Counting is a primordial part of science. From counting days to counting stars, a systematic quantitative approach to observation is crucial for objectifying the description of human experience. Counting is closely related to making measurements. And reproducible measurements are what distinguish physical particles from other narrative devices like genies or ghosts. So in this article we tackle questions about physical particles by counting quarks.
To summarize developments so far, we have defined seeds by objectifying some common sensations. Seeds are the elementary components of EthnoPhysics. All other objects are subsequently defined by aggregations of seeds. This approach is not new, it is influenced by the ancient philosophy of Anaxagoras.
Then we considered pairs of seeds and called them quarks. Quarks are discussed in more detail over the next few pages, but we can already use them to make this rudimentary definition; physical particles are compound quarks. But quarks are defined by sensation, so influenced by David Hume, we ultimately understand physical particles to be bundles of sensation.
EthnoPhysics then expands on Hume’s idea in an effort to understand particle mechanics without resorting to mysteriously received notions about length, mass and time. First we remarked that experiencing a sensation is itself an event. Then we organized a way of mathematically describing events using ordered-sets called chains of events generically noted by
Recognizing patterns of sensation, and identifying particles, requires some repetition within a stream of consciousness. So physical particles are mathematically represented using orbital chains of events where some bundle of sensation is experienced over and over again. Then, if we speak informally of the quarks in a particle, we mean the quarks in one bundle. For instance we may say that particle contains the quarks and or we may write phrases like
as an abbreviation for writing out the full expression for the chain
where the convention that seeds are conserved requires that
From these general considerations, different sorts of particles can be obtained from rules that specify new quark combinations. Starting with anti-particles: The anti-particle of any particle is noted by and defined by exchanging ordinary-quarks and anti-quarks of the same type. So for example if contains and then is composed from and And here is a quick introduction to some more compound quarks.
- Frames of Reference are compound quarks where the total number of quarks is usually enormous. They provide a descriptive context for other particles.
- Clocks are defined from compound quarks that have a fixed relationship with events on Earth.
- Nuclear Particles are compound quarks that are very symmetric so that they are stable enough to be measured.
- Photons and Gravitons are compound quarks that are always on the move. They are ethereal, and so mostly known by their effect on other particles.
- Newtonian Particles are compound quarks that are dense enough so that they can absorb a few photons or gravitons without decaying.
- Spaces and Fields are described by mathematical sets of quarks too. Different kinds of fields are defined from different distributions of quark types.
So in brief, EthnoPhysics employs sensations, seeds and quarks to define all physical things.
A Quark Index
Next we specify a quark index because when considering quarks it is often more convenient to identify them by number instead of a letter. We start with a non-conjugate seed noted by Z that is used to define an ordinary quark and its associated anti-quark These quarks are occasionally referred to using the Greek letter zeta, as shown in the adjoining table. When used like this, zeta is called a quark index. The two particles and are sometimes collectively called -type or Z-type quarks. This notation is especially helpful when using summation notation.
Counting quarks is a way to scientifically describe sensation. More exactly, we start by counting seeds. Let P be a generic particle composed of some aggregation of seeds. A simple way to make a mathematical description of P is just to sort-out the number of different types of seeds in P. To satisfy Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we require that seeds are perfectly distinct. Therefore seed counts always report a positive integer or zero, never fractions or negative numbers.
If all seeds are paired in quarks, then P can also be represented as a set of quarks and mathematically described by counting quarks. We note the results of such an inventory using the letter in a serified italic font. These numbers are called quark coefficients because they can be interpreted as factors in a nuclear reaction that yields P. For example if then the quark coefficients of P are and . Quark coefficients are always non-negative integers because quarks are defined from perfectly distinct pairs of perfectly distinct seeds.
|coefficients of ordinary quarks|
|coefficients of anti-quarks|
|the total number of Z-type quarks|
|the net number of Z-type quarks|
|the total number of all types of quarks|
The Roman letter Z, or the Greek letter are used to indicate quark-type. In general, we use the symbols or to note the coefficients of ordinary quarks. Coefficients of anti-quarks are written with an overline. A few other numbers used for describing particles are defined in the accompanying table.
