Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

Abstract

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

Weak equivalence principle in quantum space

“…Note that for m 1 = 1 kg, m 2 = 0.1 kg in the case of deformation function F( β |P|) 1 + βP 2 form Eq. 23 we obtain great violation of the weak equivalence principle Δa/a ≈ 0.1 which has not been seen experimentally (Gnatenko and Tkachuk, 2020). From the tests of the weak equivalence principle it follows that this principle holds with high accuracy.…”

“…33-35 if the relation of the parameter of deformation with mass Eq. 26 is satisfied (Gnatenko and Tkachuk, 2020).…”

“…where the constant γ is the same for different particles and does not depend on mass (Quesne and Tkachuk, 2010;Tkachuk, 2012;Gnatenko and Tkachuk, 2020).…”

“…So, the weak equivalence principle is recovered due to the assumption Eq. 24 (Tkachuk, 2012;Gnatenko and Tkachuk, 2020).…”

“…It is also important to mention that the relation Eq. 26 gives a possibility to preserve the additivity property of the kinetic energy in a space with GUP and to solve the problem of the significant effect of the GUP on the kinetic energy of a macroscopic body [for details see (Gnatenko and Tkachuk, 2020)].…”