The dynamics of a quantum wave packet of a neutron bouncing under the influence of gravity - Newton's law and the question of extra dimensions of space-time

量子力学波包在地球引力场中从坚硬表面反弹的动力学将量子理论与牛顿力学在短距离上的各个方面结合起来。我们提议用超冷中子在一个系统中实现这样一个量子弹跳球，在这个系统中，我们之前已经测量了地球引力场中最低的稳态量子态。为了达到新的目的，必须仔细测量镜面上方的中子密度分布，并且必须开发空间中子探测器。这个实验对长度小于10 μm的类似重力的力很敏感，我们已经设置了限制。由于牛顿引力和假设的第五种力随不同的相位信息演化，因此可以通过研究波包的动力学来显著提高极限。这种力可以通过在高维空间中传播的规范玻色子来调节，因此这个实验可以测试对亚毫米大小的时空的大额外维度的推测，或者宇宙中宇宙常数的起源，在这个实验的有趣范围内预测了效应，并可能在改进的设置中给出信号。

The dynamics of a quantum mechanical wave packet bouncing off a hard surface in the gravitational field of the earth combines quantum theory with aspects of Newtonian mechanics at short distances. We propose to realize such a quantum bouncing ball with ultracold neutrons in a system, in which we have measured before the lowest stationary quantum states in the earth’s gravitational field. For the new purpose, a careful measurement of the neutron density distribution above the mirror is necessary, and spatial neutron detectors must be developed. This experiment is sensitive to gravity-like forces at a length scale below 10 μm, where we already place limits. The limits can be significantly improved by studying the dynamics of the wave packets, because Newtonian gravity and hypothetical fifth forces evolve with different phase information. Such forces can be mediated from gauge bosons propagating in a higher dimensional space and this experiment can therefore test speculations on large extra dimensions of submillimeter size of space-time or the origin of the cosmological constant in the universe, where effects are predicted in the interesting range of this experiment and might give a signal in an improved setup.