On Higher-Dimensional Dynamics

Abstract

Technical results are presented on motion in N(>4)D manifolds to clarify the physics of Kaluza-Klein theory, brane theory and string theory. The so-called canonical or warp metric in 5D effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force (per unit mass) parallel to the 4D velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10^{-65} gm or less which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(>4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved.

References in corpus (3)

• Null Geodesics in Five Dimensional Manifolds
• Embeddings in Non-Vacuum Spacetimes
• Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

Cited by in corpus (15)

• Is Mass Quantized?
• Astrophysical Implications of Higher-Dimensional Gravity
• Variation of G, ${\Lambda }_{(4)}$ and Vacuum Energy From Brane-World Models
• An Embedding for General Relativity and its Implications for New Physics
• Brane-world models emerging from collisions of plane waves in 5D
• An analytic model for the transition from decelerated to accelerated cosmic expansion
• Stabilization of test particles in Induced Matter Kaluza-Klein theory
• Space-Time Uncertainty from Higher-Dimensional Determinism (or: How Heisenberg was right in 4D because Einstein was right in 5D)
• The Equivalence Principle as a Symmetry
• FLRW Universes from "Wave-Like" Cosmologies in 5D
• Self-similar cosmologies in 5D: Our universe as a topological separation from an empty 5D Minkowski space
• Semiclassical corrections to the Einstein equation and Induced Matter Theory
• Embeddings for 4D Einstein equations with a cosmological constant
• Dark Matter: The Problem of Motion
• Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory