We have shown throughoutÂ this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” that observations of our environment indicate that the universe is composed of four *spatial* dimensions instead of four-dimensional space-time and a vacuum contains a measurable quantity of continuous non-quantized field of mass/energy.

One of these observations is called the Casimir effect.

The Casimir effect is a small attractive or repulsive force which acts between two close parallel-*uncharged* conducting plates, which many physics believe is due to quantum vacuum fluctuations of the electromagnetic field.

According to modern physics, a vacuum is full of fluctuating electromagnetic waves of all possible wavelengths, which imbue it with a vast amount of energy.Â Casimir realized that between two plates, only those electromagnetic waves whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy.Â As the gap between the plates is narrowed, fewer waves can contribute to the vacuum energy and so the energy density between the plates falls below the energy density of the surrounding space.Â This generates either an attractive or a repulsive force depending on the specific arrangement of the two plates.Â This is because Quantum theory requires that each of these vibrations be quantized and therefore the field, at each point in space would be a simple harmonic oscillator that has the energy of the particle associated with the force that Casimir observed to be pushing the plates together.

In the article â€The Photon: a matter wave?â€ Oct. 1, 2007 it was shown that one can derive the quantum mechanical properties of an electromagnetic wave by extrapolating the laws of classical resonance in a three-dimensional environment to resonant system in a continuous non-quantized field of energy/mass and four *spatial* dimension.

**(Louis de Broglie was the first to predict the existence of a continuous non-quantized form of energy/mass when he theorized that all particles have a wave component.Â His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)Â **

Briefly, it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one composed of four.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.Â This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in a continuous non-quantized field of energy/mass.

As was shown it the article â€Why is mass and energy quantized?â€œ Oct.4, 2007 these resonant systems are responsible for the quantum mechanical properties of energy/mass.

Yet it can also be shown they are responsible for the Casimir effect because observations of resonant systems in a classical environment indicate the number of simple harmonic oscillators that can be established in a given environment is dependent on the distance or “gap” between the “end points” of their environments.

But same concept can be applied to two uncharged metallic plates in a vacuum, because even without any external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating or have thermal energy because they are not at absolute zero.Â These random vibrations of their electromagnetic components will result in a random electromagnetic field to be generated between the plates.

However, classical wave mechanics tells us these random electromagnetic vibrations would be reinforced only at certain points in space.Â The number of simple harmonic oscillators in the space between two plates formed by this reinforcing would decreases as the gap between them decreases.Â In other words, the smaller the gap between the plates the fewer number of quantum fields or particles that gap could support.

This means as was shown in the article â€Why is energy/mass quantized?â€œ there will be a greater number simple harmonic oscillators impacting the plates from outside of the gap than between it.Â This will cause a force that will push the plates together because the energy density associated with the harmonic oscillations outside of the gap would be greater than inside of it.

However, it also tells us there will be also be places where the distance between the plates will be equal to the wavelength associated with a fundamental or harmonic of the fundamental frequency of a quantum fluctuation.Â At those distances their energy will reinforce force each other and push them apart.

Therefore, if one assumes as us done here that the quantum mechanical properties of energy/mass are a result of a resonant system in four *spatial* dimension one can understand why the specific arrangement of the two plates causes an attractive or repulsive force to be developed by extrapolating the properties of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2008