Dimensionally-dependent uncertainty relations, or why we (probably) won’t see micro-black holes at the LHC, even if large extra dimensions exist

Frontiers in Astronomy and Space Sciences

Astronomy and Space Sciences

Anucha Watcharapasorn¹  Matthew J. Lake²  Shi-Dong Liang³ 

[1] Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand;Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand;National Astronomical Research Institute of Thailand, Chiang Mai, Thailand;Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand;School of Physics, Sun Yat-Sen University, Guangzhou, China;Department of Physics, Babeş-Bolyai University, Cluj-Napoca, Romania;Office of Research Administration, Chiang Mai University, Chiang Mai, Thailand;School of Physics, Sun Yat-Sen University, Guangzhou, China;State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, Sun Yat-Sen University, Guangzhou, China;

关键词: compactification;    higher dimensions;    compton wavelength;    primordial black holes;    generalised uncertainty relations contents;    self-gravity;   

DOI  :  10.3389/fspas.2023.1155667

 received in 2023-01-31, accepted in 2023-03-08,  发布年份 2023

来源: Frontiers

【 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.

【 授权许可】

Unknown   
Copyright © 2023 Lake, Liang and Watcharapasorn.