PART I
CHAPTER
3
STEP 1
Bottom of Step 1: The Fractional Charge of Quarks
Top of Step 1: Triplet Substructures of Unit Particles
There were four steps of deduction were followed in deducing the existence of the background of matter.
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PREVIOUS: Chapter 1 The Background of Matter
Question: The Problem of Fractional Charge of Fundamental Quarks
Answer: Quark Partial Group Math  ratios of unit charge, units of matter
QUESTION:
THE PROBLEM OF FRACTIONAL CHARGE ON FUNDAMENTAL QUARKS
The known fractional electrical charge of quarks is a troublesome concept given that
quarks are by theory fundamental particles.
The problem is, how can quarks possess fractional electrical charge and be fundamental
particles? Fractional charge indicates is a ratio or division of charge, not a unitary
fundamental type particle.
The concept that quarks are fundamental and have fractional electrical charge causes
mental anguish on purely aesthetic grounds. It is aesthetically displeasing that
electrons and positrons, the lightest mass charged particles observed to come into
existence as an independent entity, would come into existence as unit charge particles,
while the greater mass up and down quarks would come into existence in fractions
of unit charge. Fractional charge on the greater mass quarks over the lighter mass
electrons is an aesthetically displeasing concept given the seemingly fundamental
and unit charge nature of the lighter mass electrons. The fractional charge of the
greater mass quarks would more aesthetically indicate a ratio of unit charges composing
the quark, something more than what composes an electron.
The up quark and the down quark are the components of the proton and the neutron.
A proton is composed of two up quarks and one down quark, while a neutron is composed
of two down quarks and one up quark. The up and down quarks have been determined
to possess fractional electrical charge. Table 1 lists the fractional electrical
charge of the up and down quarks, the quarks that compose normal everyday matter,
protons and neutrons. Table 2 lists the fractional electrical charge of the antimatter
counterparts of normal matter quarks, antiup and antidown, which compose antiprotons.
Matter 
AntiMatter 

up = +2/3 
antiup = 2/3 

down = 1/3 
antidown = +1/3 
Fractional electrical charge on quarks is grounded in solid
scientific experimental observation and in solid mathematical theory. Yet, the concept
of fractional charge on quarks runs completely counter to logic if quarks are theorized
to be fundamental entities of matter.
The fractional electrical charge mathematics of quarks is a glaring signal that there
must be a substructure involved in quarks. Fractional electrical charge signals that
quarks have a composite structure with the quarks being made of more fundamental
unit charge particle components, which account for the ratios of unit electrical
charge values exhibited by quarks.
The logic is simply this:
A fundamental charge cannot be divided, by definiton. 
The electrical charge of a quark is expressed fractionally. 
Since quark fractional electrical charge is a ratio of charge which indicates division, it follows that quarks are divisible and not fundamental. 
The existence of quarks as components of matter, and the existence
of fractional electrical charge on quarks, has been established through scientific
experimental observation. Therefore, one must question the theory side which rather
arbitrarily holds quarks to be fundamental particles.
A fundamental particle cannot be divided, or by definition, it is not fundamental.
Since the fractional charge of quarks is an observed fact, and since the fundamental
nature of quarks is an inference, one must question the inference and consider whether
quarks might have a substructure.
The bottom line is this, if the electrical charge of quarks can be divided into fractions,
it is not fundamental. Since quark charge is expressed in ratios, and ratios are
division, quarks cannot be fundamental, by following the math alone. In fact, the
fractional math indicates a substructure involving a ratio of unit charges with a
three in the denominator, and either a one or a two in the numerator.
The only logical option is to suppose that quarks are not fundamental and to suppose
that quarks might have a substructure.
ANSWER:
QUARK PARTIAL GROUP MATHEMATICS
LOGIC PATHWAY TO THE DISCOVERY OF QUARK PARTIAL GROUP MATH
This section describes the logic pathway the author followed in deciphering that the fractional charge math of quarks was partial group math of triplet groups of unit charge particles. If the reader would like to skip the description of the how quark partial group math was deduced, and the reader would like to go straight to a description of how quark partial group math works, go to the next section QUARK PARTIAL GROUP MATHEMATICS.
Since the denominator of quark fractional charge is three,
the first structure to investigate is the smallest allowable group of unit charge
particles which adds to three, which is three. Suppose then, that quarks have a substructure
composed of three unit charge particles of matter.
