For example the density of mass to energy in the early universe must have been very close to a specific value to explain how stars could have evolved because if their concentrations were not it would depart rapidly from the one that would allow them to form over cosmic time.  Calculations suggest that it could not have departed more than one part in 10⁶² from that value.   This leads cosmologists to question how the initial density came to be so closely fine-tuned to this ‘special’ value that would have allowed stars and therefore life to evolve.
This has come to be called the flatness problem because the density of matter and energy which affects the curvature of space-time must have very specific value to give it the flat geometry required for stars to form and life to evolve.  In other words if the energy of the universe expansion was much larger it would have overpowered gravity preventing the formation of stars while if gravity was to strong they would have formed to quickly thereby not give life as we know it time to evolve.  `

The problem was first mentioned by Robert Dicke in 1969. 

The most commonly accepted solution among cosmologists is cosmic inflation or the idea that the early universe underwent an extremely rapid exponential expansion by a factor of at least 10⁷⁸ in volume, driven by a negative-pressure vacuum energy density.

This solves the flatness problem because the act of inflation actually flattens the universe.  Picture a uninflated balloon, which can have all kinds of wrinkles and other abnormalities, however as the balloon expands the surface smoothes out.  According to inflation theory, this happens to the fabric of the universe as well.

However, many view the inflationary theory as a contrived or “adhoc” solution because the exact mechanism that would cause it to turn on and then off is not known.

Yet, if one defines energy/mass density of our universe in terms of its spatial properties instead of the temporal ones of four dimensional space-time one can explain and predict why it has the correct proportions to cause its geometry to be hospitable to life as we know it by extrapolating the laws of classical physics in a three-dimensional environment to one of four *spatial* dimensions.

Einstein gave us the ability to do this when he defined its geometry in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 because when he used the constant velocity of light in that equation he provided a method of converting a unit of space-time he associated with energy to a unit of space he associated with mass.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a quantitative and qualitative means of redefining his temporal properties of a space-time universe in terms of the spatial ones of four *spatial* dimensions. 

However, doing so makes easier to understand the mechanisms responsible for creating a flat universe that would enable life to evolve because flatness is associated more with the properties of spatial environment than those of a temporal one.

For example it would allow one to derive the momentum and the gravitational potential of the universe mass components as was done in the in the article “Defining potential and kinetic energy?” Nov. 26, 2007 in terms of, oppositely directed curvatures in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words if one can define the gravitational potential of mass in terms of a depression in its “surface” one could derive momentum of its expansion in terms of elevation in it.

This differs from Einsteinâ€s theoretical definition of energy in that he only defines mass or its gravitational potential in terms of a temporal displacement in a four dimensional space-time manifold.

This difference is significant to our understanding of the shape or flatness of our universe because it allows one to define the geometry of its mass component in terms the spatial properties of a “downward” directed curvature in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimensions while defining its energy component in term an upwardly directed one.

Additionally Einstein’s equation E=mc^2 and Second Law of Thermodynamics tells us there would be a dynamic relationship between the curvature created by the gravitational potential of the universeâ€s mass and the oppositely directed momentum of its expansion.  In other words because that law tell us that energy flows from area of high density to low; if the energy density was too high in the early universe it would have been channeled into creating more matter while if the matter component was excessive it would have been converted to energy. 

Granted it also tells us the curvature caused by its energy component is c^2 greater than that caused by mass but it also tells the one caused by mass would be more concentrated and therefore deeper than the one caused by energy.  However the deeper curvature associated with mass would be offset by the shallower and more draw out curvature associated with energy thereby make the universe flat and therefore hospitable to life as we know it.

This process would be similar to what happens to interstellar gas as it collapses to form a star.  The gas heats due to its contraction which causes energy to be created by nuclear reactions in its core converting mass to energy which opposes further gravitational collapses.  If too much energy is created it will escape from the star allowing gravity to take over again. 

After a given about of time the creation of energy is exactly offsets gravity and the star enters a period where the curvature in space associated with its energy exactly matches the oppositely directed curvature associated with its gravity and no further change takes place making its spatial geometry be flat because the curvatures counteract each other.  Additional this geometry would be frozen in time until the star evolved to new stage in its life.

Similarly the equation E=mc^2 tells us in the early universe there was an interchange between energy and the creation of mass in the form of baryons and the components of dark matter.  Additional as was the case in the formation of a star the second law of thermodynamic tells us that energy flows from areas higher density to lower ones while E=mc^2 tells us if the energy density was too high in the early universe it would have been channeled into creating baryons and dark matter while if they were too abundant they would have been converted to energy.

In other words second law of thermodynamic and E=mc^2 tells us as the universe evolves it would move towards a flat geometry because as was just mentioned if its energy density was too high it would have been channeled into creating mass while if its mass were to abundant it would have been converted to energy.  This geometry would become frozen in time when the universe cooled enough for its mass and energy components to become stable.

This shows why one does not have to assume that a complicated change of events must have occurred such as inflation to give our universe the geometry needed to support beginnings of life because as was shown above that story is told by the Second Law of Thermodynamics and Einstein’s equation E=mc^2.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The story of life in four spatial dimensions. appeared first on Unifying Quantum and Relativistic Theories.

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 observed for the Casmir made by Quantum Field Theory and those of vacuum energy that it assumes is responsible for 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 vibration 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 quantum mechanics associates with the Casmir effect that it associates with our expanding universe.

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  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.

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.

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

The post The vacuum catastrophe: A classical interpretation appeared first on Unifying Quantum and Relativistic Theories.