Criticism of the uncertainty principle

Ya-Ting Wang, He-Ling Li

Abstract Significant evidence is available to support the quantum effects of gravity that lead to the generalized uncertainty principle (GUP) and the minimum observable length. Usually in quantum mechanics, statistical physics does not take gravity into account. Thermodynamic properties of ideal Bose gases in different external power-law potentials are studied under the GUP with a statistical physical method. Critical temperature, internal energy, heat capacity, entropy, particle number of ground state and excited state are calculated analytically to ideal Bose gases in the external potentials under the GUP. Below the critical temperature, taking the rubidium and sodium atoms, ideal Bose gases whose particle densities are under standard and experimental conditions, respectively, as examples, the relations of internal energy, heat capacity and entropy with temperature are analyzed numerically. Theoretical and numerical calculations show that: (1) the GUP leads to an increase in the critical temperature. (2) When the temperature is lower than the critical temperature and slightly higher than 0 K, the GUP’s amendments to internal energy, heat capacity and entropy etc are positive. As the temperature increases to a certain value, these amendments become negative. (3) The external potentials can increase or decrease the influence of the GUP on thermodynamic properties. When ε = 1 J, ε is the quantity that reflects the external potential intensity, and atomic density n = 2.687 × 10 25 m −3 , the GUP’s amendments to the internal energy, heat capacity and entropy of the rubidium atoms ideal Bose gas first decrease and then increase with the increase of X (where X ≡ Σ i 1/ t i is sum of the reciprocal of the exponents of the power function). In three-dimensional harmonic potential, the relative correction term of the GUP is 26 orders of magnitude larger than that of a free-particle system in a fixed container. (4) When ε ≈10 −31 J and n ≈ 10 20 m −3 (which are the experimental data when BEC was first verified by sodium atomic gas), the influence of the GUP can be completely ignored. (5) Under certain conditions, GUP may become the dominant factor governing the thermodynamic properties of the system.

J. P. Wesley

Asma Tahar Taiba, Abdelâali Boudjemâa

We study the thermodynamics of quadrupolar Bose-Einstein condensates in the realm of the generalized uncertainty principle (GUP) for the quest of understanding and testing quantum gravity (QG). Using both quadratic GUP (QGUP) and linear-quadratic GUP (LQGUP) which incorporate modified density of states, we calculate corrections to the condensed fraction, critical temperature, equation of state and other thermodynamic quantities. We find that the intriguing interplay of quadrupole-quadrupole interactions (QQIs) and the GUP may strongly modify the finite-temperature properties of the condensate, with the LQGUP generally predicting larger corrections than the QGUP, although their relative magnitudes depend on the chosen parameters and the validity of the perturbative expansion. We further estimate the sensitivity of the critical temperature to GUP-induced effects by imposing an assumed fractional temperature resolution which provides projected upper bounds on the GUP deformation parameters. Our findings demonstrate that quadrupole-quadrupole interacting Bose gases provide a promising platform for testing GUP-induced deviations from standard quantum mechanics and for probing QG phenomenology through measurements of finite-temperature many-body observables. They also motivate future studies using realistic system-specific parameters.

Jan Hilgevoord, Jos Uffink

P Marquardt, G. Galeczki

Abhishek Majhi

If Cauchy would have been more careful about his own language, then he could have written down the ``Heisenberg'' uncertainty principle a century earlier than Heisenberg. Such logico-linguistic self-criticism can provide new insights to physicists in the pursuit of truth and reality.