The proposed composition of up and down quarks is shown in Figure 1. Each quark is
proposed to be composed of three unit charge particles of matter.
The up quark is proposed to be composed of two positive units
of matter and one negative unit particle of charged matter. The down quark is proposed
to be composed of two negative unit particles of matter and one positive unit particle
of charged matter.
Since up quarks are two thirds positive, the first solution to investigate is to
suppose that the up quark is constructed from two positive units out of the three
total units explaining the positive two thirds ratio. The third unit could be neutral
and the ratio of positive matter would still be two thirds positive, however to make
the particles composed of quarks have the correct electrical charge, the third unit
charge particle must be a negative unit. Therefore, the first solution to a two thirds
positive up quark is that the up quark be composed of two positive unit charge particles
and one negative unit charge particle.
The proposed composition of the up quark is obviously two thirds positive, but how
would one then get 1/3 for the down quark, which has two of three units negative?
For the up quark, the quantity being counted in the ratio is positive units of matter
to the total units in the group, giving the +2/3 ratio of positive units to the group
total. Therefore for down quarks, since the quantity being counted in the numerator
is positive units of matter, the numerator is 1 because the down quark as proposed
only has one unit of positive matter.
The product of the group charge and the ratio of positive matter units to the group,
gives the charge value of the quark.
For normal matter down quarks, the type of matter being counted is positive units
of matter, and the ratio of positive units of matter in the down quark is 1/3. The
total group charge of the down quark is 1. The ratio of positive units multiplied
by the total group charge, which is 1, gives 1/3.
Why are ratios of positive matter what are presently counted in normal matter quarks?
The answer is that the first quantity of concern initially was protons, and protons
are positive.
The negative matter units in normal matter quarks are accounted for implicitly through
the total group charge. The partial group charge is the group charge multiplied by
the ratio of the type of matter being counted, which for normal matter is positive
matter units.
It becomes evident that only the two quark structures shown in Figure 1 are required
to explain the electrical charge values of both normal matter quarks and antimatter
quarks. The symmetry of the proposed quark structures allows for all of the different
electrical charge values of first family quarks to be explained with the corresponding
symmetry of the partial group mathematics.
Table 2 gives a charge value of 2/3 for the antiup quark. If for antimatter, ratios
of negative matter are counted, then an antiup quark needs to be composed of two
negative units and one positive unit so that the antiup quark will be two thirds
negative matter. The antidown quark must have a structural composition that allows
for it to be composed of one third negative units, because it has a one third negative
charge.
Through the symmetry of the proposed quark structures, the up quark and the antidown
quark are seen to be the same entity.
The +1/3 charge of the antidown quark and the +2/3 charge of the up quark leads
one to conclude that the up quark and the antidown quark are different entities
because they have different electrical charges, while in fact they are the same entity
and the entity that is different is the charge matter ratio. Antidown is +1/3 because
for antiparticles, negative matter ratios are what is employed and the ratio of
negative units in antidown is 1/3, multiplied by the total group charge, which is
+1 gives +1/3.
The symmetry of the proposed up and down quark structures allows symmetrical explanations
of symmetrical particles. For instance, the discussion above of why an up quark and
an antidown quark are the same entity has a symmetrical explanation for why the
down quark and the antiup quark are the same entity.
QUARK PARTIAL GROUP MATHEMATICS
The methods of accounting for quark electrical
charge will be referred to as quark partial group mathematics.
The symmetry of the proposed structures of the up and down quarks allows for corresponding
symmetrical methods of accounting for quark electrical charge, positive matter
charge ratios and negative matter charge ratios.
Partial group mathematics is ratios of one type of unit in
the group over the group as a whole. One of the two types, positive or negative,
is represented in the numerator of the partial group charge.
Quark electrical charge is a partial group charge.
Partial group mathematics works like this:
Quark fractional charges are partial group charge ratios.
partial group charge ratio = partial charge ratio multiplied by group charge
Partial charge ratios are ratios of units of charge where:
numerator = number of one type of unit charge of the group
denominator = total number of units of charge in the group
The partial charge ratio is always a positive ratio as units
of charge are what are being counted, not charge itself. For instance, up has 2 positive
units of charge out of 3 units of charge total in the substructure and therefore
has a partial charge ratio for positive units of two thirds.
The charge of the particle not represented in the numerator is accounted for implicitly
by the group charge. The symmetry of the group mathematics accounts for the charge
of the other unit charge particle implicitly through the charge of the group.
