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Journal of Physical Studies 27(1), Article 1001 [19 pages] (2023)
DOI: https://doi.org/10.30970/jps.27.1001 DEFORMED HEISENBERG ALGEBRAS OF DIFFERENT TYPES WITH PRESERVED WEAK EQUIVALENCE PRINCIPLE
Kh. P. Gnatenko
Professor Ivan Vakarchuk Department for Theoretical Physics,
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In the paper, a review of the results for recovering the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta is presented. Different types of deformed algebras leading to a space quantization are considered, among them noncommutative algebra of a canonical type, algebra of the Lie type, the Snyder algebra, the Kempf algebra and nonlinear deformed algebra with an arbitrary function of deformation depending on momenta. The motion of a particle and a composite system in a gravitational field is examined and the implementation of the weak equivalence principle is studied. We conclude that the Eötvös parameter is not equal to zero even in the case when the gravitational mass is equal to the inertial mass. The principle is preserved in a quantized space if we consider parameters of deformed algebras to be dependent on mass. It is also shown that the dependencies of parameters of deformed algebras on mass lead to preserving the properties of the kinetic energy in quantized spaces and solving the problem of the significant effect of space quantization on the motion of macroscopic bodies (the problem is known as the soccer-ball problem).
Key words: quantum space, minimal length, deformed Heisenberg algebra, weak equivalence principle, macroscopic body, soccer-ball problem, kinetic energy.
