The vacuum catastrophe is name given to the disagreement of over 100 orders of magnitude between measured values of the vacuum energy density and the theoretical zero-point energy predicted by Quantum Field Theory.  This discrepancy has been described as "the worst theoretical prediction in the history of physics."

Supernovae Ia and Vacuum Energy Density

The effects of vacuum energy can be experimentally observed in various phenomena such as the accelerated expansion of the universe and the Casmir effect.

Unfortunately as was just mentioned there is a very large discrepancy between the values predicted for vacuum energy made by Quantum Field Theory and the observed value for both Casmir effect and the universe’s expansion. 

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

According to modern quantum 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 Casimir 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 predicted by quantum mechanics.

Nevertheless one may be able to understand why if instead of deriving vacuum or zero point energy purely from a mathematical perspective as Quantum Field Theory does one derives it from the observations associated with the Casimir effect.

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 energy/mass and electromagnetic waves by extrapolating the laws of classical resonance in a three-dimensional environment to matter wave in four *spatial* dimension. 

(Louis de Broglie was the first to predict the existence of wave properties of a quantum system 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.) 

(Einstein gave us the ability to do this when he used the constant velocity of light to define the geometric properties of space-time 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 mathematically derive a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.)

Briefly, that article 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 the field properties of energy/mass (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 field consisting 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 shows the reason zero-point energy predicted by quantum mechanics is so much higher than what is observed in the Casmir effect is because, according to it each zero point mode of oscillation is subject to the Heisenberg uncertainty principle.  That produces a tiny amount of energy in each point, but the number of modes is enormous.  Since energy density is mathematically determined by multiplying the density of modes times the energy per mode 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.

Yet as was shown above the Casmir effect may not be 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 every point in space may not experience random fluctuations as is required by quantum field theory but instead it may have a fundamental oscillating frequency that requires a volume that is larger that of a single point. 

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

However one can use the known the value for both the Casmir effect and as mentioned earlier the accelerated expansion of the universe to mathematically determine the energy associated with that fundamental harmonic and determine if it agrees with the observed value of each.

This would give one the ability to experimentally verify or falsify the hypotheses outlined above because as was mentioned earlier vacuum energy is assumed not only responsible for the Casimir effect but also for the accelerated expansion of the universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2016
 

   

 

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Quantum Chromodynamics a subset of the Standard Model of Particle Physics gives a very accurate mathematical description of the strong force that hold quarks together in protons and neutrons in terms of a gauge theory with the symmetry group of SU(3).

However it does not define how that force physically interacts with them to do that.  In other words it mathematically defines a SU(3) group but it does not define how it interacts with our observable environment to create that force.

The Strong Force: A Chat with Nobel Laureate David Gross

Despite this shortfall some feel that a physical connection must exist between the math defining Quantum Chromodynamics, the Standard Model of Particle Physics and the physical reality of the observable environment humans occupy because their quantitative predictions so accurately describes the properties and forces associated with quarks.  This is true even though gravity which is part of that environment has yet to be incorporated into it.

However the fact that one can mathematically describe properties of an environment does not necessary mean that it accurately depicts its reality.

For example there are many ways to mathematically define why there are five apples on a table.  One could say that originally there were six and one was taken away or that there were four and one was added.  Both accurately described the observed number of apples on the table.  However if originally there were four apples the one that assumed there were six does not define the reality of their environment that produced them.

Similarly there may be several ways to describe the existence quarks.

If so how can we determine which one not only describes what we observe but also defines the reality of the environment that created them?

One way to increasing the possibility of getting it right would to define their environment based on what we observe and then derive its mathematical properties instead of defining them only in terms of its mathematical ones which is what Quantum Chromodynamics does.

For example, observations of the neutron and proton indicate they are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.  Additionally they tell us the binding energy associated with the strong force is only depended on the distance between them.  In other words it does not vary with time

This suggests, because that forces remain constant through time their existence is related to the spatial not the time properties of their environment.

This may be also be the reason why as was mentioned earlier gravity is has not yet been incorporated in it the Standard Model because presently the only viable theory we have; Einstein’s General Theory of Relativity defines it in term of the temporal properties of a space-time dimension. 

However Einstein gave us the ability resolve this conflict when defined his space-time environment  in terms of the constant velocity of light because that allows one to convert a unit of time in it 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.

In other words the symmetry of his mathematics provides a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Doing so may allow one to define an environment which is responsible the forces and the fractional charge of quarks and how they interact to form particles in terms of the geometry four *spatial* dimension.

For example the article Defining energy Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a physical displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how Einstein derived gravity in terms of a physical displacement in a space-time manifold.

However, we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface".  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means one could define the environment responsible for the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or "colors" of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it can also explain why it takes three quarks of different "colors" to form a stable particle because, as the article "Why is energy/mass quantized?" Oct, 4 2007 showed one can define one in terms of a resonant system on a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

(Briefly that article showed the four conditions required for resonance to occur in any 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 be available in one consisting of four *spatial* dimensions,

The existence of four *spatial* dimensions would give a continuous non-quantized field of energy/mass (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.

Therefore, these oscillations would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.)

Yet this gives us a method of mathematically deriving the strong force in terms of the physical properties of predefined environment that it is a part of because we know two of its parameters; the electrical forces pushing them apart and the distance between them. Therefore we should be able to determine the magnitude strong force required to prevent that from happening using the geometric relationship describe above.

As was shown earlier the symmetry of Einstein’s mathematics provides a qualitative and quantitative means of redefining gravity in his space-time universe in terms of the geometry of four *spatial* dimensions.

Doing so would allow for the anchoring the mathematics defining both gravity and the strong force in terms of the physical properties a common environment something which Quantum Chromodynamics and the Standard Model of Particle Physics have been unable to do.

It should be remember Einstein’s genius and the fact that he defined the geometry of space-time in terms of the constant velocity of light allows us to choose to define our universe in either a space-time environment or one consisting of four *spatial* dimension when. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the temporal properties of our universe giving us a new perspective on how the forces it contains interacts with it.

Later Jeff

Copyright 2016 Jeffrey O’Callaghan

 

     

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