridge the gap between the scale of the accepted model for particle physics (the 'Standard Model'), and the scale at which the force of gravity becomes as strong as all other forces in nature (about 23 orders of magnitudes smaller than the size of an atom), predicting modifications to Newton's law at much longer length scales, up to 1mm. Recently, there have been several experiments designed to detect or constrain deviations from Newton's law at this macroscopic length scale. At Stanford we have built such an experiment based on a low temperature probe to measure forces as low as attoNewton between masses separated by distances on the order of 20 micrometers. In our experiment a cryogenic helium gas bearing is used to rotate a disc containing a drive mass pattern of alternating density under a small test mass mounted on a micromachined cantilever. Any mass-dependent force between the two will produce a time-varying force on the test mass, and consequently a time-varying displacement of the cantilever. The holy grail of theoretical physics is to provide a compact and elegant theory that unifies all forces of nature. While the Electromagnetic (force between charged particles), Strong (force that holds the nucleus together), and Weak (force associated with certain decays of nuclei) forces are well understood, the force of gravity, the first force that human beings probably experienced, is poorly understood, and unifying it with the other forces poses an enormous intellectual challenge. The new theoretical insight in this field gave researchers an opportunity to try and contribute to this field of research through precision, 'table-top' experiments. At Stanford University we utilized advanced techniques used in physics, chemistry, materials science, and engineering to build an apparatus that can measure forces that are more than twenty orders of magnitudes smaller than the force measured by a normal scale. The challenge to design, to construct, to test, and to use in a real experiment such an apparatus forced us to come up with many elegant solutions to engineering problems. This benefitted not only the students working on the project, but also other researchers working in different fields. For example, the miniature cantilevers that we developed for the project are now being used as torque magnetometers for measuring magnetic properties of nano-samples. In another example, a solution we found for controlling the speed of a spinning rotor in our experiment bears on a fundamental physics law of pressure exerted by radiation.