Mass – EthnoPhysics

Outline

A particle’s mass is extraordinarily significant for understanding its mechanics. This is true for particles large and small, from planets to apples. The careers of thousands of physicists have been devoted to measuring mass because it is such an important property. So based on decades of their work, here is a theory about mass that is quantitative, concise and candid.

Definition of Rest Mass

Let particle P be characterized by its enthalpy $H$ and the work $W$ required to bring together its component quarks. Then the rest mass of P is defined by

$m \equiv \dfrac{ \sqrt{H^{2}-W^{2}} }{ c^{2} }$

where $c$ is a constant called the speed of light. The enthalpy and work are both defined exclusively from the quarks in P. They do not rely on an external reference-frame. So the rest-mass is an intrinsic trait as well.

Roughly speaking, the foregoing definition expresses how the mass of P is the due to the energy leftover after assembling P from its component quarks. Particles are classified by their mass type $\delta_{m}$ defined by

$\delta_{m} \equiv \begin{cases} \; +1 & \text{\sf{if}} \; m^{2} \! > 0 \\ \hspace{7px} 0 & \text{\sf{if}} \; m^{2} \! = 0 \\ \; -1 & \text{\sf{if}} \; m^{2} \! < 0 \end{cases}$

If $m^{2} \! > \! 0$ then P is called a material particle, like a coin or a bullet. If P has $m^{2} \! = \! 0$ then we call it an ethereal particle, like a photon. And if $m^{2} \! < \! 0$ then we say that P has an imaginary mass, like a neutrino. The term imaginary is used here with its mathematical meaning.

Any particle $\mathsf{P}$ has the same rest-mass as $\mathsf{\overline{P}} ,$ its conjugate twin. This is because $H \! ( \mathsf{P} ) \! = \! - H \! ( \overline{\mathsf{P}} )$ and $W \! ( \mathsf{P} ) \! = \! W \! ( \mathsf{\overline{P}} )$ as determined from their definitions. But mass is defined from the square of these quantities, so $m ( \mathsf{P} ) \! = \! m ( \mathsf{\overline{P}} ) .$ This means, for example, that both electrons and positrons are classified as material particles, even though they are made of different types of matter.

Sensory interpretation: Recall that the enthalpy $H$ characterizes the size of an event when considered over all classes of sensation, including thermal sensations. But the work $W$ does not depend on thermal sensation. The mass is established from the contrast between $H$ and $W$ which is therefore mostly due to thermal sensation. So for material particles, thermal qualities are more relevant than visual characteristics. But for particles with an imaginary mass, visual and lateral sensations dominate awareness. So from a distance, audio-visual senses are foremost.

Experimental Comparison

The EthnoPhysics strategy for describing mass has been tested by extensive quantitative analysis. Theoretical evaluations of nuclear particle mass have been compared with laboratory observations. Our most important reference for these observations is provided by the Particle Data Group , an international collaboration of physicists that compile and reanalyze published results. Its supporters include; the European Organization for Nuclear Research (CERN), the United States Department of Energy, and the Japanese Ministry of Letters and Science.

Comparative results are grouped together for each nuclear family. To see summaries, select a specific family from this illustrated menu. More detailed results for some individual particles are presented in small spreadsheets along with their family reports. And finally, there is also a large spreadsheet that summarizes all particles.

At present, more than 400 nuclear particles have been assessed. All but a handful have a calculated mass that is within experimental uncertainty of observation.

Despite this extensively agreeable result, there are still some problems. The 𝞚(1405) baryon has a mass that is low by 0.1%. The 𝞢_c(2455) baryon is low by 0.007%. And calculations for the 𝝍(2S) meson give a rest mass that is lower than the observed value by 0.0004%. These deviations are tiny, but they continue to call for attention. For more detail, please see the discussion about errors.

