The existence of antimatter was predicted by Paul Dirac when he realized his relativistic quantum theory of an electron yielded up twice as many solutions as he thought he needed. Two of the solutions correspond to the spin-up and spin-down orientations of the electron. So what did the other two solutions correspond to?  He had some ideas of his own, but finally concluded in 1931 that they had to represent the spin-up and spin-down orientations of a previously unknown positive electron.  Dirac had discovered anti-matter.  The ‘positron the anti-particle of the electron, was subsequently found in experiments on cosmic rays, formed high in the earthâ€s atmosphere by collisions involving high-energy particles.

However he soon realized this meant that every particle has a symmetrical or mirror-image antiparticle with nearly identical properties, except for an opposite electric charge.  And just as protons, neutrons and electrons combine to form atoms and matter, antiprotons, antineutrons and anti-electrons (called positrons) combine to form anti-atoms and antimatter.

Yet this presents a problem because if one assumes particles are three-dimensional objects occupying a four dimensional *spatial*-time environment the only thing they can be symmetrical or “image” against would be the time dimension. 

This was necessary because one cannot define the asymmetrical or oppositely directed energy component of antiparticles by assuming they are made up of negative mass because in the relativistic formula the mass that defines energy or E=mc^2 is squared and therefore it will always be positive.  This means the only way one can define the asymmetrical relativistic properties of matter and antimatter in terms of a negative time.

This is why in Quantum electrodynamics antiparticles are represented as their particle brothers moving backwards in time.

However this presents a problem for theoreticians because no one has ever observed time to move backwards.  How then can they justify defining antiparticles in terms of the existence of negative time when it has never been observed?

Additionally even thought the equations of Relativity permit time to move backwards no one has ever observed that to happen.

Yet Some would argue that that is the only way in which one can explain the mathematical solutions of Dirac’s equations and the existence of antimatter therefore we must assume that time can move backwards.

This would be true if Einstein had not provided another way of deriving the asymmetrical relationship between matter and antimatter when he defined the geometric properties of space-time in terms energy/mass and the constant velocity of light because it gave us the ability to define that relationship in terms of the physical properties of a spatial dimension instead of one made of time.

This is because when he used the constant velocity of light and equation E=mc^2 to define its properties he provided a method of converting a unit of space-time he associated with energy to unit of space associated with mass in an environment of four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between the time related properties of a space-time universe with the spatial properties of one made up of four *spatial* dimensions.

In other words by defining the geometry 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 the curvature or displacement he associated with energy/mass in a space-time environment to a displacement in a fourth *spatial* dimension

One of the primary advantages of using this process to reformulate Einstein’s space-time concepts to its four *spatial* dimension equivalent is that it allows one to understand the asymmetry between matter and antimatter in terms of the observable properties of three-dimensional space.

As was shown above when Einstein define the geometric properties of energy and mass in terms of the constant velocity of light in a space time environment he showed the quantity of energy/mass in a environment can be derived in terms of a curvature of displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature or displacement in a space-time manifold. 

As mentioned earlier the problem with defining the asymmetrical properties of matter and antimatter in terms of time is that no one has ever observed it to move backwards.

Yet this would not be a problem if one viewed their properties in terms of four *spatial* dimensions instead of four dimensional space-time because we have all observed that we can move backwards and forwards or in a positive of negative direction in three dimensional space therefore allowing one to derive the asymmetry between mass and antimatter in terms equal but oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

This also means, if this is a valid representation of the “reality” of matter and antimatter that one should be able to mathematically redefine Paul Dirac relativistic quantum theory of an electron in terms of the “reality” of a physical boundary between the third and fourth *spatial* dimension by using Einstein’s equations to convert his space-time model to its equivalent one in four *spatial* dimensions.

Another significant advantage to redefining Einstein’s space-time geometry to four *spatial* dimension is that would give one the ability derive a physical mechanism for why an antiparticle is created whenever a particle is based on observations of our three-dimensional environment

Classical hydrodynamics tells us if we push down on the surface of water in a closed container 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 a equal but oppositely “upward” directed displacement.

However, as was shown in the article “Defining potential and kinetic energy?” Nov. 26, 2007 one can define all forms of energy/mass in terms of a spatial displacement in a “surface” of a three dimensional space manifold. 

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

In other words if one creates a depression in the “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension associated with the mass of a particle one will also create equal and oppositely directed elevation associated with an antiparticle.

This would define why particle and antiparticle are always created in pairs.

It should be remember Einstein’s genius allows us to chose weather to solve all issues related to mass and energy, such the ones presented here in either four spatial dimension of four dimensional space-time  This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe.

Later Jeff

Copyright 2014 Jeffrey O’Callaghan

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