Supersymmetry in four *spatial* dimensions

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This blog has shown 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 by extrapolating observations of three-dimensional environment to a fourth *spatial* dimension while defining the theoretical advantages to adopting this perspective over that of his theories.

One is that it would allow one to define the abstract mathematical “realities” of the Standard Model of Particle Physics in terms of the observable reality of our three-dimensional environment.

For the past 25 years, the Standard Model of Particle Physics has given us a complete mathematical description of the particles and forces that shape our world.  Its predictions have matched experimental data, decimal place for decimal place, with amazing precision. However, most of its predictions are based on abstract mathematics. 

They indicate the laws of nature are symmetrical with respect to production of particles and antiparticles.  In other words when one creates a particle in an accelerator one must also create an antiparticle whose energy/mass is equal and opposite to it.

However, mathematical symmetry is defined as an attribute of a shape or relation which is an exact reflection of form on opposite sides of a dividing line or plane.

Therefore, if the standard model does describe the particles and forces that shape our world then it should be able to physically define what the dividing line is between a particle and antiparticle because our world is not made up of equations but physical objects.

This is extremely difficult to do in terms of the space-time geometry of Relativity because time is only observed to move in one direction forward and therefore could not provide a dividing line required to define symmetry.

Therefore, one cannot define the reality of the negative or opposite directed energy the Standard Model ascribes to anti-particles without assuming they are made up of negative mass.  This is because the only term other than mass in relativistic formula that define energy or E=mc^2 is squared and therefore is always positive.  This means the only way one can define the physical reality of negative energy in terms of space-time geometry is to assume the existence of negative mass.  Unfortunately, the abstract mathematics of the Standard Model does not permit the existence of negative mass.

Granted some like Richard Feynman have tried to use vectors to define negative energy/mass associated with anti-particles by assuming time moves backwards in them with respect to particles.  However, this methodology cannot define its reality in terms of General Relativity because the time component of energy in Relativistic formulas is also squared which means that energy must always be positive. 

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

As mentioned earlier this blog showed it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical to those of Einstein’s General and Special Theories of Relativity by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

In the article “The reality of the fourth *spatial* dimension” Dec 1, 2010 it was shown that one can define all forms of energy in terms of a displacement in a *surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

We have all observed the symmetry in a three-dimensional environment with respect to a dimensional plain.  For example we can observe the symmetry imposed by a two-dimensional plane or boundary in our three-dimensional environment.

However if it is true, as we are suggesting that energy/mass is caused by a displacement in a “surface” of a three dimensional space manifold with respect to fourth *spatial* dimensions one could extrapolate the symmetrical properties associated with a two-dimensional plane or boundary in three-dimensions to the boundary between a third and fourth *spatial* dimension.

In other words one could define the abstract mathematical symmetry of the standard model in terms of the “reality” of a boundary between the third and fourth *spatial* dimension.

This means the proponents of the Standard Model could define the mathematical symmetry it associates with the energy/mass of particles and anti-particles terms of oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of having to rely purely on the abstract “reality” of mathematical logic.

However, it also would allow them to define 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 a small area 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 a equal but opposite volume displaced in the upward direction.

However, as mentioned earlier the article “The reality of the fourth *spatial* dimension” showed one can define all forms of energy/mass in terms of a spatial displacement in a “surface” of a three dimensional space manifold.

Therefore 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.

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 a symmetrical one must be created on that surface.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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