AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

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In summary, quantum field theory predicts that the vacuum is an interlaced cobweb of
quantum fields which are never strictly at rest, and which exhibit zero-point
fluctuations. These fluctuations give rise to real and measurable phenomenon, with the
Casimir effect being the most poignant. It seems only natural to attempt to relate the
ideas from the previous section regarding a ubiquitous dark energy field to this
quantum vacuum energy. If a relationship can be established, one would be a step
closer to the technological realization of warp drive.
5. Extra Space Dimensions
In connection with the Casimir effect, extra dimensions provide a rich arena for one to
generate models that explain the origin of dark energy. Technically speaking, the
Casimir effect is a direct consequence of the non-trivial boundary conditions that the
presence of the conducting plates imposes upon the quantum vacuum. The quantum
modes on the interior region of the plates are restricted, and there is a pressure
difference when compared to the quantum vacuum on the exterior region of the plates.
It is this pressure difference that causes the plates to attract. 7
A very similar phenomenon to the Casimir effect can occur when the quantum vacuum
energy in extra space dimensions are considered. The exploration of this idea has
important ramifications in the context of explaining dark energy. Before one can
address these ideas it is necessary to review the role of higher space dimensions in
physics.
It was Riemann, with his development of differential geometry in the 19th century, who
provided the necessary tools to study higher dimensional descriptions of the world
(Reference 26). Riemann held the belief that 3-dimensional space was not enough to
provide an adequate description of nature. Improvements in physics led to Maxwell's
unified theory of electricity and magnetism, and then GR, which unified space and time
with Special Relativity (SR). Inspired by these unifications, physicists of the early 20th
century wanted to unify gravity and electromagnetism. The first attempt was by
Nordstrom in 1914, who used a scalar potential for the gravitational field. Later Weyl
and Kaluza, using Einstein's tensor potential, followed two separate paths. Weyl's
attempt involved an alteration of the geometry of spacetime in four dimensions. His
early attempts had physical consequences which did not match experimental data.
However, Weyl's work was extended by Einstein and Schrodinger independently in the
Einstein-Schrodinger non-symmetric field theory, which is widely regarded as the most
advanced unified field theory based on classical physics.
5.1 KALUZA- KLEIN THEORY
In 1919 Kaluza (Reference 27) offered a unique approach to unifying gravity and
electromagnetism which involved adding an additional spatial dimension to GR, and
populating this extra dimension with two mathematical objects called a vector potential
A1i and a scalar potential </J. The line element in this theory is given by:
7 This analogy Is not strictly true as different geometries can, in fact, create repulsive Casimir forces and so the
pressure analogy breaks down. It is, however, a useful visualization tool.
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