相对局部性与足球问题
Relative locality and the soccer ball problem
摘要：
我们考虑的相对局域性的框架内，这是最近提出的普朗克尺度修改的相对论性动力学的粒子被描述为产生的动量空间的几何形状中的变形的宏观机构的行为。这导致在能量-动量关系和守恒定律中增加了非线性项，而这些项被所涉及的粒子的能量E与普朗克质量M_P之间的比率的幂所抑制。我们考虑并解决了反对这种建议的一个共同的反对意见，即即使在目前的实验中对基本粒子的修正很小，当应用于复合系统如足球、行星和恒星时，它们是巨大的，能量E_{macro}远大于M_P。我们表明，这种“足球问题”不会在相对定域性的框架内出现，因为对于具有N个基本粒子的复合系统的动力学的非线性效应最多出现在E_{macro} / N M_{P}阶。
英文摘要：
We consider the behavior of macroscopic bodies within the framework of relative locality, which is a recent proposal for Planck scale modifications of the relativistic dynamics of particles which are described as arising from deformations in the geometry of momentum space. These lead to the addition of non-linear terms to the energy-momentum relations and conservation laws, which are suppressed by powers of ratio between the energy E of the particles involved and the Planck mass M_P. We consider and resolve a common objection against such proposals, which is that, even if the corrections are small for elementary particles in current experiments, they are huge when applied to composite systems such as soccer balls, planets and stars, with energies E_{macro} much larger than M_P. We show that this "soccer-ball problem" does not arise within the framework of relative locality, because the non-linear effects for the dynamics of a composite system with N elementary particles appear at most of order E_{macro}/ N M_{P}.
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