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Quirks and Quarks

Outline

Red Maple Leaf

Quirks are key details that regulate how quarks are combined to form larger particles. Some quarks are bigger than others. And some are hot. We specifically consider thermodynamic quarks and characterize them by their energies and temperatures.

For EthnoPhysics the energy of a particle is a number that mathematically represents the quirky characteristic of sensory magnitude or size. The relationship between size and energy is articulated using a calorimetric thought experiment to define specific energy.

We also consider that the temperature of a particle is an account of the urgency of any feelings that are reified in the particle. The connection is made by discussing a thermometric thought experiment to define the vis viva.

Thermodynamic Quarks

Quark Type

Quark IndexInternal EnergyTemperature

\mathsf{Z}

 \zeta

U (MeV)

T (℃)

U1243-815
D20-1,034
E3-32676
G4298-1,185
M51,186-6,401
A636,529
T7150222
B8-850
S950-252
C10-53100

These numbers, the vis-viva and the specific-energy, are then used to make descriptions of experience that are more complete than a skeletal account of Anaxagorean sensations. Discussion starts with a hypothesis about conjugate symmetry. For simplicity we just assume that ordinary-quarks and anti-quarks are much the same as each other. Then laboratory experiments are introduced to move away from quirky thought experiments toward more collective perceptions. The audibility is used to compare and contrast different classes of sensation. And finally, these differences are used to make some numerical statements about internal energy and temperature. Results are summarized in the adjoining table where the large negative temperatures of some quarks are later associated with robust stability.

The quirks of thermodyamic quarks are ultimately represented using just three numbers: The internal energy  U characterizes the quirk of size. Variations in size between quarks and anti-quarks are described by  \Delta U. And the temperature  T notes a quality that is more like urgency. So, here are three quirks to master quarks …

The First Quirk is Size

The magnitude of a quirk expresses how we are more aware of some sensations than others. It is the most important quirk even though it is difficult to say exactly what makes us more or less conscious of a perception. We might use words like significance, rank or caliber to describe this quality. But usually we just call it the size.

Here is a thought experiment to try to be more definite about this quirky notion of size. It is called a calorimetric thought experiment. First select some sensation and call it the calorimetric reference sensation. Mathematically represent this reference sensation using a positive number noted as k_{C}.

Do the experiment by comparing the calorimetric reference sensation with the Anaxagorean sensation associated with seed Z. Determine the numbers  a and  b such that perceiving  a copies of the calorimetric reference presents the same sensory size as experiencing  b copies of Z. Report the result as

\widehat{E} \left( \mathsf{Z} \right) \equiv \dfrac{a}{b} k_{C}

The number \widehat{E} is called the specific energy of the seed Z. It is always greater than zero because  a,  b and k_{C} are all positive numbers. Thus specific energy is fundamentally understood as a ratio of sensation.

The forgoing is a thought experiment, and results are quirky. There might be statistically significant patterns within large groups of people, but even the gross categories used in the experiment depend on anthropological and linguistic quirks that are not universal. So a deeper analysis of sensory size must appeal to other disciplines like physiology and psychology.

A portrait of Harold Innis in uniform for the First World War.
Harold Adams Innis, FRSC. Circa 1916.

For instance Canadian academic work relating sensory ratios to space and time has been led by a political economist Harold Innis. And if that seems dubious, then recall Schrödinger’s observation1Erwin Schrödinger, Mind and Matter, page 76. Cambridge University Press, 1959. about how much of our physical knowledge is “suggested mainly by communication with other human beings”. Accordingly, EthnoPhysics is informed by the Toronto School of communications. And so, in order to tackle some outstanding physics problems, we intend to consider more than just physics.

An awareness of information about different sensory ratios is also beneficial for developing physical intuition. And that is why EthnoPhysics is illustrated with quantized ethnographic art. But personal acumen is always fragmentary. So later we use the results of calibrated laboratory experiments to develop the quirky idea of specific energy into a scientific account of internal energy.

Specific energy is understood as a balance between different sensations, somewhat like the ratios shown in this Sumatran tampan.
Tampan, Paminggir people. Lampung region of Sumatra, 19th century, 76 x 70 cm. Photograph by D Dunlop.

