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的表面反弹的动力学，在短距离内结合了量子理论和牛顿力学的各个方面。我们计划在一个系统中实现这样一个具有超冷中子的量子弹跳球，在这个系统中，我们已经测量了地球引力场中最低稳定量子态之前的量子弹跳球。为了达到新的目的，必须对反射镜上方的中子密度分布进行仔细的测量，并且必须研制空间中子探测器。这项实验对长度低于10μm的类似重力的力很敏感，我们已经在那里设置了限制。通过研究波包的动力学可以显著地改善极限，因为牛顿引力和假设的第五种力随着不同的相位信息而演变。这种作用力可以通过在高维空间传播的规范玻色子来调节，因此这个实验可以测试关于时空大小为亚毫米大小的额外大维度或宇宙中宇宙常数的起源的推测，在这个实验的有趣范围内预测了影响，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.