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

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must be abandoned for more erudite mathematical constructions which are better
suited at describing the building blocks of nature (Reference 18-20).
If one takes the Fourier transform of a free quantum field,5 each mode of a fixed
wavelength behaves like a simple harmonic oscillator. A quantum mechanical property
of a simple harmonic oscillator is that the ground state exhibits zero-point fluctuations
as a consequence of the Heisenberg Uncertainty Principle. One way to understand these
zero-point fluctuations is to imagine releasing a pendulum and watching as dissipative
forces slowly try to bring the pendulum to a stop. The uncertainty principle would
ensure that the pendulum was never able to come to a complete rest, but instead
would exhibit microscopic oscillations around the equilibrium position indefinitely. Of
course, for a real macroscopic pendulum, these fluctuations would be miniscule and all
but impossible to detect; however, the analogy with a quantum harmonic oscillator
holds well. The expectation value of the energy associated with the ground state energy
of a quantum oscillator is:
(4.1)
In this formula c and n are the speed of light and Planck's reduced constant (1.055 x
10-34 J.s), respectively, and k is the wave-vector related to the momentum of the
quantum field. One of the features of this ground state energy is that the wave vector
has an infinite degree of freedom. Clearly this sum is divergent; however, this is a
common feature of quantum field theory, and an array of mathematical techniques
known as renormalization exists to deal with the infinities that arise.
4 .1 THE CASIMIR EFFECT
The quantum fluctuations of the vacuum fields give rise to a number of phenomena;
however, one is particularly striking. The Casimir Effect, which will be explored in more
detail in this paper, is arguably the most salient manifestation of the quantum vacuum.
In 1948, H. Casimir published a profound paper where he explained the van der Waals
interaction in terms of the zero-point energy of a quantized field (Reference 19). In its
most basic form, the Casimir Effect it is realized through the interaction of a pair of
neutral parallel conducting plates (with separation distanced). The presence of the
plates modifies the quantum vacuum, and this modification causes the plates to be
pulled toward each other with a force:
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(4.2)
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This is a profound result in the sense that the origin of this force cannot be traced back
to one of the four fundamental forces of nature (gravity, electromagnetism, and the two
nuclear forces), but is a force that is entirely due to a modification of the quantum
vacuum.
5 By "free" we mean that the field does not interact with other fields.
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