Positive matter ratios and negative matter ratios are two different sides of the
same coin. Physicists employ positive matter ratios in reference to normal matter
quarks, and physicists employ negative matter ratios in reference to antimatter
quarks.
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 
Table 3 and Table 4 show that for both normal
matter and for antimatter, there are positive matter ratios and negative matter
ratios.
Physicists employ positive matter ratios in accounting for quark electrical charge
for normal matter quarks, the left side column of Table 3. Positive matter
ratios count positive unit charge unit particles of matter in relation to the total
group of units of matter composing the quark.
For antimatter quarks, Table 4, it is the negative matter ratios that are
employed to account for quark electrical charge (the left side column). Negative
matter ratios count negative unit charge particle ratios in relation to the total
group composing the quark.
Because of the quark structural symmetry, the physicists were required to explicity
count only one unit matter ratio for each quark. The other unit matter ratio for
each quark (the right side columns) are not required, and their existence was, until
now, was not realized.
The left side column of Table 3 shows the known fractional
electrical charge for normal matter quarks. For normal matter up and down quarks,
physicists track positive matter and employ positive matter ratios. Positive matter
ratios explicitly count positive unit charges, while implicitly accounting for the
negative unit charges through the group charge.
Negative matter ratios track negative matter by explicitly counting ratios of negative
units of matter while accounting for the positive units of matter implicitly through
the total group charge.
Since the positive unit charge of the proton was of main concern, it was the positive
matter ratios of the two types of ratios that was used. Since for the antimatter
antiproton, the negative net unit charge of the antiproton was the main concern,
negative matter ratios were employed.
The right side columns of Table 3 and Table 4 represent the ratios
that are not presently tracked, meaning that their contribution sums to zero. For
instance, in a normal matter proton, the negative matter ratios for each quark sum
to zero, there is no net negative matter in a proton.
Up and antidown are the same structural entity, but for antidown it is negative
matter ratios that are tracked. Antidown is +1/3 because negative matter ratios
are employed for antimatter, and negative matter ratios count ratios of negative
units of matter. The ratio of negative units in antidown is 1/3, and the group total
charge is +1, resulting in the +1/3 charge of antidown.
TOP OF STEP 1
TRIPLET SUBSTRUCTURES OF UNIT PARTICLES
Quarks
Protons
Pions
QUARKS
First Family of Quarks
The up quark has a total group charge of +1. The down quark has a total group charge of 1.
Up Quark  Down Quark  
Total Group Charge 
+ 1 
 1 
Up Quark Structure  Partial Group Charge 
Positive Matter Ratio 
+ 2/3 
Negative Matter Ratio 
+ 1/3 
Total Group Charge 
+ 1 
Up Quark Structure  
UP  ANTIDOWN  
Positive Matter Ratio 
+ 2/3 
+ 2/3 
Negative Matter Ratio 
+ 1/3 
+ 1/3 
Total Charge Group 
+ 1 
+ 1 
Down Quark Structure  Partial Group Charge 
Positive Matter 
 1/3 
Negative Matter 
 2/3 
Total Group Charge 
 1 
Down Quark Structure  
DOWN  ANTIUP  
Positive Matter Ratio 
 1/3 
 1/3 
Negative Matter Ratio 
 2/3 
 2/3 
Total Group Charge 
 1 
 1 
Two up quarks have four
positive unit charges and the down quark has one positive unit charge for a total
of five positive unit charges in the proton. The up quarks contribute one each negative
unit charge and the down quark contributes two negative unit charges for a total
of four negative unit charges in the proton. Therefore, in total, the proton is five
positive and four negative for a net of one positive.
The one positive unit charge in the down quark, counts as negative in positive matter
ratios because it is one third positive unit of a negative one group.
ELECTRICAL CHARGE OF A PROTON
Positive matter ratios count the positive unit
charges contribution to the charge of the proton. The net positive matter in the
proton is one, or +1.
There is no net negative matter in the proton as each up quark contributes +1/3 negative
matter and the down quark contributes 2/3 negative matter, giving a total of zero
net negative matter.
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 
down up
Neutral Pion
The arrow beside the illustrated pion indicates
north for the two magnetic dipoles of the composing quarks.
Title Page of
the Nature of Matter
Table of Contents of the Nature of Matter
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Last Update: October 7, 2000
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Starlight Publishing Company
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