2. SPACE
Several months after reading "Quarks" I decided to look at the book again to see if a spatial model or metaphor of the quarks could be developed beyond the vague description of six flavors, three colors, two spins and little round balls. Such a model would be comparable to the "ball and stick" model in chemistry. The fractional electric charges seemed like a good a starting point. If a scheme for the fractional charges could be produced then it might be possible to develop a model of quarks. The resulting model has been called the "Elementary Particle Spatial Model" and shall be abbreviated as EPSM throughout this effort to distinguish the models from the actual particles. Because the effort builds upon previous EPSMs to develop new EPSMs, the first dozen or so EPSMs are very important in order to understand the concept. (The following is an abbreviated version of the original 1994 manuscript.)
A simple starting point to combine multiples of positive and negative 1/3 charges in a three dimensional world is the structure shown in Figure 1-1. This structure was initially drawn on a piece of graph paper with the ends labeled with positive and negative coordinates. The structure resembles the six-pointed pieces in the childhood game of jacks.
Figure 1-1: ESU or Einstein Space Unit EPSM in graph form. The figure is rotated clockwise about 45 degree for convenience of presentation.
The drawing could be thought to represent a piece of space. For convenience the orientation is turned about 45 degrees clockwise so that all six directions can be seen. This piece of space will be called an Einstein Space Unit (ESU) within EPSM. Figure 1-2 shows the ESU EPSM in a three dimensional model form. The positive (+) and negative (-) directions have been labeled on the ESU EPSM to correspond to the directions in Figure 1-1 above. This model and the others to follow were made from plastic tubing; however, the actual "shape" of the model pieces is not what is important to the hypothesis. What is important is the relationships or relative positions of the model segments. If the models were made with different materials, even the smallest of strings, then they could have a very different appearance but still have the same underlying structure.
Figure 1-2: ESU EPSM in model form. Each charge will be assigned either a a +1/3 ecu or -1/3 ecu corresponding to its directional orientation.
One can envisioned that the ESU could be, or could have been, a part of a large space structure with the pluses and minuses connected. Particle~antiparticle pairs can be formed from space; thus, if this were representative of a piece of space then one should be able to make particles and antiparticles out of it. So, the ESU was mentally dropped onto the floor and the simplest ESU segments were looked at. At first, only the ESU segments with three mutually perpendicular lines, or dimensionalities, were examined because this could naturally lead to a three dimensional world. Figure 1-3 shows some of these simple ESU segments. In the first few figures the dimensionalities have been marked as "+" or "-" in accordance with the directions in Figure 1-1 and Figure 1-2 as an aid to interpret the pictures. What this efforts lacks in equations it makes up for in pictures.
Figure 1-3: Initial segments of the ESU EPSM. Each dimensionality is assigned either a +1/3 ecu or -1/3 ecu corresponding to its directional orientation.
By assigning a 1/3 electric charge unit (ecu) to each dimensionality as either +1/3 or -1/3 depending upon its direction then whole or one-third fractional electrical charges were possible. The convention of having the orientation of the positive charges being in the positive directions and of having the negative charges being in the negative directions is used through out most of this effort.
So far, so good. EPSM had 3 dimensions and candidates for the electron (-1 ecu), the positron (+1 ecu), the d quark (-1/3 ecu), and the d* antiquark (+1/3 ecu). However, +2/3 ecu and -2/3 ecu segments were needed for the u quark and the u* antiquark. At this time the next simplest step was to join two of the ESU segments together by joining a positive dimensionality to a negative dimensionality, i.e., "+" to "-", as they might have been originally joined. This gave numerous possibilities including those in Figure 1-4.
Figure 1-4: Some of the possibilities with two ESU segments joined. Each dimensionality is assigned either a +1/3 ecu or -1/3 ecu corresponding to its directional orientation.
The connected dimensionalities cancel each other; thus, only the net charge of the dimensionalities that are not connected to another dimensionality have to be considered. Appropriately enough, these shall be called free dimensionalities. The electric charges for the particles in Figure 1-4 can be determined by counting only the positive free dimensionalities, subtracting the negative free dimensionalities and dividing by three to obtain the normal charge units. The charge determination in Figure 1-4 becomes:
(4-0)/3 ecu = +4/3 ecu
(4-2)/3 ecu = +2/3 ecu
(2-4)/3 ecu = -2/3 ecu
(0-4)/3 ecu = -4/3 ecu
By getting the +4/3 and -4/3 electric charge particles one gets more than is needed but one does get the +2/3 and -2/3 electric charge particles in a very simple model. So far it was interesting but there is not a picture of anything definite yet. The proton, the uud quark structure, probably provides the best starting point for an elementary particle structure because it is the only stable free hadron. The neutron, also a hadron, is only stable inside atomic nuclei; however, a free neutron decays with a 10 minute half-life which is to say that 1/2 of the free neutrons will decay every 10 minutes.
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