Geodesics, Mass and the Uncertainty Principle in a Warped de Sitter Space-time

TL;DR

This paper solves geodesic equations in a warped de Sitter space-time, revealing how extra dimensions influence particle mass and the uncertainty principle, with implications for forces constraining particles on the brane.

Contribution

It provides explicit solutions to geodesic equations in a Randall-Sundrum warped de Sitter space and analyzes the resulting time-dependent effects on particle mass and quantum uncertainty.

Findings

Particle moves in the bulk, not restricted to the 3-brane.

Time-dependent mass and uncertainty principle emerge from extra-dimensional effects.

Classical corrections can be removed, but quantum corrections restore the effects.

Abstract

We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the 3-brane, the test particle moves with uniform velocity, giving the appearance that it is not subject to a force. But computing the particle's energy using the energy-momentum tensor yields a time-dependent energy that suggests a time-dependent mass. Thus, the extra force, which is the effect of the warped extra dimension on the particle's motion on the 3-brane, does not change the velocity but the mass of the particle. The particle's motion in the bulk also results in a time-dependent modification of the Heisenberg uncertainty principle as viewed on the 3-brane. These two results show that the classical physics along the extra dimension results in the time-dependence of particle masses and the uncertainty principle. If the particle masses are time-independent and the Heisenberg's uncertainty principle is to remain unchanged, then there must be a non-gravitational force that will restrict all particles on the 3-brane. Finally, we just note that although classically, these time-dependent corrections on the 3-brane can be removed, quantum mechanical corrections along the extra dimension will restore back the problem.