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’s 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


 

The Imagineer’s
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Recently there have been many observations that are extremely difficult to integrate into the currently accepted theoretical models.

Particularly the force called Dark Energy has eluded any attempt make it a part of the "The Standard Model of Particle Physics" one of the most successful theories ever created. 

However what makes this even more troubling is that the Standard model is based on two other very successful theories, that of Einstein Theory of Relativity and Quantum Field Theory.

Therefore if, despite continued efforts to developed a theoretical understanding of Dark Energy in terms of these theories we still cannot succeed, should we assume that, due to how interconnected these theories are we must discard them and look in a new direction.

Not necessarily because we may be able to understand its causality in terms of our current theories if instead of trying to make Dark Energy conform to them we allow its observed properties to guide us to a more complete understanding their validly.

Most scientists would agree that the best way of determining how one should interpret a theoretical model would be to list all observations regarding the forces in its domain and try to define them in terms of the rules it lays out.

Dr. Michio Kaku
The Physics of the future

For example observations of the expansive force called Dark Energy tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed 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 used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy responsible for geometric properties of space-time because it provided a method of converting the space-time displacement he associated with energy in a space-time universe to a spatial one in a universe consisting of only four *spatial* dimensions.  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 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 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, 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.

As mentioned earlier it is difficult to integrate the causality of how three-dimensional space can be expanding towards a higher *spatial" dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one redefines Einstein’s space-time universe, as was done above in terms of four *spatial* dimensions because a higher or fourth *spatial* dimension would be an integral part of its theoretical structure.

Yet it also allows one use Einstein theories and the laws of thermodynamics to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe because it gives one the ability to qualitatively and quantitatively 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 one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high 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 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 presently 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 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 the Einstein’s theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere so therefore its effects will increase as space expands.  In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart. Therefore they feel the rate at which the universe expands will increase as time go by resulting in galaxies, stars, the solar system, 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.

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 and yet because the quantity of energy/mass of the universe remains constant through its history its gravitational potential will also.

Therefore in the future the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy because, as mentioned earlier according to this theoretical model its accelerative forces should decrease as the universe expands. This would be true even though its components may be separated by extremely large distances because, as just mentioned if the above theoretical scenario is correct the force associated with dark energy will decease relative to gravity as time goes by.

Recent observations also suggest that early in the universe evolution the gravitational forces exceeded the expansive forces of Dark Energy.

The reason is according the above theoretical model, just after the big bang when the concentration of energy and mass was high, the gravitational forces of the universe’s energy/mass would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands its 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 win because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with Dark Energy 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.

Therefore. gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

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.

This shows how one can fully integrate the observed properties of Dark Energy into Einstein General Theory of Relativity while at the same time demonstrating the advantages of allowing observations guide our understanding of our theoretical model instead of forcing them to be subservient to our preconceive theoretical ideas.

However this may also allow gravity to be integrated into the Standard Model if one can reformulate its space-time equations to their equivalent in four *spatial* dimensions as was shown above to be possible.

It should be remember that Einstein’s genius allows us to choose whether to view Dark Energy and the mathematical equations in the Standard Model 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


 

The Imagineer’s
Chronicles
Vol. 4 — 2013


 
Paperback
$13.29
E-book
$7.99

Anthology of
The Imagineer’s Chronicles
Vol. 1 thru 4

   
Ebook
$10.50

The Imagineer’s
Chronicles
Vol. 3 — 2012   
Paperback
$10.96
Ebook
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The Imagineer’s
Chronicles
Vol. 2 — 2011
 
Paperback
$8.32
Ebook
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The Reality
of the Fourth
Spatial
Dimension
 
Paperback
$9.77
Ebook

$6.24

The Imagineer’s
Chronicles
2007 thru 2010
 
Paperback
$14.97
Ebook
$7.82

 
     
 

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