QUARK FRACTIONAL CHARGE INDICATES A SUBSTRUCTURE
by James Rees
Copyright © 1997
Starlight Publishing Company
Hermosa Beach, California
ABSTRACT
This article presents an explanation of the fractional charge of up and down quarks using group mathematics based on a quark substructure. The fractional charge mathematics of up and down quarks is shown to indicate a substructure with each quark composed of a group of three unit charge particles of matter. The proposed triplet of unit charge substructure is proposed to be the source of SU(3) symmetry in quark interactions.
INTRODUCTION
The fractional electrical charge on quarks, although well established experimentally,
causes mental anguish on purely logical grounds because it is illogical that electrons
and positrons, the lightess mass charged particles observed to come into existence
as an independent entity, would come into existence as unit charge particles and
that the greater mass supposed fundamental particles, the up and down quarks, would
come into existence in fractions of unit charge. Fractional charge of the greater
mass quarks is an aesthetically unsettling concept given the seemingly fundamental
nature of electrons and positrons.
The logic is simply this:
Therefore, fractional charge on a fundamental particle is an impossibility on purely logical grounds. What can be divided is not fundamental.
A fundamental unit cannot be divided, so by definition a quark is not fundamental.
The experimentally proven fractional charge of quarks is in logical conflict with the speculated fundamental nature of quarks. Fractional charge is an experimental fact, whereas the fundamental nature of quarks is inferred and totally speculative.
The conflict of quarks being fundamental versus quark fractional charge can be resolved by following the mathematical logic which indicates a substructure for the quarks due to the fact that quark electrical charge is divisible, and then by supposing a substructure for quarks with the substructure being a group of charged particles because group mathematics can account for the fractional charge ratios.
In the interest of brevity, only the first family of quarks are
dealt with in this article. The single goal of this article is to communicate that
group mathematics can account for quark fractional charge based on a triplet substructure
of quarks.
I UP AND DOWN QUARKS TRIPLET SUBSTRUCTURE
The fractional electrical charge mathematics of quarks is a strong signal that quarks must have a composite structure with the quarks made from more fundamental electrically charged particle components which taken as a group account for the fractional charge mathematics.
The first group to investigate, since the denominator of the fractional charge is three, is the smallest group of unit charge particles which can form thirds, a group with three members.
In order to consider the proposed explanation of group mathematics for fractional charge, allow the supposition that the up quark and the down quark are each composed of a group of three unit charge particles.
Suppose the up quark is composed of two positive unit charges and one negative unit charge. Suppose the down quark is composed of two negative unit charges and one positive unit charge.
FIGURE 1
The avenue to explore from this clue is whether a group accounting
of positive matter units in normal matter quarks corresponds to quark fractional
charge mathematics.
II QUARK ELECTRICAL CHARGE ACCOUNTING
Two methods of accounting for the electrical charge of quarks are presently employed in modern physics. This section explains the two methods.
Quark Electrical Charge Accounting consists of two partial methods of accounting depending on whether the quark in question is normal matter or antimatter. The two methods of accounting are referred to here as Positive Matter Accounting, which is employed for normal matter, and Negative Matter Accounting, which is employed for antimatter. Just as matter and antimatter are symmetrical reflections of one another, the two methods of accounting are also symmetrical reflections of one another.
Positive Matter Accounting is the method presently employed in modern physics to calculate the electrical charge of quarks if the quarks are normal matter. If the quarks are antimatter, Negative Matter Accounting is the method employed to calculate the charge of the antiquarks. The other half of each method is not presently used explicitly in modern physical theory and is shown in the grayed boxes in Tables 2 and 3.
Quark Electrical Charge Accounting Methods
Normal Matter 
AntiMatter 

Positive Matter 
Negative Matter 
Negative Matter 
Positive Matter 

up = +2/3  up = +1/3  antiup = 2/3  antiup = 1/3  
down = 1/3  down = 2/3  antidown = +1/3  antidown = +2/3 
Positive Matter Accounting tracks positive matter explicitly. Negative Matter Accounting tracks negative matter explicitly. Each partial method independently accounts for the charge of the opposite unit charge components implicitly through the total group charge, which is the sign attached to each ratio. The group sign is the overall charge of the group.
