Macroscopic body in Snyder space and minimal length estimation

Abstract

We study a problem of description of macroscopic body motion in the frame of nonrelativistic Snyder model. It is found that the motion of the center-of-mass of a body is described by an effective parameter which depends on the parameters of Snyder algebra for coordinates and momenta of particles forming the body and their masses. We also show that there is reduction of the effective parameter with respect to parameters of Snyder algebra for coordinates and momenta of individual particles. As a result the problem of extremely small result for the minimal length obtained on the basis of studies of the Mercury motion in the Snyder space is solved. In addition we find that relation of parameter of Snyder algebra with mass opens possibility to preserve the property of independence of the kinetic energy on composition, to recover the weak equivalence principle, to consider coordinates as kinematic variables, to recover proportionality of momenta to mass and to consider Snyder algebra for coordinates and momenta of the center-of-mass of a body defined in the traditional way.

References in corpus (22)

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• Composite system in deformed space with minimal length
• Classical and quantum mechanics of the nonrelativistic Snyder model
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Cited by in corpus (5)

• Dark Matter as an effect of a minimal length
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Cyclotron frequency and the quantum clock