THE NATURE OF MATTER

CHAPTER 3  THE STEPS OF DEDUCTION

STEP 1  TRIPLET SUBSTRUCTURES

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.

NEXT: STEP 2 Doublet Substructures
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 anti-matter counterparts of normal matter quarks, anti-up and anti-down, which compose anti-protons.

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:

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 anti-matter 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 anti-up quark. If for anti-matter, ratios of negative matter are counted, then an anti-up quark needs to be composed of two negative units and one positive unit so that the anti-up quark will be two thirds negative matter. The anti-down 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 anti-down quark are seen to be the same entity.

The +1/3 charge of the anti-down quark and the +2/3 charge of the up quark leads one to conclude that the up quark and the anti-down 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. Anti-down is +1/3 because for anti-particles, negative matter ratios are what is employed and the ratio of negative units in anti-down 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 anti-down quark are the same entity has a symmetrical explanation for why the down quark and the anti-up 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 anti-matter quarks.

Table 3 and Table 4 show that for both normal matter and for anti-matter, 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 anti-matter 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 anti-matter anti-proton, the negative net unit charge of the anti-proton 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 anti-down are the same structural entity, but for anti-down it is negative matter ratios that are tracked. Anti-down is +1/3 because negative matter ratios are employed for anti-matter, and negative matter ratios count ratios of negative units of matter. The ratio of negative units in anti-down is 1/3, and the group total charge is +1, resulting in the +1/3 charge of anti-down.

TOP OF STEP 1
TRIPLET SUBSTRUCTURES OF UNIT PARTICLES

Quarks
Protons
Pions

QUARKS

The up quark has a total group charge of +1. The down quark has a total group charge of -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.

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Last Update: October 7, 2000Created: April 4, 1997