- Same idea that may be used to rectify nonthermal
fluctuations from ZPE
Zero-Point Energy Can be Utilized with a Casimir Force Based Device: A Smooth
and Seamless Explanation
By Fabrizio Pinto,
President and CEO of Interstellar Technologies Corp.
means of the Schrödinger equation, it is possible to determine all possible
states of the electron in the electric field of the proton in a hydrogen atom.
Such states are described by mathematical objects referred to as the wave
functions, which describe the probability of finding the electron at any
position in space. Despite further progress from the old quantum theory, we are
still unable to determine why the electron should transition from one state of
higher energy to one of lower energy.
In order to do so, we must
implement the rules of quantum physics not only in our description of the
electron, but also in that of the electromagnetic field itself. For as long as
we keep our description of the electromagnetic field classical, it is impossible
to show that the higher energy states of the hydrogen atom are unstable and, in
time, they will decay into the ground state with the emission of one or more
The theory that describes
not only matter, but all fields as well, by means of quantum principles is
referred to as quantum electrodynamics (QED). In its most complete form, it
naturally includes Einstein's special theory of relativity and it is therefore
more advanced than even the non-relativistic Schrödinger equation. In much the
same way as the position and momentum of a particle represent a pair of
quantities that cannot be both measured at the same time with infinite
precision, so also in QED the components of the electric field and of the
magnetic field represent such a pair in the sense given by the uncertainty
Intuitively, this means
that, even in a state of vacuum (absence of all sources) in any volume of space,
the uncertainty principle, applied now to the electromagnetic field itself,
implies the existence of a "ground state" for such vacuum. In other words, we
must visualize the vacuum not as an absolutely empty region of space, but as one
where, in accordance with the uncertainty principle, the electromagnetic field
randomly changes form place to place. According to QED, it is impossible to ever
obtain a state "emptier" than such vacuum in free space. Perhaps the most
provocative concept about this quantum vacuum is that, if we attempt to compute
its total energy density, we obtain an infinite number.
This shocking finding is
traditionally interpreted as meaning that, in order to extract information from
QED, we have to somehow eliminate, subtract, or renormalize our results so as to
avoid its infinities. Since the structure of the theory allows for this to be
done, the diverging energy density of the quantum vacuum has not represented an
insurmountable obstacle to use it in practice. However, this procedure of course
does not mean that this infinite energy simply does not exist and, in fact, a
long-standing debate has been taking place as to whether its appearance is
simply due to mathematical gadgetry or to its actual physical existence.
us now once again consider our two parallel plates. In the QED framework, any
volume of empty space both within and without the gap between the plates
actually contains electromagnetic zero-point energy (ZPE) due to the electric
and magnetic fields fluctuating because of the uncertainty principle. Such
fluctuating fields correspond to photons that appear and disappear continuously.
Unlike photons we experience in our daily lives, referred to as real photons,
these photons cannot be directly detected nor can they exist for an infinitely
long time because their existence violates the principle of the conservation of
energy. They are referred to as virtual photons.
Because of the same
arguments we discussed in the case of the acoustic Casimir effect, the presence
of the two boundaries alters the energy density in the region between the two
surfaces. Although this number is infinite, it is possible to devise techniques
to subtract it from the energy density outside of the gap, which is also
infinite. The result so obtained is a finite value.
This important finding
shows that the presence of the two surfaces causes a change in the zero-point
energy of the system that depends on the distance between the plates: the
smaller the distance, the larger the change. This is the ultimate origin of the
It is natural to wonder
whether it is possible to view the Casimir force in QED as a result of radiation
pressure, given the fact that, in this case, no real photon field actually
exists. The answer is affirmative, as it has been shown that the Casimir effect
can be explained as the result of radiation pressure of the virtual photons upon
From the mathematical
standpoint, there is absolutely no difference between the SED and QED treatments
of the problem. Also, depending on the boundary conditions, the Casimir force
may be repulsive - as is the case for instance in the interaction between a
perfectly conducting and an infinitely magnetic plate.
Read the whole paper at the link above.