Urgency is the Second Quirk

The intensity of a sensation is a quirk that describes feelings of need or exigency. Recall Ernst Mach’s remark that the perception of sensation is connected to “dispositions of mind, feelings, and volitions”2Ernst Mach, The Analysis of Sensations and the Relation of the Physical to the Psychical, page 2. Translated by C. M. Williams and Sydney Waterlow.  The Open Court Publishing Company, Chicago and London, 1914.. Some sensations are just more compelling than others.

So even when perceptions exhibit the same size, they may still be distinguished by their vividness or affect. A feeling may be attractive or scary, perhaps pleasant, or maybe painful. Anyway let us call this quality the urgency and try to clarify it with the following thought experiment.

The experiment is called a thermometric thought experiment. First select some sensation and call it the thermometric reference sensation. Represent it using a positive number noted by k_{T}. Compare this thermometric reference sensation with the Anaxagorean sensation associated with seed Z. Determine the numbers  a and  b such that perceiving  a copies of the thermometric reference presents the same sensory urgency as experiencing  b copies of Z. Report the result as

\widehat{K} \left( \mathsf{Z} \right) \equiv \dfrac{a}{b} k_{T}

The number \widehat{K} is called the vis viva of the seed Z. It is always greater than zero because  a,  b and k_{T} are all positive numbers. Thus the vis viva is fundamentally understood as a ratio of sensation.

The forgoing is a thought experiment, and results are idiosyncratic. There may well be statistically significant patterns among large groups of people, but even the gross categories used in the experiment depend on anthropological and linguistic factors that are not universal. So a deeper analysis of sensory urgency must appeal to other disciplines like physiology and psychology.

Marshall McLuhan, age 56.
Marshall McLuhan on Television, 1967.

For example Canadian academic work relating sensory ratios to space and time has been led by a professor of English literature Marshall McLuhan. And if that seems surprising, then recall Schrödinger’s observation3Erwin Schrödinger, Mind and Matter, page 76. Cambridge University Press, 1959. about how much of our physical knowledge is “suggested mainly by communication with other human beings”. Accordingly, EthnoPhysics is informed by the Toronto School of communications. And in an effort to gain a deeper understand of physics, we intend to consider more than just physics.

Detailed knowledge concerning sensory proportion is also helpful for expanding physical intuition. And that is why EthnoPhysics is illustrated with quantized ethnographic art. But personal information is ultimately limited. So later we use the results of calibrated laboratory experiments to develop the quirky notion of vis viva into a scientific account of temperature.

Conjugate Symmetry

Conjugate symmetry is obtained if sensations exhibit equivalent size and urgency when compared between left and right sides. If feeling a sensation on the left side always presents the same sensory size as feeling it on the right, then \widehat{E}, the specific energy, of an odd conjugate seed is equal to the specific energy of an ordinary conjugate seed. And if their urgency is the same, then \widehat{K}, the vis viva, of an odd conjugate seed is equal to that of an ordinary conjugate seed. We often assume that all sensory experience is perfectly balanced in this way.

Assumption of Conjugate Symmetry
\widehat{E} ( \mathsf{O} )  = \widehat{E} ( \overline{\mathsf{O}}  )

and

\widehat{K} ( \mathsf{O} )  = \widehat{K} ( \overline{\mathsf{O}} )

Conjugate symmetry relieves us from having to pay very much attention to whether a sensation is experienced on the left or right side. The assumption simplifies analysis because it makes ordinary-quarks and anti-quarks much the same as each other. If left and right get mixed-up, the outcome of a calculation using the specific energy or vis viva may remain unchanged. So using this hypothesis is a way of objectifying the description of sensation.