When Z represents a thermodynamic or chemical quark, but not a conjugate quark, then can also be used to represent the number of Z-type seeds in a particle. This is because there is just one non-conjugate seed in each quark. So we often refer to as a seed coefficient when discussing thermodynamic or chemical seeds.
Anti-particles are defined by exchanging quarks and anti-quarks. So the quark coefficients for some particle and its anti-particle are related as
Then can be written as
This is just some simple arithmetic known as the anticommutative property of subtraction. However, when we apply it to counting quarks it expresses a fundamental physical symmetry between matter and anti-matter. So we refer back to it often.
Quarks are Conserved
Quarks are conserved because physics depends on mathematics. Recall that a logical style of description that uses counting and mathematics requires that seeds are conserved. For the same reasons, when we shift the description to counting quarks, then quarks must be conserved too. The overall quantity and quality of the quarks in a description cannot change. As a narrative convention, we say that quarks are indestructible. Whenever some compound quarks , and are combined or decomposed, if
then the coefficients of any specific type of quark are related as
And counting out a sum over all types of quarks is constrained as
Quark Coefficients are Integers
To satisfy Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we require that every seed Z is perfectly distinct. Seeds are always distinguished from each other, either by their innate characteristics, or by their association with other particles in nested sets. Therefore when counting seeds we always report a positive integer or zero, never fractions or negative numbers. So
For the same reasons, when we define quarks from seeds, and shift the description to counting quarks, then quark coefficients must be integers too. That is, is always a non-negative integer because quarks are defined from perfectly distinct pairs of perfectly distinct seeds. We write
The foregoing relationships are the logical basis for a variety of conservation laws that are found throughout physics. We often refer back to them. But next we look at how counting quarks leads to particle classification using quantum numbers.
Quantum numbers are used to identify and classify particles. They are employed in both atomic and nuclear physics. The atomic quantum numbers are discussed later. We start here by specifying the nuclear numbers from quark coefficients noted by and The total angular momentum quantum number is defined by
The charge quantum number is
The lepton number is defined as
The baryon number is given by
And finally the strangeness quantum number is defined as
|a charged particle|
|a neutral particle|
|a strange particle|
Recall that quark coefficients are always integers. So these formulae all yield integer multiples of one-eighth. But later, if we assume spatial homogenity, then and are also restricted to being integers.
Particles may be classified by their quantum numbers into a few different1By definition, the strangeness quantum number describes how a particle is rotating. It is not necessarily related to strange quarks. But some well known particles like kaons have both and lots of strange quarks. So there is some overlap, and the word strange can be imprecise if used without context. types as shown in the accompanying table. In general, particle identities and attributes are quantized because EthnoPhysics is fundamentally based on a finite categorical scheme of binary distinctions. Any characteristic defined using a quark coefficient is necessarily quantized because quark coefficients are always integers.
Now considering anti-particles, recall that for any seed Z, the net number of quarks in particle and its anti-particle are related as
This relationship implies that the charge, strangeness, lepton-number and baryon-number of particles and anti-particles have the same absolute value, but opposite signs. That is,
Quarks are conserved. So the overall quantity of each quark-type in any given description may not change. Whenever some generic compound quarks , and interact, if then the coefficients for any sort of quark are related as
But the lepton number, for example, is defined above from sums of quark coefficients. So by the associative properties of addition we have
Thus the lepton number is conserved too. This reasoning also applies to the baryon number and charge, so we write
However, the strangeness and angular momentum quantum-numbers are defined using absolute-value functions which are not generally associative. So and are not always conserved when compound quarks are formed or decomposed.
|1||By definition, the strangeness quantum number describes how a particle is rotating. It is not necessarily related to strange quarks. But some well known particles like kaons have both and lots of strange quarks. So there is some overlap, and the word strange can be imprecise if used without context.|