The negative sign on the charge of the normal matter down quark indicates the overall group charge. The overall group charge is how the negative matter is accounted in Positive Matter Accounting. The overall group charge of the down quark is one net unit negative.
It is important to realize that two different quantities are represented by the 1/3 value assigned the down quark, one quantity is the ratio of positive units in the group, and the other quantity is the overall group charge.
In other words, the overall group charge of the down quark is one unit negative and Positive Matter Accounting is only tracking positive units, so the group count of positive matter units for the down quark is 1/3.
For antimatter, Negative Matter Accounting is the method presently employed. Negative Matter Accounting tracks negative matter explicitly and positive matter implicitly through the overall group sign.
Negative matter is not presently tracked independently when the quarks are normal matter. Likewise, positive matter is not presently tracked independently if the quarks are antimatter.
If both positive and negative matter are counted, the total charge of the quark is unitary. In other words, when both methods are employed, the total is unitary.
ELECTRICAL CHARGE ACCOUNTING OF PROTONS
FIGURE 2
The rows in Table 4 and Table 5 show both partial methods of accounting. For Positive Matter Accounting, the positive matter in a proton adds to one net positive unit. For Negative Matter Accounting, the net negative matter in the proton is zero. There is no net negative matter in the proton.
Up  Down  Up  Proton  
Positive Matter  +2/3  +  1/3  +  +2/3  =  +1 
Negative Matter  +1/3  +  2/3  +  +1/3  =  0 
Overall charge  +1  +  1  +  +1  =  +1 
AntiUp  AntiDown  AntiUp  AntiProton  
Negative Matter  2/3  +  +1/3  +  2/3  =  1 
Positive Matter  1/3  +  +2/3  +  1/3  =  0 
Overall charge  1  +  +1  +  1  =  1 
SU(3) symmtery is presently theorized to be caused by the force carriers of the strong nuclear force. The question that begs answering however is, why is the strong force tripolar?
The proposed quark substructure provides an answer for why quark
interactions are tripolar in nature. The answer is that the internal structure of
the quarks is tripolar, a triplet of matter. The strong force within the quark is
divided among three units of matter interacting in a complex space which manifests
as SU(3) symmetry.
IV EXPERIMENTAL EVIDENCE FOR AND AGAINST
Many physicists believe that the Standard Model, though well founded, is not representative of the bottom level of matter because it is too complicated.
The trouble with speculating quarks to be fundamental is that there is already evidence to the contrary, namely fractional charge ratios.
Proving a particle to be fundamental is like proving a theory, it can only be disproved, never proven, except by the lack of proof to the contrary. The assertion that quarks are fundamental is purely speculative because the assertion is interpreted from theory and not based on hard physical evidence. There is no way to prove that higher energy collision experiments would not manifest a quark substructure.
The developments at the Fermi National Accelerator Laboratory by
the CDF Collaboration which indicate a quark substructure have now met the qualification
of disproving the fundamental nature of quarks. It is time to consider the internal
structure of quarks which is indicated by the mathematics of fractional charge.
A very important clue to quark triplet substructure is the evidence of quark interactions
exhibiting SU(3) symmetry. The evidence of quark interactions exhibiting SU(3) symmetry
is strong evidence in favor of a triplet substructure.
The author claims that the proposed substructure of quarks in no
way counters the Standard Model, only interpretations made from it.
V CONCLUSION
The immediate question this article seeks to answer
is whether a triplet internal structure of quarks could explain their fractional
charge mathematics. The answer to the question is elucidated in this article in the
affirmative.
A framework has been presented in this article which provides a
plausible explanation for the fractional electrical charge mathematics of up and
down quarks based on a substructure of three unit charge particles of matter.
Comments: jrees@starlightpub.com
October 31, 1996