普朗克尺度足球问题：一个错误的同一性案例
Planck-scale soccer-ball problem: a case of mistaken identity
摘要：
在过去的十年中，人们发现动量组成的非线性定律被一些替代的方法预测到“真实的”4D量子引力，并通过所有的降维（3D）量子引力耦合到物质的公式。不同的量子引力模型之间可能的相关性激发了一些研究，但这种兴趣正在受到关注，即动量相加的非线性定律可能不可避免地产生对宏观物体总动量的病态描述。我在这里表明，这种担忧是没有道理的，发现他们植根于未能欣赏的两个角色之间的差异法律组成的动量在物理学。以前的结果完全依赖于动量合成定律在描述时空定域性中的作用。然而，多粒子系统的总动量概念并不是定域性的表现，而是反映了平移不变性。通过在量子时空的一个说明性的例子中工作，我明确地表明时空定域性确实反映在动量组成的非线性定律中，但是平移不变性仍然导致动量增加的未变形线性定律，从而建立了多粒子系统的总动量。
英文摘要：
Over the last decade it has been found that nonlinear laws of composition of momenta are predicted by some alternative approaches to "real" 4D quantum gravity, and by all formulations of dimensionally-reduced (3D) quantum gravity coupled to matter. The possible relevance for rather different quantum-gravity models has motivated several studies, but this interest is being tempered by concerns that a nonlinear law of addition of momenta might inevitably produce a pathological description of the total momentum of a macroscopic body. I here show that such concerns are unjustified, finding that they are rooted in failure to appreciate the differences between two roles for laws composition of momentum in physics. Previous results relied exclusively on the role of a law of momentum composition in the description of spacetime locality. However, the notion of total momentum of a multi-particle system is not a manifestation of locality, but rather reflects translational invariance. By working within an illustrative example of quantum spacetime I show explicitly that spacetime locality is indeed reflected in a nonlinear law of composition of momenta, but translational invariance still results in an undeformed linear law of addition of momenta building up the total momentum of a multi-particle system.
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