维度相关的不确定关系，或为什么即使存在大额外维度，我们（可能）也不会在LHC中看到微型黑洞
Dimensionally-dependent uncertainty relations, or why we (probably) won't see micro-black holes at the LHC, even if large extra dimensions exist
AI总结：
本研究通过思想实验证明引力自能守恒导致质量-半径关系的维度依赖性，提出高维不确定关系，排除大额外维度下LHC的TeV尺度微型黑洞形成可能。
摘要：
我们提出了一个简单的思想实验，其中一个致密物体穿越具有三个宏观空间维度和$n$个紧致维度的时空。紧致化半径可随物体在四维空间中的位置变化，我们证明引力自能守恒意味着质量-半径关系具有维度依赖性。在额外维度在普朗克尺度紧致化的时空中，未发现与四维结果的偏差；但在额外维度远大于普朗克长度的时空中，能量守恒意味着与标准康普顿波长公式存在偏差。新的关系恢复了质量-半径图上康普顿波长线与史瓦西半径线之间的对称性，并且即使存在大额外维度，也排除了TeV尺度下黑洞形成的可能性。我们直观地说明，这是紧致化尺度以下距离处引力场强度增强的直接结果。将这些结果与海森堡不确定原理带来的康普顿波长和位置不确定度最小值的启发式对应相结合，表明存在广义的高维不确定关系。这些关系有望适用于高维时空中的自引力量子波包，对额外维度场景下的粒子物理和宇宙学具有有趣的意义。
英文摘要：
We present a simple gedanken experiment in which a compact object traverses a spacetime with three macroscopic spatial dimensions and $n$ compact dimensions. The compactification radius is allowed to vary, as a function of the object's position in the four-dimensional space, and we show that the conservation of gravitational self-energy implies the dimensional dependence of the mass-radius relation. In spacetimes with extra dimensions that are compactified at the Planck scale, no deviation from the four-dimensional result is found, but, in spacetimes with extra dimensions that are much larger than the Planck length, energy conservation implies a deviation from the normal Compton wavelength formula. The new relation restores the symmetry between the Compton wavelength and Schwarzschild radius lines on the mass-radius diagram and precludes the formation of black holes at TeV scales, even if large extra dimensions exist. We show how this follows, intuitively, as a direct consequence of the increased gravitational field strength at distances below the compactification scale. Combining these results with the heuristic identification between the Compton wavelength and the minimum value of the position uncertainty, due to the Heisenberg uncertainty principle, suggests the existence of generalised, higher-dimensional uncertainty relations. These relations may be expected to hold for self-gravitating quantum wave packets, in higher-dimensional spacetimes, with interesting implications for particle physics and cosmology in extra-dimensional scenarios.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
