Before the discovery of Dark Energy cosmologists had two models of how the universe’s expansion would end.

In first scenario, there would be enough matter in the universe to slow the expansion to the point it would come to a halt and gravitational forces would  cause it to begin contracting which eventually would result in a fiery death called the "Big Crunch.

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing but never stopping. This would end in a vast, dark, and cold state: a "Big Chill," as the stars faded and died out.

However the discovery of a force causing the expansion of the universe to accelerate called Dark Energy opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to understand the forces involved based on the most successful theories we have regarding the macroscopic properties of the universe.

The End of the Universe: Big Crunch, Big Chill or Big Rip?

However modern theories only address two of them.  For example the laws of thermodynamics which defines the forces associated with heat early in the universe and Einstein General Theory of Relativity which defines the gravitational forces which effect its evolution are two of the most success theories we have.  Unfortunately neither of them, in their present form addresses the expansive force called Dark Energy.

This is true even though Einstein foresaw the existence of Dark Energy when he added a cosmological constant to his General Theory of Relativity to make it conform to his belief in a static universe. 

Granted he added it in an "adhoc" manner to force it, in keeping with physicists thinking at the time to predict a stationary universe.  However when it became clear that the universe wasn’t static, but was expanding Einstein abandoned the constant, calling it the “biggest blunder" of his life.

But lately scientists have revived Einstein’s cosmological constant (denoted by the Greek capital letter lambda) to explain this mysterious force which as mentioned earlier is causing the expansion of our universe to accelerate even though they have been unable to Einstein integrate it into the theoretical structure of his General Theory of Relativity.

However we may find clue as to why by observing how our universe is expanding.

For example observations of the universe’s expansion tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the how the expansive force called dark energy is accelerating the spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time manifold he associated with energy to its equivalent displacement in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one qualitative and 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 qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the 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 displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space time manifold.

As mentioned earlier one reason why it is difficult to integrate the accelerated special expansion of three-dimensional space towards a higher space dimension into Einstein space-time universe because it does not define one. 

However it is easy to do if one redefined it, as was done above in terms of four *spatial* dimension because that higher spatial dimension would become an integral part of its theoretical structure.

Yet it also allows one to understand how and why Dark Energy is causing the accelerated spatial expansion of the universe and what its ultimate fate will be in terms the laws of thermodynamics and the concepts of Einstein’s theories.

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

For example, if the walls of an above ground pool filled with water collapse the 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.

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

However this means that 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 two dimensional surface of the water in the pool the particles that occupy that elevated region of three-dimensional space and the space they occupy will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein’s theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of those theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands. et because the mass of the universe remains constant throughout its history the gravitational potential associated with it will also. 

Therefore the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy even though its components may be separated by extremely large distances because as just mentioned the force associated with dark energy will decease relative to gravity as time goes by.

However the equivalence between mass and energy defined by Einstein tells us that energy also possess gravitational potential.

Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands the gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will overcome those of Dark energy because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with it will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

However this is not the end of the story for our universe because after a certain point in time the heat generated by its gravitational collapse will raise its temperature to the point where its expansive properties will exceed gravitational forces causing it to reexpand.

Yet many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and therefore it would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three-dimensional universe to oscillate around a point in the fourth *spatial* dimension.

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

In other words if this theoretical model is correct our universe has never ending future which exists between an icy death caused by Dark Energy and a fiery rebirth created by gravity.

There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

Later Jeff

Copyright Jeffrey O’Callaghan 2014


 

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The Higgs Boson which was tentatively confirmed to exist on 14 March 2013 appears to confirm the existence of the Higgs field.  Its discovery is pivotal to the Standard Model and other theories within particle physics because it explains, in terms of an asymmetry created by it why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless.  Many feel this discovery will allow physicists to finally validate the last untested area of the Standard Model’s approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in New Physics.

We have a discovery:
the future of the Higgs boson

However it may also provide a way of integrating gravity into the Standard Model because it would allow one to physically connect its particle concept of mass associated with the Higgs field to the field properties Einstein associated with gravity. 

This is true because even though Einstein was only able tell us how mass interacts with the field properties of space-time not what it was.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

In other words Einstein was only able to explain how the field properties of space interact to create gravity while the Standard Model defines how the asymmetry of those fields gives particles their mass.

However this suggests that one may be able to integrate Einstein’s concept of gravity into the Standard Model if one can define a common physical mechanism responsible for how particles break the symmetry of space to create mass while at the same time explaining how and why the field properties of his space-time universe interact to create the force of gravity.

Einstein gave us a method for accomplishing this when he said "If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless."