Conjugate Asymmetry is the Third Quirk

Conjugate Differences

of Internal Energy in (µeV)

 \zeta \mathsf{Z} \Delta U
1U12.2
2D-1.10
3E-0.024
4G209
5M-290
7T78.3
8B78.1
9S1.60
10C4.36
15?
1639.0

all others

0

Perfect conjugate symmetry implies that a particle and its corresponding anti-particle have the same mass. This has been experimentally tested.4 W.-M. Yao et al. (Particle Data Group). J. Phys. G, 33, 1 (2006). For protons the ratio  \left| \; m^{\mathsf{p^{+}}} \! - m^{\mathsf{p^{-}}} \right| \, / \, m^{\mathsf{p}^{+}} is less than 6\mathsf{x}10^{-8} and for electrons it is less than eight parts in a billion. So the approximation is excellent for nuclear particles.

But atomic spectroscopy measurements are now about a million times more exact, some are reported to a few parts in 10^{15} . And so small asymmetries may be observed in the finely-balanced mechanical system of a hydrogen atom. Variations in size between quarks and anti-quarks are described using their internal energy  U. For any sort of quark \mathsf{Z}, the conjugate difference is given by

\Delta U^{\mathsf{Z}} \equiv \dfrac{ U^{\mathsf{\overline{z}}} - \, U^{\mathsf{z}} }{2}

These energy differences are typically stated in micro electronvolts, as shown in the accompanying table. For more detail, please see the discussion of fine structure in the spectrum of hydrogen.

Measuring Quirks

Measurement and doing laboratory experiments are important ways of making sensory descriptions that are scientific. Different people in different societies may have profoundly different ways of seeing things. So we make measurements to cope with perceptual variation. Mensuration is also a way to transcend personal sensory limitations. Indeed, a systematic quantitative approach to observation is crucial for objectifying the description of sensation.

Laboratory experiments began simply enough, for example here is a woodcut showing a determination of the mean length of a foot in a German town during the 16th century.
Sixteeen Men Emerge from Church to Determine the Foot from Geometrei by Jakob Köbel. Frankfurt, circa 1575.

Measurement techniques can be quite arbitrary to start, for example some determinations of length began by referring to people’s feet. But nonetheless observational methods have become very precise and dependable because experimental physicists have invested an enormous effort in developing calibration standards and highly accurate techniques.

For example, atomic clocks can be used to make time measurements that are good to about one part in 10^{14}. By comparison, in 2013 the US economy was 17 trillion dollars or about 10^{15} cents. So physicists can be fussy in a way that is like counting every dime spent in the USA per year. When we speak of doing laboratory experiments, we mean that observations are being made and reported in this fastidious style.

ReferenceConstantUnits
Whiteness is illustrated by this icon for a binary description of grey visual sensations.not seeing the Sun U^{\mathsf{d}} = 0(MeV)
Coldness is illustrated by this icon for burning or freezing sensations.touching ice T^{\mathsf{b}} = 0(℃)
Warmness is illustrated by this icon for warm or cool sensations.touching steam T^{\mathsf{c}} = 100(℃)
A heart shaped icon for somatic sensations.hearing a heartbeat  \raisebox{-0.04cm}{\it{N}} ^{\hspace{-.15cm}^{\mdsmblkcircle}} \rule{0px}{6px}^{\hspace{1px} \mathbf{\Theta}} = 86,400(s/day)

For EthnoPhysics, discussing laboratory practice starts with the reference sensations that are benchmarks from which all perceptions are judged and recognized. These sensations are mathematically represented by constants. And sometimes, the constants express calibration standards. See the accompanying table for examples where  T notes the temperature,  U marks the internal energy, and  \raisebox{-0.04cm}{\it{N}} ^{\hspace{-.15cm}^{\mdsmblkcircle}} is a number of daily occurrences. Quarks are represented by  \mathsf{b} ,  \mathsf{c} or  \mathsf{d} for the bottom, charmed and down types. For more detail about any reference sensation just click on its icon, here and on other pages too.

Numerical values for these constants are established by convention, and are without any claim of universal validity. They can be altered by collective agreement if expedient. So, due to the variety of possibilities, a statement of measurement units is usually included with any complete experimental report. As measurement techniques become more refined, calibration standards are adjusted and so these constants actually represent historical standards. For example, the internal energy of a down-quark is almost always taken as zero, as shown in the table. But precise observations of hydrogen reveal a tiny value of a few micro electronvolts.

