A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations

  • M. J. Lake School of Physics, Sun Yat-sen University
Keywords: generalized uncertainty principle, extended uncertainty principle, dark energy, quantum gravity

Abstract

We propose a new method for generating generalized uncertainty relations (GURs) including the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalized uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar´e invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multi-particle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the “soccer ball problem” that plagues current approaches to GURs.

References

F. Scardigli. Generalized uncertainty principle in quantum gravity from micro - black hole Gedanken experiment. Phys. Lett. B 452, 39 (1999). https://doi.org/10.1016/S0370-2693(99)00167-7

R.J. Adler, D.I. Santiago. On gravity and the uncertainty principle. Mod. Phys. Lett. A 14, 1371 (1999). https://doi.org/10.1142/S0217732399001462

M.i. Park. The generalized uncertainty principle in (A)dS space and the modification of Hawking temperature from the minimal length. Phys. Lett. B 659, 698 (2008). https://doi.org/10.1016/j.physletb.2007.11.090

C. Bambi, F.R. Urban. Natural extension of the generalized uncertainty principle. Class. Quant. Grav. 25, 095006 (2008). https://doi.org/10.1088/0264-9381/25/9/095006

S. Hossenfelder. The soccer-ball problem. SIGMA 10, 074 (2014). https://doi.org/10.3842/SIGMA.2014.074

A.N. Tawfik, A.M. Diab. Generalized uncertainty principle: Approaches and applications. Int. J. Mod. Phys. D 23 (12), 1430025 (2014). https://doi.org/10.1142/S0218271814300250

M.J. Lake, M. Miller, R.F. Ganardi, Z. Liu, S.D. Liang, T. Paterek. Generalised uncertainty relations from superpositions of geometries. Class. Quant. Grav. 36 (15), 155012 (2019). https://doi.org/10.1088/1361-6382/ab2160

A.I.M. Rae. Quantum Mechanics. (Taylor & Francis, 2002).

C.J. Isham. Lectures on Quantum Theory: Mathematical and Structural Foundations (Imperial College Press, 1995). https://doi.org/10.1142/p001

M.P. Hobson, G.P. Efstathiou, A.N. Lasenby. General Relativity: An Introduction for Physicists (Cambridge Univ. Press, 2006). https://doi.org/10.1017/CBO9780511790904

A. Kempf. On quantum field theory with nonzero minimal uncertainties in positions and momenta. J. Math. Phys. 38, 1347 (1997). https://doi.org/10.1063/1.531814

S. Hossenfelder. Minimal length scale scenarios for quantum gravity. Living Rev. Rel. 16, 2 (2013). https://doi.org/10.12942/lrr-2013-2

Published
2019-11-25
How to Cite
Lake, M. (2019). A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations. Ukrainian Journal of Physics, 64(11), 1036. https://doi.org/10.15407/ujpe64.11.1036
Section
Fields and elementary particles