On Higher-Dimensional Dynamics

TL;DR

This paper explores higher-dimensional dynamics in N-dimensional manifolds, revealing how extra forces and mass quantization emerge in theories like Kaluza-Klein and string theory, with implications for quantum and gravitational systems.

Contribution

It introduces a general framework for particle motion in higher dimensions, linking extra forces to vacuum energy and demonstrating mass quantization at extremely small scales.

Findings

Extra force is independent of metric form but tiny for unbound particles.

Mass quantization occurs at an unobservable level (~10^{-65} g).

Particles can move on null paths in higher dimensions, aligning with quantum field theory insights.

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.