Internal Energy

Internal energy extends the notion of specific energy so that the size of a particle can be established from calibrated laboratory experiments. Consider a generic particle P characterized by some repetitive chain of events noted as

\Psi^{\mathsf{P}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\Omega}_{3} \; \ldots \; \right)

where each orbital cycle is a bundle of  N_{\! \mathsf{s}} seeds

\mathsf{\Omega^{P}} = \left( \mathsf{Z}_{1}, \, \mathsf{Z}_{2} \; \ldots \;      \mathsf{Z}_{i} \; \ldots \; \mathsf{Z}_{N_{\! \mathsf{s}}} \right)

Let each seed be described by \widehat{E} the specific energy and  \varepsilon the audibility. We characterize P using a sum over all of these component seeds

\displaystyle U \equiv \sum_{i \, \mathsf{=1}}^{N_{\! \mathsf{s}}} \varepsilon_{i} \widehat{E}_{i}

The number  U is called the internal energy of P. The internal energy may be positive, negative or zero depending on a particle’s composition and some choice for the calorimetric reference sensation. A laboratory device used to measure the internal energy is called a calorimeter.

The internal energy of down quarks is represented by the black background in this icon for achromatic visual sensation.

To establish numerical values for the internal energy consider a down quark defined by the pair of seeds \mathsf{d} \equiv \{ \mathsf{D}, \mathsf{O} \}. Applying the foregoing definition of internal energy gives U^{\mathsf{d}} = \widehat{E} \! \left( \mathsf{O} \right) - \widehat{E} \! \left( \mathsf{D} \right). If a down-seed has just about the same specific energy as an ordinary conjugate-seed, then

  \widehat{E} \! \left( \mathsf{D} \right) \simeq \widehat{E} \! \left( \mathsf{O} \right)

and

 U^{\mathsf{d}} \simeq 0

Internal Energy
 \zeta \mathsf{Z} \widetilde{U}(eV)
1U242 926 032 _{\bullet}
2D-0 _{\bullet}000 027 2
3E-31 966 250 _{\bullet}
4G298 359 162 _{\bullet}
5M1 185 795 604 _{\bullet}
6A3 122 059 _{\bullet}
7T149 556 239 _{\bullet}
8B-85 011 771 _{\bullet}
9S50 119 218 _{\bullet}
10C-53 062 870 _{\bullet}
11-2 _{\bullet}22
12-1 _{\bullet}80
13-2 _{\bullet}11
14-2 _{\bullet}55
15-0 _{\bullet}028 8
16-0 _{\bullet}049 0

Let us require experimental practice to obtain this consistently; for example, by using the down quark as a reference particle to set the null value when measuring internal energy. Down quarks are objectified from black sensations, so this requirement could be interpreted as closing any shutters and using insulation so that a calorimeter is completely isolated and in the dark when indicating zero.

The other numbers shown in the accompanying table are obtained by juggling quark coefficients with observations of molecular bond strength and nuclear particle mass. The conventional unit used for reporting these measurements is the electronvolt abbreviated as (eV).

Results are presented without the use of scientific notation to graphically emphasize how quark energies range over seventeen orders of magnitude. The structure of this huge variation divides analysis into roughly three different regimes, but with lots of overlap. Namely:

  • Nuclear physics for Z ∈ { U, E, G, M, A, T, B, S, C }.
  • Atomic physics when Z ∈ { Ⓐ, Ⓑ, Ⓘ, Ⓦ, Ⓓ, Ⓛ }.
  • Astro physics if Z=D.

In general, we use a conjugate difference  \Delta U ^{\mathsf{Z}} and a conjugate mean  \widetilde{U}^{\mathsf{Z}} to describe the relationship between quarks and anti-quarks

 \Delta U^{\mathsf{Z}} \equiv \dfrac{U^{\mathsf{\overline{z}}} - \, U^{\mathsf{z}} }{2}

 \widetilde{U}^{\mathsf{Z}} \equiv \dfrac{U^{\mathsf{\overline{z}}} + \, U^{\mathsf{z}} }{2}

But if conjugate symmetry can be assumed, then an ordinary quark and its associated anti-quark have the same internal energy. For example consider the generic quarks

