2) How 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.

http://www.interstellartechcorp.com/phyTheoretical.html

Quantum-Electro-Dynamics (QED)

By 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 photons.

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 principle.

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.

The Casimir Effect

Let 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 Casimir force.

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 the boundaries.

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.