For example one of the most obvious problems of assuming the universe will Rip apart is that it violates one of most treasured laws of physics that of the law of conservation of mass/energy.

That law tells us the kinetic energy of the universeâ€s expansion associated with the big bang and the accelerative forces of Dark Energy cannot exceed the total combined energy of its energy/mass.  However that is exactly what would have to happen for the Big Rip to occur. 

For example for a rocket to escape or be “Rip” from the earth’s gravitational influence one must provide it with more kinetic energy than the combined gravitational potential of both its and the earth’s energy/mass.

Similarly for the universe to be “Rip” apart one would have to provide its components with enough kinetic energy to overcome the total gravitational potential of its energy/mass.

However as was just mentioned the law of conservation energy/mass tells us that since by definition the universe is a closed system the kinetic energy of the universe’s components cannot exceed the gravitational potential of its energy/mass.

Therefore if we are to assume that the universe will be Rip apart by Dark Energy we must also assume that energy/mass can be created and that the law of conservation of energy/mass is invalid.

However as also mentioned early the best way of to understand why the Big Rip” cannot occur is to show, using the currently accepted theoretical models and laws of physics to understand why Dark energy is causing the accelerated expansion of our universe and why, based on those laws and theoretical models it theoretical models why it cannot possibly cause it to be rip apart.

Einstein’s General Theory of Relativity, the previewing theory governing the evolution of the universe tells us that its future depends the interaction of the contractive force of gravity, the expansive force associated with the kinetic energy left over from the Big bang and Dark Energy.

Unfortunately in its present form it cannot address the causality of the expansive force of Dark Energy and how or why it would interact with its environment to cause it to accelerate because observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, in order 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 Einsteinâ€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 its geometric properties in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions. 

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 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 and qualitatively derive the physical properties of energy in a space-time universe in terms of its spatial properties 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 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 why three-dimensional space 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 reformulates it, as was shown above to be possible in terms higher fourth *spatial* dimension because a higher dimension is an integral part of its theoretical structure.

Yet this also allows one to understand how and why the force called Dark Energy is causing an accelerated spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use Einstein’s equations 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.

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 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 this means according to concepts developed in the article “Defining energy” that the three-dimensional “surface” occupied by the particles in 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.

In other words by reformulating Einstein’s theories in terms of four *spatial* dimensions one can 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 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 would 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 its will decline as it expands. 

Yet, because the laws of conservation the total quantity of the universeâ€s energy/mass remains constant throughout 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.

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

The reason is that according the above theoretical model, just after the big bang when the concentration of energy and mass was high, the gravitational forces with it 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 it will decrease as it expands.

This means that eventually gravitational forces will predominant  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.

In other words if someone spends the time, as we done above analyzing what observations have taught us about Dark Energy and integrating them into Einstein’s Theories one would one find that the assumption that it would “Rip” the universe apart does not have foundation in logic or science.

It should be remember that Einstein’s genius allows us to choose whether to view Dark Energy 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 2015 Jeffrey O’Callaghan

The post Why the “Big Rip” cannot happen appeared first on Unifying Quantum and Relativistic Theories.

We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einsteinâ€s Special and General Theories of Relativity while at the same time defining several theoretical advantages to adopting this perspective over that of his theories.

One is that it would allow theoreticians to conceptually define the origin of antimatter by extrapolating the classical laws of three-dimensional space to the geometry of four *spatial* dimensions.
In Einstein’s Theory of Relativity the total energy of body consist of two parts, its rest energy defined by the equation E= mc^2 and its kinetic energy defined by KE=1/2mv^2.  However, Einstein tells us that because of the interaction of time and space the total energy of a body is defined by Pythagoras rule for right triangles or that the square of the hypotenuse equals the sum of the square of the other two sides.  In other words according to Einstein the total energy of a body “E” is equal to the square root of the sum or the squares of it rest energy or mc^2 and its kinetic energy or 1/2mv^2.

However, when Oscar Klein tried to derive the quantum mechanical properties of an electron defined by Schrödinger’s equation he discovered that there were positive and negative solutions to the equations that defined its energy because the square root of a number can be either positive or negative.  Paul Dirac had a similar problem when he attempted to solve the total energy problem in terms of matrices.  He also discovered that it predicted the existence of electron with both positive and negative energy.

The symmetry imposed upon matter by these two solutions indicated to many scientists in1928 that there might be an “antiparticle” to the electron.  In other words it showed that there should be a particle with the same energy/mass as an electron but with an oppositely directed or positive charge that would annihilate each other if they came in contact. 