\mathsf{z} = \left\{ \mathsf{Z}, \, \mathsf{O} \right\}

and

\overline{\mathsf{z}} = \left\{ \mathsf{Z}, \, \overline{\mathsf{O}} \right\}

By the foregoing definition, the internal energy for these particles is given by

U^{\mathsf{z}} = \widehat{E} \! \left( \mathsf{Z} \right) - \widehat{E} \! \left( \mathsf{O} \right)

and

U^{\mathsf{\overline{z}}} = \widehat{E} \! \left( \mathsf{Z} \right) - \widehat{E} \! \left( \mathsf{\overline{O}} \right)

But if  \widehat{E} ( {\mathsf{O}} ) = \widehat{E} ( \overline{\mathsf{O}} ) then both quarks have the same energy, and we may use  \zeta the quark index to refer to either quark. So, conjugate symmetry implies that

 U^{\mathsf{z}} = U^{\mathsf{\overline{z}}} = \widetilde{U}^{\mathsf{Z}} = U^{\zeta}

Internal Energy is Conserved

Consider that each each orbital cycle of P may also be described as a bundle of  N_{\! \mathsf{q}} quarks

\mathsf{\Omega^{P}} = \left\{  \mathsf{q}_{1}, \, \mathsf{q}_{2} \; \ldots \; \mathsf{q}_{j} \; \ldots \; \mathsf{q}_{N_{\! \mathsf{q}}} \right\}

Each quark is composed from a pair of seeds \mathsf{q} = \left\{ \mathsf{Z}, \, \mathsf{Z}^{\prime} \right\} . And from the foregoing definition of internal energy

U^{\mathsf{q}} = \varepsilon \widehat{E} + \varepsilon^{\prime} \widehat{E}^{\prime}

Then changing the sum over seeds, to a sum over quarks, gives

\displaystyle U^{\mathsf{P}} \equiv \sum_{i \, {\mathsf{=1}}}^{N_{\!\mathsf{s}}} \varepsilon_{i} \widehat{E}_{i} = \sum_{j\mathsf{=1}}^{N_{\!\mathsf{q}}} \varepsilon_{j} \widehat{E}_{j} + \varepsilon^{\prime}_{j} \widehat{E}^{\prime}_{j} = \sum_{j \mathsf{=1}}^{N_{\!\mathsf{q}}} U_{j}^{\mathsf{q}}

So the internal energy of a compound quark is just the sum its parts. But quarks are conserved. And the internal energy of each quark has a fixed value. So whenever some generic compound quarks   \mathbb{X} ,   \mathbb{Y} and   \mathbb{Z} interact, if

\mathbb{ X} + \mathbb{ Y} \leftrightarrow \mathbb{ Z}

then

U^{\mathbb{X}} + U^{\mathbb{Y}} = U^{\mathbb{Z}}

Thus internal energy is conserved when particles are formed or decay. Moreover, if there is conjugate symmetry, then swapping ordinary quarks with anti-quarks does not change the internal energy of P because  U^{\mathsf{z}} = U^{\mathsf{\overline{z}}}  . So any particle must have the same internal energy as its anti-particle and we write

 U \! ( \mathsf{P} ) = U \! ( \overline{\mathsf{P}} )

Internal energy is understood as a balance between different sensations, somewhat like the ratios shown in this Sumatran tampan.
Tampan, Paminggir people. Lampung region of Sumatra, Kalianda district, 19th century, 77 x 67 cm. Photograph by D Dunlop.

