Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects
Richard K. Obousy
Abstract and summary · read the original at the source · arXiv non-exclusive distribution licence 1.0; the document itself is marked all rights reserved
In one page
Richard Obousy’s Baylor doctoral thesis takes one number seriously: the energy of empty space depends on how big the universe’s curled-up extra dimensions are, and it depends on it steeply — as the inverse fourth power of their radius. Most of the thesis is careful housekeeping. He reviews what the quantum vacuum is, how the cosmological constant entered Einstein’s equations, how the Casimir force is calculated and how it was measured, and what extra dimensions are for. Then he does his own calculation: what Casimir energy a scalar field acquires when it is coupled to a vector field pointing along the fifth dimension, and whether the resulting energy can hold that dimension at a fixed size. Chapter seven is where it turns into hardware. If the radius of an extra dimension sets the local expansion rate of space, then a technology able to shrink or grow it locally would expand space behind a ship and contract it ahead — a warp bubble, arrived at from string theory rather than from exotic matter.
Why it matters hereChapter 2 gets its cleanest statement of the vacuum as an adjustable quantity rather than a fixed background: change one geometric parameter and the energy of empty space changes as its fourth power. Chapter 4 gets the mechanism that follows — a warp bubble produced by locally tuning the size of a compact dimension, with an energy budget, a speed ceiling and a named next calculation, which is the same programme the Defense Intelligence Agency later commissioned from this author.
What it claims
01The Casimir energy of a field living in a compactified fifth dimension goes as the inverse fourth power of that dimension’s radius, and for a massless scalar with periodic boundary conditions the vacuum energy density is minus three times the Riemann zeta function at five, over sixty-four pi squared times the radius to the fourth — so the vacuum energy density and the cosmological constant are tied to a single geometric number.Chapter 7, Equations 7.3.1 to 7.3.3; the same expression derived in Chapter 5, Equation 5.1.26
Published and peer-reviewed02The thesis’s own derivation adds a Lorentz-violating vector field with a non-zero expectation value only along the fifth dimension, coupled to a scalar; this splits the Kaluza-Klein tower unevenly and multiplies the Casimir energy by a single tuning parameter, but the contribution stays attractive and shrinks the extra dimension, so scalars coupled this way cannot stabilise it on their own.Chapter 5, Sections 5.1.1 to 5.1.3; Equations 5.1.1, 5.1.2 and 5.1.26
Published and peer-reviewed03Populating the bulk with the Standard Model fields and the Higgs fails to stabilise the extra dimension across the whole experimentally allowed range of Higgs masses, because the fermions’ positive Casimir energy is not balanced; adding one light anti-periodic exotic fermion — justified as a possible sterile bulk neutrino — does produce a stable minimum, sitting at negative energy density in an anti-de Sitter spacetime, and a minimum at positive energy density needs at least two additional exotic fields.Chapter 6, Sections 6.1.3 to 6.1.7; Section 6.5, Discussion
Published and peer-reviewed04Solving the vacuum Einstein equations for a five-dimensional toy universe with empty space and no cosmological constant gives the Hubble rate of the three large dimensions equal to minus the Hubble rate of the compact one — the contraction of the extra dimension inflates the others, so even in pure general relativity the physics of the compact space governs the expansion rate of the space we live in.Chapter 7, Section 7.3.1, Equations 7.3.6 to 7.3.11
Published and peer-reviewed05A sufficiently advanced technology able to increase or decrease the radius of the extra dimension locally would thereby adjust the local expansion and contraction of spacetime, creating a warp bubble; the craft always stays inside its own light cone, using expansion behind it to recede from an object and contraction ahead to approach one, at any desired speed.Chapter 7, Section 7.3.1, Equation 7.3.5 and the paragraph following it
Designed, not yet built06The thesis’s own back-of-the-envelope budget: making space expand locally at light speed needs the Hubble rate raised by ten to the twenty-six, the extra-dimensional radius shrunk by a factor of ten trillion, a local vacuum energy density near ten to the forty-two joules per cubic metre and about ten to the forty-five joules for a thousand cubic metre craft — Jupiter’s mass-energy in antimatter, dropping dramatically for a thin shell — while the Planck-length floor on the radius sets a ceiling near ten to the thirty-two times light speed; how to manipulate an extra dimension locally, perhaps by locally changing string tension or countering winding modes, is named as the vital next piece of research.Chapter 7, Sections 7.3.2 to 7.3.4, Equations 7.3.12 to 7.3.21
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Abstract
The primary focus of this dissertation is the study of the Casimir effect and the possibility that this phenomenon may serve as a mechanism to mediate higher dimensional stability, and also as a possible mechanism for creating a small but non-zero vacuum energy density. In chapter one we review the nature of the quantum vacuum and discuss the different contributions to the vacuum energy density arising from different sectors of the standard model. Next, in chapter two, we discuss cosmology and the introduction of the cosmological constant into Einstein's field equations. In chapter three we explore the Casimir effect and study a number of mathematical techniques used to obtain a finite physical result for the Casimir energy. We also review the experiments that have verified the Casimir force. In chapter four we discuss the introduction of extra dimensions into physics. We begin by reviewing Kaluza Klein theory, and then discuss three popular higher dimensional models: bosonic string theory, large extra dimensions and warped extra dimensions. Chapter five is devoted to an original derivation of the Casimir energy we derived for the scenario of a higher dimensional vector field coupled to a scalar field in the fifth dimension. In chapter six we explore a range of vacuum scenarios and discuss research we have performed regarding moduli stability. Chapter seven explores a novel approach to spacecraft propulsion we have proposed based on the idea of manipulating the extra dimensions of string/M theory. Finally, in chapter 8, we discuss some issues in heterotic string phenomenology derived from the free fermionic approach.
The way in
https://arxiv.org/abs/0901.3640Richard K. Obousy’s doctoral dissertation, submitted to the Graduate Faculty of Baylor University and accepted in December 2008, dissertation committee chaired by Gerald B. Cleaver, posted to arXiv as 0901.3640 version 1 on 23 January 2009 — 147 pages, 16 figures, 3 tables. The posting carries the arXiv non-exclusive distribution licence, which is not a Creative Commons licence, and the document’s own copyright page reserves all rights, so this sheet stays abstract-only. The abstract below is the dissertation’s own abstract page, verbatim, which is also what arXiv carries. The summary and every claim were written from the complete PDF, read on 2026-09-08 — abstract, table of contents, the original derivations of chapters five and six, the propulsion chapter seven and each chapter’s own discussion section — and every locator points to a numbered chapter, section or equation of it. Companion sheets: the same author’s earlier supersymmetry-breaking Casimir warp drive with Gerald Cleaver at /library/stm-7dfda7640a, and the Defense Intelligence Agency reference document that carries this programme forward at /library/stm-2a2a21e516.
How to cite it
Richard K. Obousy (2009) Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects. arXiv:0901.3640
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