In 1932, Carl D. Anderson confirmed their suspensions when he discovered its antiparticle the positron

But how can one define the negative energy of an electron or a positron in terms a vacuum.

Dirac explanation was that a vacuum was not actually empty but instead is a bottomless pit into which is a ladder whose rungs correspond to the positive and negative energy stated in his equations.  The top run of the ladder corresponds to zero energy and all the rings below it correspond to negative energy states for electrons.  His insight was that if the top of the ladder correspond to zero energy all the runs below it would correspond to negative energy.  If one was to remove a negative energy electron from a vacuum it would essentially leave a hole in it.  Therefore in electron positron annihilation would fill in the hole raising the level of the vacuum to zero.

However, there is a conceptual flaw within his arguments which is that the energy of a vacuum does not return to zero because when electrons and positrons combine they release the energy associated with their combine masses.

Yet  the existence of four *spatial* dimensions provides a classical interpretation of what happens in a vacuum when electrons and positrons meet and annihilate each other.

As mentioned earlier, we have shown throughout this blog it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einsteinâ€s General and Special Theories of Relativity.

In the article “Gravity in four spatial dimensions” Dec. 15, 2007 it was shown that one can define mass in terms of a “depression” or downward directed displacement in a “surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this means one could define the symmetry between the energy/mass of matter and antimatter as being the result of oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension because a spatial dimension can move in two directions up and down with respect to each other.  In other words one could define the negative energy/mass associated with a electron in terms of a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while define positive energy/mass of a positron in terms of a “elevation” in that “surface”.

Unfortunately time is only observed to move in one direction forward and therefore a vacuum composed of four-dimensional space-time would not allow the “surface” of three-dimensional space to “move” up and “down” with respect to it.  Therefore, it does not permit the existence of the negative energy.

Earlier the article “Embedded dimensions” Oct. 22, 2007 showed that one can define the total energy of a volume in terms of the magnitude of a displacement in a “surface” of three-dimensional space.

Therefore, the total energy/mass of a particle / anti-particle system would be equal to the sum of their relative displacements associated with their energy/mass.

Hence the reason particles and anti-particles annihilate each other when they meet while releasing the sum of the energy associated with their combined masses is because the “depression” in a “surface” of a three-dimensional space manifold associated with the mass of an electron will “filled in” or be cancelled by the “elevation” associated a positron’s thereby leaving no displacement in that “surface” and therefore no mass in the volume associated with it.  However as was shown in the article “Embedded dimensions“ because their displacements are oppositely directed with respect to a fourth *spatial* dimension their energy components will be additive and therefore, when the combine they will release the energy associated with their combined masses.

Therefore, it does not have the conceptual flaw inherent in Dirac solution because the energy of a vacuum would not return to zero when electrons and positrons combine instead they will release the energy associated with their combine masses.

However, it also allows one to define a conceptual mechanism in terms of the classical hydrodynamics for the creation of particle / antiparticle pairs that is independent of abstract mathematical logic. 

Classical hydrodynamics tells us if we push down on a small area on the surface of water it will become displaced.  However, it also tells us that the volume of water displaced by that downward pressure will be offset by an equal but opposite volume displaced in the upward direction.

Similarly if mass is a result of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension any “downward” displacement in its “surface” will be offset by an equal but oppositely “upward” directed displacement.

Therefore, according to classical hydrodynamics a particle could not be created without the creation of its antiparticle because as mentioned earlier it tells us that when a surface undergoes a displacement an equal but opposite one must be creates on that surface.

yet on can using the concept understand why there is more matter than antimatter in there universe.

As was mentioned earlier, one can derive the energy/mass of a particle in terms of a “downward” directed displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension while the energy/mass of an antiparticle in terms of an “upward” directed one in that same surface.

But this indicates on average it would require less energy to form a particle than an antiparticle for the same reason that it takes less energy to fill a bucket with water by pushing it down below its surface than it does by lifting the water into a bucket that is above its surface because that bucket is a higher gravitational potential . 

Therefore, there would be some energy left over if an equal number of particles and antiparticles were annihilated.  This left over energy is responsible of energy/mass of particles presently in the universe.

However, the reason this left over energy/mass takes the form of a particle and not anti particles is because the relative properties of energy means it can be defined in terms of a reference frame that would make it a particle instead of an antiparticle.

This defines the reason in terms of the geometry of four *spatial* dimensions for the asymmetry between particles and antiparticles and the observations regarding there interactions.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2011

The post The Geometry of antimatter. appeared first on Unifying Quantum and Relativistic Theories.