Temperature

Temperature extends the notion of vis viva so that the urgency of objectified feelings can be established from calibrated laboratory experiments. Consider a generic particle P characterized by some repetitive chain of events noted as

\Psi^{\mathsf{P}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2},     \, \mathsf{\Omega}_{3} \; \ldots \; \right)

where each orbital cycle is a bundle of  N_{\! \mathsf{s}} seeds

\mathsf{\Omega}^{\mathsf{P}} = \left( \mathsf{Z}_{1}, \, \mathsf{Z}_{2}   \;  \ldots \; \mathsf{Z}_{i} \; \ldots \; \mathsf{Z}_{N_{\! \mathsf{s}}} \right)

Let each seed be described by  \varepsilon, its audibility, and  \widehat{K}, its vis viva. We characterize P using a sum over all of these component seeds

\displaystyle T^{\mathsf{P}} \equiv \dfrac{2}{N_{\!\mathsf{s}} k_{B}} \sum_{i\mathsf{=1}}^{N_{\!\mathsf{s}}} \varepsilon_{i} \widehat{K}_{i}

where   k_{B} is Boltzmann’s constant. The number  T is called the temperature of P. This temperature may be positive, negative or zero depending on the particle’s composition and the choice of a thermometric reference sensation. A laboratory device used to measure the temperature is called a thermometer.

The temperature of a bottom quark is represented by this snowflace icon.

To establish numerical values for the temperature consider a bottom quark defined by the pair of seeds \mathsf{b} \equiv \{ \mathsf{B}, \mathsf{O} \}. Applying the foregoing definition of temperature gives   T^{ \mathsf{b}} \, k_{B} = \widehat{K} \! \left( \mathsf{O} \right) - \widehat{K} \! \left( \mathsf{B} \right) . If a bottom-seed has the same vis viva as a conjugate-seed, then

 \widehat{K} \! \left( \mathsf{B} \right) = \widehat{K} \! \left( \mathsf{O} \right)

and

T^{\mathsf{b}} \! =0

Temperature
 \zeta \mathsf{Z} T (℃)
1U-815
2D-1,034
3E676
4G-1,185
5M-6,401
6A6,529
7T222
8B0
9S-252
10C100
11?
12?
13?
14?
15?
16?

Let us require experimental practice to obtain this consistently; for example, by using the bottom quark as a reference particle to set the null value when measuring temperature. Bottom quarks are objectified from freezing reference sensations, so this requirement could be interpreted as adjusting a thermometer so that it indicates zero when touching ice.

But there are many different kinds of ice and to make reliable measurements we therefore need to specify the reference sensation more precisely. So, for a thermometer to ‘touch ice’ we mean that it is bathed in a slushy mix of frozen solid water and clean pure liquid water in an open container near sea level on Earth. This is an utterly conventional way of specifying zero on the Celsius temperature scale. So we write T^{\mathsf{b}} \! =0 \hspace{0.15cm} ( ^{\circ} \mathsf{C} ) and units are called Celsius degrees.

The temperature of a charmed quark is suggested by this icon of a steaming pot.

We have also defined the charmed quarks using the reference sensation of touching steam. And since there are different kinds of steam we also need to specify this sensation more carefully. So, by “touching steam” we mean a thermometer is immersed in vapors rising from an open container of pure boiling water near sea level on Earth. This is a very traditional way of specifying 100 Celsius degrees. Charmed quarks are objectified from this sensation, so we write T^{\mathsf{c}} \! = \! 100 \hspace{0.15cm} ( ^{\circ} \mathsf{C} ) .

The other temperatures listed in the accompanying table5Temperatures for the chemical quarks are not yet assigned. Perhaps they will be determined from something like a quark-based kinetic theory of gases. are obtained by juggling quark coefficients and laboratory observations of nuclear particles. The large negative temperatures indicate robust stability.

An ordinary quark and its associated anti-quark have the same temperature if conjugate symmetry can be assumed. To see this, consider the generic quarks

 \mathsf{z} = \left\{ \mathsf{Z}, \, \mathsf{O} \rule{0px}{11px} \right\}

and

 \overline{\mathsf{z}} = \left\{ \mathsf{Z}, \, \overline{\mathsf{O}} \rule{0px}{11px} \right\}

By the foregoing definition, the temperature of these particles is given by

  T^{\mathsf{z}}      = \dfrac {\widehat{K} \! ( \mathsf{Z} ) - \widehat{K} \! ( \mathsf{O} ) }{k_{B}}

and

 T^{ \mathsf{\overline{z}}} = \dfrac{ \widehat{K} \! ( \mathsf{Z} ) - \widehat{K}   \! ( \mathsf{\overline{O}} ) }{k_{B} }

