The Geometry of antimatter
We have shown throughout “The Imagineer’s Chronicles” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einstein’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 a geometry of four *spatial* dimensions.
The existence of antiparticles was first predicted by Paul Dirac because of a mathematic symmetry he discovered when tiring to define the properties of matter.
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Fermilab’s theoretical physicist, Dr. Christopher Hill explains
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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 total energy because as mentioned earlier 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.
The first 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.
Secondly as mentioned earlier Einstein Special and General theories not allow for the existence of negative energy. This because the total energy of a particle is defined by the equation for its rest mass E=mc^2 and its Kinetic energy 1/2 mv^2 must always be positive. However, in his example he assumes that both a particle and antiparticle particle have negative energy. Therefore, the mechanism that he used to define the existence of antiparticle is logically inconsistent with the concepts of Relativity because as just mentioned it does permit the existence of negative energy.
Yet the existence of four *spatial* dimensions does allow for its existence and a classical interpretation of what happen in a vacuum when electrons and positrons meet and annihilate each other.
As mentioned earlier, we have shown throughout “The Imagineer’s Chronicles” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einstein’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 the mass components of 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 be" filled in" or is 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.
As mentioned earlier the article “Gravity in four spatial dimensions” defined the mass in terms displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
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.
As mentioned earlier this cannot be done in terms of four dimensional space time because time is only observed to move in one direction forward and therefore will not allow one to define the asymmetry between matter and anti matter in terms of bidirectional displacement.
Later Jeff
Copyright Jeffrey O’Callaghan 2011
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