Types of Mass

Historically, material particles were roughly sorted by their mass into three categories. Baryons were heavy. Leptons were lightweight. And mesons were somewhere in between. But with advances in experimental physics these distinctions have become blurred. So now we associate the remaining rubrics with a particle’s quantum-numbers as noted below. As for more intangible particles; neutrinos have an imaginary mass, and ethereal particles have no mass at all.

Baryons

Baryons have a baryon number of $B \! \ne \! 0$ and a lepton number of $L \! = \! 0.$ The most prominent particles in this category are protons and neutrons. For more detail, here is a link to the main article.

Baryons

A summary of baryonic seeds, quarks and field-quanta. Discussion of the elementary baryonic charge.

Mesons

Mesons have both a lepton number of $L \! = \! 0$ and also a baryon number of $B \! = \! 0.$ For more detail, here is a link to the main article.

Mesons

A summary of the mesonic charge and some heavier particles.

Leptons

Leptons have a lepton number of $L \! \ne \! 0$ and a baryon number of $B \! = \! 0.$ Stories about leptons usually feature electrons. For more detail, here is a link to the main article.

Leptons

A summary of leptonic seeds, quarks, field-quanta and neutrinos. Also information about electrons, muons and tauons.

Imaginary Mass

Particles with $m^{2} \! < 0$ are said to have an imaginary mass. The term imaginary is used here with its mathematical meaning. A particle with an imaginary mass is no more fictitious than any other sort of nuclear particle. It can carry momentum and transmit force. The main thing about particles with an imaginary mass is that they are logically distinct from Newtonian particles. So they are not necessarily described by Newtonian laws of motion.

Neutrinos have an imaginary mass. They are all leptons, but still very distinct from the other leptons. No other particles with $m^{2} \! < 0$ have been encountered in the laboratory. Yet.

Zero Mass

Ethereal particles have no mass at all. The most notable particles in this category are the photons and their composites, the gravitons. Photons have $m \! = \! 0$ because by definition most of the quarks they contain appear in phase anti-symmetric pairs. However, a photon’s down-quarks may have ${\Delta}n^{\mathsf{D}} \! \ne \! 0 \hspace{0.5px} .$ So the central radius of a photon is given by

$\rho_{z} ( \boldsymbol{\gamma} ) = \dfrac{\, {\Delta}n^{\mathsf{D}} U^{\mathsf{D}}}{ k_{\mathsf{F}} }$

This quantity is small because $U^{\mathsf{D}} \! \sim \! 10^{-5} \hspace{0.5px} \mathsf{(eV)}.$ But it is not necessarily zero. Next we use it to assess the work required to assemble the quarks in a photon. For a terrestrial metric this is given by

$\begin{equation*} W = k_{\mathsf{F}} \left( \begin{split} & \; k_{mm} \rho_{m}^{2} + k_{ee} \rho_{e}^{2} + k_{zz} \rho_{z}^{2} \\ & + 2 k_{em} \rho_{e} \rho_{m} + 2k_{mz}\rho_{m} \rho_{z} \\ & \hspace{30px} + 2 k_{ez}\rho_{e} \rho_{z} \; \end{split} \right)^{\frac{1}{2}} \end{equation*}$

But for photons $\rho_{e} \! = \rho_{m} \! = 0$ because all leptonic-quarks are matched with their conjugate twins. And recall that $k_{zz} \! =1 .$ So the work required to produce a photon is just

$W \! ( \boldsymbol{\gamma} ) \, = \, k_{\mathsf{F}} \! \left| \, \rho_{z} \, \rule[-3px]{0px}{14px} \right| \, = \, \left| \, \Delta n^{ \mathsf{D}} U^{ \mathsf{D}} \, \rule[-3px]{0px}{14px} \right|$

This quantity is small, but not necessarily zero. Compare it to the enthalpy which is defined for any particle from the sum