For example Newton was troubled by the fact that that his gravitational theory meant ." that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

However Einstein realized that one can understand how gravity "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why "one body may act upon another at a distance" by physically connecting it to the reality of what we can see and touch.

However, as mentioned earlier he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

Similarly the Standard Model is able to define mass in terms of the symmetry breaking properties of the Higgs field however it is unable to define in terms of a physical image of how it interacts with the field properties of space-time to create gravity or the forces associated with mass.

This fact is difficult to understand because the Standard model is based on a Relativistic Quantum Field Theory which has its foundation in Einstein’s Special Theory of Relativity.  Therefore one would think that it would be easy to integrate it into his General Theory of Relativity.

However Einstein’s and modern scientist’s inability to connect the Standard Models explanation for mass to Einstein’s explanation of gravity can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in space-time is responsible for gravitational energy and because of the equivalence between energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

This suggest that one may be able to incorporate Einstein’s explanation of the gravity into the Standard Model if one converts or transposes the his space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy because that provided a method of converting the space-time displacement he associated with energy in a space-time universe to one we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative 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 qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to both qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy/mass, including that associated with the Higgs field can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimensions interacts with particles to create mass and why they are quantized in terms of a physical image formed in our three-dimensional environment.

For example one can form a physical image of why mass is quantized, as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007" by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions.

This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move on a curved surface of three-dimension space to one consisting of four dimensional space-time.

(Louis de Broglie was the first to predict the existence of the wave properties of 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 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 be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for 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 to oscillate with respect to a fourth *spatial* dimension at a 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 four *spatial* dimensions.

Classical mechanics and physical observations of our three dimensional environment tell us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

However can also understand in terms of a "physical image" of the boundaries of the point particles of the Standard Model using the above concepts.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article "Why is energy/mass quantized?" associated with a particle.

(The reasons why particles can be treated as a mathematical points in the Standard Model is because according to the above theoretical model the components of their energy/mass and forces associated with them would be evenly distributed around a point located at it center.)

This suggest the symmetry breaking properties the standard model associate with the Higgs field may be related to the geometric properties of four *spatial* dimensions.

If true one should be able to use those field concepts to explain how it interacts with particles to give them mass and why the mass of the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.

Family 1 Family 2 Family 3
Particle Mass Particle Mass Particle Mass
Electron .00054 Muon .11 Tau 1.9
Electron
Neutrino
< 10^-8 Muon
Neutrino
< .0003 Tau
Neutrino
< .033
Up Quark .0047 Charm Quark 1.6 Top Quark 189
Down Quark .0074 Strange Quark .16 Bottom Quark 5.2

As mentioned earlier the article "Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy" showed that one can derive the energy or temperature of an environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the "surface" of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article "Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families in the Standard Model have identical properties except for their mass, which grows larger in each successive family." is because of an interaction between the resonant properties defined in the article "Why is energy/mass quantized?” and the mass content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation" associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation" associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article "The geometry of quarks" Mar. 15, 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the asymmetrical field of four *spatial* dimensions.

However it also shows how one can use the asymmetrical field properties of four *spatial* dimensions or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the "reality" of what we can see and touch in our three dimensional environment.  This is similar to how Einstein, as mentioned earlier was able to shown that a mass "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold.

As mentioned earlier the article "Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the energy associated with displacement in the "surface" of three-dimensional space associated the environment it is occupying.

However if one assumes, as was done above the Higgs field is created by a spatial displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can also understand how its asymmetric properties interacts with particles to create their mass in terms of the physical image formed by water in a dam.

This is because the potential energy of water molecule in a dam is defined by its asymmetrical spatial separation with respect to the bottom of the dam.

Similarly, according to the above theoretical model, the potential energy or mass contained in particles would be defined by an asymmetrical displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words it gives one the ability to define the asymmetrical properties the Standard Model associates with the Higgs field in terms of a physical image of water in a dam because as mentioned earlier the potential energy of water in a dam is solely dependent on the height of the dam while that of a particle would be dependent on magnitude of the spatial separation or the "height" of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

However, as was mentioned earlier Einstein also defined gravity in terms of an asymmetrical displacement or curvature or a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension or a space-time manifold.

This suggest that one may be able to unite Einstein’s concept of gravity with the Standard Model if one can find a way of integrating the effects an asymmetrical curvature in "surface" of a three-dimensional manifold with respect to either space-time or a higher or fourth *spatial* dimension would have on a particle with the asymmetrical properties of the Higgs field.

It should be remember that Einstein’s genius allows us to choose whether to view the reality of the Higgs Field in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2014  


 

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Vol. 4 — 2013



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