But the assumption of conjugate symmetry asserts that  \widehat{K} \! ( {\mathsf{O}} ) = \widehat{K} \! ( \overline{\mathsf{O}} ) . So both quarks have the same temperature and we can use  \zeta the quark index to refer to either quark

 T^{\mathsf{z}} = T^{\mathsf{\overline{z}}} = T^{\zeta}

Temperature of Compound Quarks

Consider that each each orbital cycle of P may also be described as a bundle of  N_{\!\mathsf{q}} quarks

\mathsf{\Omega}^{\mathsf{P}} = \left( \mathsf{q}_{1}, \, \mathsf{q}_{2} \; \ldots \; \mathsf{q}_{j} \; \ldots \; \mathsf{q}_{N_{\!\mathsf{q}}} \right)

And let seeds be paired in sequence such that \mathsf{q}_{j} = \left\{ \mathsf{Z}_{j}, \, \mathsf{Z}_{j+1} \right\}. Then the temperature, as defined above, can be changed from a sum over seeds to a sum over quarks

    \begin{equation*} \begin{split} T^{\mathsf{P}} & \equiv \dfrac{2}{N_{\!\mathsf{s}} k_{B}} \sum_{i\mathsf{=1}}^{N_{\!\mathsf{s}}} \varepsilon_{i} \widehat{K}_{i}  \\  &= \dfrac{2}{N_{\!\mathsf{s}} k_{B}} \sum_{j\mathsf{=1}}^{  N_{\mathsf{q}}} \varepsilon_{j} \widehat{K}_{j}  +  \varepsilon_{j+1} \widehat{K}_{j+1} \end{split} \end{equation*}

If P happens to be a solitary quark  \mathsf{q}_{j} then the number seeds is just  N_{\!\mathsf{s}} \! = \! 2 and so

T ( \mathsf{q}_{j} ) = \dfrac{1}{k_{B}} \left( \varepsilon_{j} \widehat{K}_{j}  +  \varepsilon_{j+1} \widehat{K}_{j+1} \right)

We can eliminate \widehat{K} terms by substituting this back into the general expression for P’s temperature to obtain

\displaystyle T^{\mathsf{P}} = \dfrac{2}{N_{\!\mathsf{s}}} \sum_{j\mathsf{=1}}^{N_{\mathsf{q}}} \; T ( \mathsf{q}_{j} )

But  N_{\!\mathsf{s}} = 2N_{\mathsf{q}} because by definition there are always two seeds in every quark. So finally

\displaystyle T^{\mathsf{P}} = \dfrac{1}{N_{\mathsf{q}}} \sum_{j\mathsf{=1}}^{N_{\mathsf{q}}} \; T ( \mathsf{q}_{j} )

This expression is the arithmetic definition of an average or mean-value. Thus the temperature of a compound quark is just the average temperature of its component quarks. Swapping ordinary quarks with anti-quarks cannot change this average because  T^{\mathsf{z}} = T^{\mathsf{\overline{z}}}. Thus any particle has the same temperature as its associated anti-particle. We write

T ( \mathsf{P} ) = T ( \overline{\mathsf{P}} )

The temperature represents feelings of urgency and movement, somwhat like those presented in this Sumatran Tatibin.
Tatibin, Paminggir people. Lampung region of Sumatra, Kota Agung district, 19th century, 59 x 41 cm. Ship motif. Photograph by D Dunlop.
Next

EthnoPhysics faviconErgonomic Quark Models

A look at the size and shape of a particle. Definitions of radii and metrics lead to quark-space as a venue for the presentation and analysis of quark models.
References
1, 3Erwin Schrödinger, Mind and Matter, page 76. Cambridge University Press, 1959.
2Ernst Mach, The Analysis of Sensations and the Relation of the Physical to the Psychical, page 2. Translated by C. M. Williams and Sydney Waterlow.  The Open Court Publishing Company, Chicago and London, 1914.
4 W.-M. Yao et al. (Particle Data Group). J. Phys. G, 33, 1 (2006).
5Temperatures for the chemical quarks are not yet assigned. Perhaps they will be determined from something like a quark-based kinetic theory of gases.