$\displaystyle H \equiv \sum_{\zeta=1}^{16} \Delta n^{\zeta} U^{\zeta}$

For photons, all $\Delta n$ terms are null except for the down-quarks, so $H\! ( \boldsymbol{\gamma} ) = \Delta n^{\mathsf{D}} U^{\mathsf{D}} .$ Again this quantity is small, but not necessarily zero. However its modulus is exactly the same as the work

$\left| H\! ( \boldsymbol{\gamma} ) \rule[-3px]{0px}{14px} \right| = W\! ( \boldsymbol{\gamma} )$

So $H \! ( \boldsymbol{\gamma} )^{2} \! = \! W\! ( \boldsymbol{\gamma} )^{2} .$ Substituting this result back into the definition of mass shows that all photons must have $m \! = \! 0$ . Not just close to zero, but perfectly zero.

Matter

The following particles have lifetimes that are long enough that we usually assume they do not decay. They are therefore key actors in narratives linking cause and effect. And importantly, they are also susceptible of precise measurement. Some experimentally determined facts about these particles are considered to be essential knowledge about our environment. These are particles that matter.

Protons

Protons are forever. They are the primordial seed-aggregate. They are everywhere. And they are in almost everything. So there is a lot to say about them: Here is a link to the main article about protons.

The Proton

A summary of various models of the proton. Analysis of its mass, lifetime, charge and rotation.

Electrons

Modern life depends on electrons. Almost everybody relies on electric lighting, telephones or computers. Electronic technologies underpin contemporary industry, agriculture and medicine. So here is a link to the main article about these crucial particles.

The Electron

A summary of various models of the electron. Mass, charge and rotation are discussed.

Neutrons

Finally, free neutrons do decay. But their lifetimes are measured in minutes. So they are still relevant for understanding cause-and-effect relationships occurring over time spans that are within direct human experience. Neutrons are essential for understanding atoms, the periodic table of elements, and lots of chemistry.

The Neutron

A summary of neutron composition, mass, lifetime and rotation. Various excited states of the neutron are assessed for mass and parity.

Anti-Matter

Consider some particle P that is defined by a repetitive chain of events. And let each repeated cycle $\mathsf{\Omega}$ be parsed into two sets of quarks noted by $\mathbb{D}$ and $\mathbb{S}$ . Let all of the ordinary-quarks in P be assigned to $\mathbb{D} .$ And all of P’s anti-quarks be put in $\mathbb{S} .$ We express this symbolically as

$\mathbb{S}^{\mathsf{P}} = \left\{ \overline{\mathsf{q}}_{1}, \, \overline{\mathsf{q}}_{2}, \, \overline{\mathsf{q}}_{3} \; \ldots \; \right\} \hspace{5px} \textsf{the anti-quarks in P}$

$\mathbb{D}^{\mathsf{P}} = \left\{ \mathsf{q}_{1}, \, \mathsf{q}_{2}, \, \mathsf{q}_{3} \; \ldots \; \right\} \hspace{5px} \textsf{the ordinary-quarks in P}$

$\mathsf{\Omega}^{\mathsf{P}} = \left\{ \mathbb{S}^{\mathsf{P}} , \, \mathbb{D}^{\mathsf{P}} \rule{0pt}{11px} \right\}$

The compound-quarks $\mathbb{D}$ and $\mathbb{S}$ are called lateral components of P. The set of ordinary-quarks $\mathbb{D}$ is called the dextral component. And $\mathbb{S}$ is called the sinistral component.

Sensory interpretation: The difference between an ordinary quark and its associated anti-quark is whether it contains an ordinary seed or an odd seed. These two kinds of seeds are objectified from two different lateral sensations. Ordinary-seeds are reified from right-side sensations. And odd-seeds are objectified from feelings on the left-side. So the sinistral set $\mathbb{S}$ represents a collection of feelings on the left-side. And the dextral component $\mathbb{D}$ is a bundle of sensations felt on the right-side.

Consider the size of a lateral-component of P as represented by its internal-energy $U \! ( \mathbb{D} )$ or $U \! ( \mathbb{S} ) .$ The relative size of these components determines if a particle is made of ordinary-matter or anti-matter.

