2011/08/03 by Jose A. Magpantay, Magpantay, Jose A.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane #Classical mechanics #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Extra dimensions #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geodesic #Geometry #Gravitation #Massive particle #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle (ecology) #Particle physics #Physics #Quantum #Quantum mechanics #Spacetime #Tensor (intrinsic definition) #Test particle #Theoretical physics #Uncertainty principle #Universe #gr-qc
paper · pdf · doi:10.48550/arxiv.1108.0750
8 pages
arxiv created 2011/08/03 · openalex publication_date 2011/08/03 · arxiv updated 2011/08/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.