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Both Einstein’s Special and General Theories of Relativity have a perfect record of predicting and explaining what we observe in our environment.

However, the same cannot be said for Bohr’s concepts regarding the quantum properties of energy/mass.

For example, the fact that vacuum energy exists has been confirmed by both the observation of Dark Energy, which is causing the expansion of the universe to accelerate and experimentally in what has come to be called the Casimir effect.
However if one uses Quantum Field Theory which is based on Bohr concepts to derive the vacuum or zero point energy of space one gets a value that is 100 orders of magnitude larger than its measured value.  This discrepancy has been described as “the worst theoretical prediction in the history of physics.”

In most cases scientists could create auxiliary hypothesis to explain why this is true.  However this is not the case with Quantum Field Theory because that prediction is based on one of its fundamental assumptions: that of a defining the probability of particle being in a specific position in terms of it being a one dimensional “object” and Heisenberg uncertainty principle.  If any one of them is not valid, the entire theory must be discarded.

Quantum field theory predicts such a large value for vacuum energy because it DEMANDS WITHOUT EXCEPTION each mode of oscillation in space is subject to the Heisenberg uncertainty principle.  That produces a tiny amount of energy in each point mode, but the number of modes is enormous because there can be an infinite number point sources or “objects” in any given volume of space.  The energy density is mathematically determined by multiplying the density of modes times the energy per mode.  In other words, the product of the tiny point source of energy times the huge spatial density of modes yields a very high theoretical zero-point energy density per cubic centimeter.

To resolve the issue Quantum Field Theory has with vacuum energy one would have to either assume that the Heisenberg uncertainty principle is invalid or the oscillations it associates with that principal cannot occur at every point in space.  We can be pretty sure that the Heisenberg uncertainty principle is valid because we can observe the effects it has on the measurement of the position and momentum of particles in a quantum environment.

Therefore, to account for the large discrepancy between the predicted and observed value of vacuum energy one must assume that one cannot define the oscillating mode it associates with it in terms of a one-dimensional point.  However, this means the entire probabilistic interpretation of quantum field theory, which is based on the mathematical properties of one a dimensional point does not exist and therefore must be discarded.  There is no other option.

Einstein also predicted the existence of vacuum energy when he added a constant force call a cosmological constant to keep the universe static and unchanging.

In others words he realize a vacuum could contain energy such as that associated with Dark Energy that could counteract the spatially contractive properties of gravity,

Granted his creditability may have been diminished by the fact the force he predicted was supposed to keep the universe static while that associated with Dark energy is causing its expansion to accelerate.

However, he did not define or explain its causality even though he predicted its existence. This may be because he chose to define all forms of energy in terms of temporal properties of a space-time dimension and not its spatial properties.  In other words because the energy associated with both his cosmological constant and Dark Energy must interact with the spatial properties of the universe to counter act gravity it would have been difficult to define its causality terms of its temporal ones. 

This suggests one may be able to derive their casualty and that of vacuum energy in intergalactic space if one could define it in terms of the spatial instead of the temporal properties of the environment it interacts with. 

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define geometric properties of energy/mass because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use the Einstein’s equations to qualitatively and qualitatively derive the displacement he associated with energy and mass in a space-time environment in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However, as was shown in the article “Dark Energy in four *spatial* dimensions” Oct 1, 2012 it also allows one to use the laws of thermodynamics to understand how and why Dark Energy is causing the accelerated expansion of our universe. because it gives one the ability to define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of temporal one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high to ones of low density very similar to how water flows form an elevated point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the water molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

This shows how one can fully integrate the observed properties of Dark Energy into the conceptual framework of both Einstein General and spatial Theories of Relativity.

However it also provides the ability to understand the casualty vacuum energy in the Casimir effect in terms of the concepts developed by Einstein.

As was mentioned earlier Casimir effect is the 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 Quantum Field Theory, a vacuum is full of fluctuating electromagnetic waves of all possible wavelengths, which imbue it with a vast amount of energy.  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.  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.  This generates either an attractive or a repulsive force depending on the specific arrangement of the two plates.  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 observed to be pushing the plates together.

However as was just mentioned there is very large discrepancy between the observed vacuum energy density associated with the Casimir effect and value of the zero-point energy predicted by quantum mechanics.

As was mentioned earlier one may be able to understand the causality of vacuum energy by redefining the temporal properties of Einstein space-time universe in terms of it spatial ones.

For example in the article ”Why is mass and energy quantized?“ Oct.4, 2007 it was shown that one can derive the quantum mechanical properties of particles by extrapolating the laws of classical resonance in a three-dimensional environment to matter wave on a continuous non-quantized field of energy/mass to 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.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.) 

Briefly, that articled 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 space (the substance) 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.  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.

However 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 this same concept can be applied to two uncharged metallic plates in a vacuum, because even without an 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.  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.  The number of simple harmonic oscillators in the space between two plates formed by this reinforcement would decreases as the gap between them decreases.  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 ”Why is energy/mass quantized?“ there will be a greater number simple harmonic oscillators impacting the plates from outside of the gap than between it.  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 these oscillations.  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.

However it also tells the reason the zero-point energy predicted by quantum mechanics is so much higher than what is observed in the Casimir effect is because it is not the result of the summation of a large number of individual zero point harmonic oscillators acting individually but only those that are defined by a fundamental resonant property of space and distance between the plates.

In other words the magnitude of vacuum energy would be defined by the size of the fundamental harmonic of space and not by the random fluctuations associated with the zero point energy of a quantum vacuum.

However, the fact as mentioned earlier that no auxiliary hypothesis can be derive to explain the very large discrepancy between Quantum Field theory predictions and the observed magnitude of vacuum energy without negating at least one of its fundamental concepts presents a serious blow to its overall creditability.

One the other hand, as was shown above using the fundamental concepts of Einstein’s theories one can understand at least one creditable mechanism that could account magnitude of vacuum energy observed in both Dark Energy and the Casimir effect.

Copyright Jeffrey O’Callaghan 2016

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