The distinction also depends on if P is magnetic or imaginary. Muonic quarks are broadly associated with magnetism. And if P has an imaginary mass it is noted by $\delta_{m} \hspace{1px}$ the mass type. So $\delta_{m}$ and P’s muonic lepton-number $L_{\mu}$ quantify these influences. Both traits modify the balance between matter and anti-matter. Their combined effect is represented by $\mathbf{U} ,$ the full-size of a lateral-component. For $\mathbb{D}$ the full-size is defined as

$\mathbf{U} ( \mathbb{D} ) \equiv \left( L_{\mu}^{2} + \frac{1}{2} \delta_{m} \right) U \! ( \hspace{0.5pt} \mathbb{D} \hspace{0.5pt} )$

and likewise for $\mathbb{S} .$ Comparing the full-size of P’s lateral-components determines the sort of matter embodied by P. This is mathematically described by $\delta_{\mathfrak{m}}$ the matter-type defined by

$\delta_{\mathfrak{m}} \equiv \begin{cases} +1 & \text{\sf{if}} \; \; \mathbf{U} ( \hspace{0.5pt} \mathbb{S} \hspace{0.5pt} ) > \mathbf{U} ( \hspace{0.5pt} \mathbb{D} \hspace{0.5pt} ) \\ \, \, 0 & \text{\sf{if}} \; \; \mathbf{U} ( \hspace{0.5pt} \mathbb{S} \hspace{0.5pt} ) = \mathbf{U} ( \hspace{0.5pt} \mathbb{D} \hspace{0.5pt} ) \\ -1 & \text{\sf{if}} \; \; \mathbf{U} ( \hspace{0.5pt} \mathbb{S} \hspace{0.5pt} ) < \mathbf{U} ( \hspace{0.5pt} \mathbb{D} \hspace{0.5pt} ) \end{cases}$

If $\delta_{\mathfrak{m}} \hspace{-3px} = \! 1$ we say that P is a particle of ordinary matter like a coin or a bullet. If $\delta_{\mathfrak{m}} \hspace{-3px} = \! 0$ then P is like a graviton and we say it is balanced between matter and anti-matter. And if $\delta_{\mathfrak{m}} \hspace{-3px} = \! -1$ then we say that P is a particle of anti-matter, like a positron.

Consider a pair of conjugate twins $\mathsf{P}$ and $\overline{\mathsf{P}}$ that are related by exchanging ordinary-quarks and anti-quarks. The lateral-components of any particle, $\mathbb{D}$ and $\mathbb{S} ,$ are defined from sets composed exclusively of either quarks or anti-quarks, so

$\mathbb{D} ( \mathsf{P} ) = \mathbb{S} ( \mathsf{\overline{P}} )$

and

$\mathbb{S} ( \mathsf{P} ) = \mathbb{D} ( \mathsf{\overline{P}} )$

So the full-sizes of these components are related to each other by

$\mathbf{U} ( \hspace{1px} \mathbb{D}^{\mathsf{P}} \hspace{1px} ) = \mathbf{U} ( \hspace{1px} \mathbb{S}^{\mathsf{\overline{P}}} \hspace{1px} )$

and

$\mathbf{U} ( \hspace{1px} \mathbb{S}^{\mathsf{P}} \hspace{1px} ) = \mathbf{U} ( \hspace{1px} \mathbb{D}^{\mathsf{\overline{P}}} \hspace{1px} )$

