标题： 测地线、质量与弯曲德西特时空中的不确定性原理 显示英文标题

标题： Geodesics, Mass and the Uncertainty Principle in a Warped de Sitter Space-time

摘要： 我们给出了Randall-Sundrum提出的扭曲de Sitter时空中测地线方程的显式解。 我们发现，测试粒子在体空间中运动，并不限制在3-膜上（作为我们的宇宙）。 在3-膜上，测试粒子以匀速运动，看起来不受力的作用。 但使用能量动量张量计算粒子的能量时，得到的是随时间变化的能量，这表明质量是随时间变化的。 因此，额外的力——即扭曲的额外维对3-膜上粒子运动的影响——不会改变粒子的速度，而是改变其质量。 粒子在体空间中的运动也导致了从3-膜视角观察到的海森堡不确定性原理的时间依赖性修正。 这两个结果表明，额外维上的经典物理导致了粒子质量的时变性和不确定性原理的变化。 如果粒子质量是时间不变的，并且海森堡不确定性原理要保持不变，那么必须存在一种非引力的力，将所有粒子限制在3-膜上。 最后，我们仅指出，尽管在经典情况下，这些3-膜上的时间依赖性修正可以被去除，但沿着额外维的量子力学修正将重新恢复这个问题。 显示英文摘要

摘要： We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the 3-brane, the test particle moves with uniform velocity, giving the appearance that it is not subject to a force. But computing the particle's energy using the energy-momentum tensor yields a time-dependent energy that suggests a time-dependent mass. Thus, the extra force, which is the effect of the warped extra dimension on the particle's motion on the 3-brane, does not change the velocity but the mass of the particle. The particle's motion in the bulk also results in a time-dependent modification of the Heisenberg uncertainty principle as viewed on the 3-brane. These two results show that the classical physics along the extra dimension results in the time-dependence of particle masses and the uncertainty principle. If the particle masses are time-independent and the Heisenberg's uncertainty principle is to remain unchanged, then there must be a non-gravitational force that will restrict all particles on the 3-brane. Finally, we just note that although classically, these time-dependent corrections on the 3-brane can be removed, quantum mechanical corrections along the extra dimension will restore back the problem.