On higher-dimensional dynamics

Abstract

Technical results are presented on motion in N(Ͼ4)D manifolds to clarify the physics of brane theory, Kaluza-Klein theory, induced-matter theory, and string theory. The so-called canonical or warp metric in five dimensions ͑5D͒ effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force ͑per unit mass͒ parallel to the four-dimensional ͑4D͒ 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 Ϫ65 g 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(Ͼ4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved.

Nematic Structure of Space-Time and Its Topological Defects in 5D Kaluza-Klein Theory

“…F = 0  α = 0. This choice has been used in works by a number of other authors [16], where an effective matter involves "fifth coordinate dependency" of 5D metric. Easy to see, that, the canonical frame of 5D metric G = g αβ (x, η)(dx α ⊗ dx β ) + εdη ⊗ dη, α, β = 0, 1, 2, 3, introduced in [16] and in a number of earlier works of the author, just can be related to the considered particular class of solutions to (23).…”

“…Before deriving equilibrium equations let's clear out nematic properties of space-time with lagrangian (16). For this purpose we need to remind general facts of common 3D nematic crystals physics and generalize it for 5D case.…”

“…To express (16) in terms of Frank's moduluses we need express it in terms of independent quadratic invariant combinations, which are 5D generalizations of those in (17). The first and second terms in (17) have trivial generalizations:…”

“…It attracts many theorists today due to profound insight of its central paradigm -extradimensions and its physical manifestations -on the one hand, and due to development of the theory within more contemporary framework on the other [15,16,17,18,19]. The more general (than original Kaluza-Klein) formulations and interpretings of the theory have allowed to establish unified geometrical background for a wide class of phenomena.…”

Letter: Space-Time Uncertainty from Higher-Dimensional Determinism

“…We will use the Lagrangian approach, but the results are compatible with a longer approach based on the geodesic equation 14,15 . Conventional units are retained for ease of physical interpretation.…”