Now let P be a particle of ordinary-matter such that $\delta_{\mathfrak{m}}^{\, \mathsf{P}} \hspace{-3px} = \! 1 .$ From the definition of matter-type we have $\mathbf{U} ( \hspace{0.5pt} \mathbb{S}^{\mathsf{P}} \hspace{0.5pt} ) \! > \! \mathbf{U} ( \hspace{0.5pt} \mathbb{D}^{\mathsf{P}} \hspace{0.5pt} ) .$ So by substitution, the components of $\overline{\mathsf{P}}$ are related by $\mathbf{U} ( \hspace{1px} \mathbb{D}^{\mathsf{\overline{P}}} \hspace{1px} ) \! > \! \mathbf{U} ( \hspace{1px} \mathbb{S}^{\mathsf{\overline{P}}} \hspace{1px} ) .$ Then by definition $\delta_{\mathfrak{m}}^{\, \mathsf{\overline{P}}} \hspace{-3px} = \! -1 .$ Thus if $\mathsf{P}$ is a particle of ordinary-matter then $\overline{\mathsf{P}}$ is made of anti-matter, and vice versa. Particles and their conjugate-twins are always made of opposite types of matter. We write

$\delta_{\mathfrak{m}} ( \mathsf{P} ) = - \delta_{\mathfrak{m}} ( \mathsf{\overline{P}} )$

Please notice that this newly defined quantity, the matter-type $\delta_{\mathfrak{m}} \hspace{1px} \textsf{,}$ is not the same as the mass-type $\delta_{m} \hspace{1px} \textsf{,}$ which was discussed earlier. Briefly summarized, the mass-type sets apart neutrinos, photons and material-particles by their mass. Whereas the matter-type distinguishes between anti-particles, gravitons and ordinary-particles by their size.

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Experimental Comparison

The foregoing analysis of anti-matter gives the correct matter-type for all observed particles except for some Nucleon Resonances, perhaps some neutral Kaons, and a couple charmed Xi Baryons.

Center of Mass

When some particle absorbs a graviton Γ, we say that the position of the graviton defines a center of mass for the particle. To be more specific about this location let us examine some of the radii we use for describing particles.

The radius vector of a graviton is noted by $\overline{\rho} \! \left( \hspace{0.5pt} \mathsf{\Gamma} \hspace{0.5pt} \right)$ and defined by sums over quarks. Then since gravitons are defined as $\mathsf{\Gamma} \! \equiv \! \left\{ \, \boldsymbol{\gamma}, \, \overline{\boldsymbol{\gamma}} \, \right\} \! ,$ and quarks are conserved $\hspace{0.7pt} ,$ we obtain $\overline{\rho} \! \left( \hspace{0.5pt} \mathsf{\Gamma} \hspace{0.5pt} \right) = \overline{\rho} ( \boldsymbol{\gamma} ) + \overline{\rho} ( \overline{\boldsymbol{\gamma}} )$ by the associative properties of addition. But any particle and its conjugate twin have symmetrically opposed radius-vectors, so $\overline{\rho} ( \boldsymbol{\gamma} ) \! = \! - \overline{\rho} ( \overline{\boldsymbol{\gamma}} ) .$ Thus for any graviton

$\overline{\rho} \! \left( \hspace{0.5pt} \mathsf{\Gamma} \hspace{0.5pt} \right) = (0, 0, 0)$

and

$\left\| \; \overline{\rho} \! \left( \hspace{0.5pt} \mathsf{\Gamma} \hspace{0.5pt} \right) \, \right\| = 0$

Also, by definition gravitons must have $\Delta n^{\mathsf{Z}} \! = \! 0$ for all types of quarks, including down-quarks. So the inner radius of any graviton is nil, and we write

$\mathcal{R}_{in} \! \left( \hspace{0.5pt} \mathsf{\Gamma} \hspace{0.5pt} \right) \! = \! 0$

All of these null values indicate that the graviton is positioned at the spatial-origin of a particle-centered reference-frame. So that is where we locate the center-of-mass.

Gravitons are objectified from highly symmetric combinations of sensations, as suggested by this bead panel from Borneo. — Baby Carrier panel, Ngaju people. Borneo 20th century, 41 x 26 cm. Photograph by D Dunlop.

Dense Newtonian Particles

Newtonian particles are defined by their density and surrounding equilibrium. Conservation of their mechanical energy and momentum is evaluated.