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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} }

MassDefinition
heavyW^{2}  \,   \ll     \,  H^{2}
materialW^{2}   \,  <   \,  H^{2}
etherealW^{2}   \,  =   \,  H^{2}
imaginaryW^{2}   \,  >   \,  H^{2}

where  c is a constant. This definition distinguishes several types of particles by their mass. If  m is positive then P is a material particle; an ordinary particle of matter, like a coin or a bullet. There is an important special case for material particles when the work required to make them is negligible compared to their enthalpy, then we say they are heavy particles. If the mass is zero then P is ethereal. Finally if  m^{2} < 0 then P has an imaginary mass.1The term imaginary is used here with its mathematical meaning . Particles with an imaginary mass are no more fictitious than any other sort of nuclear particle. They carry momentum and transmit forces like other particles. The main thing about having an imaginary mass is that it puts a particle in a logical category that is different from Newtonian particles. So they are not necessarily required to follow Newtonian laws of motion. Roughly speaking, the rest mass describes how much internal energy is leftover after the work of assembling a particle has been completed. We may use the mass to describe the hardness or density of a particle. Recall that  \left\| \, \overline{\rho} \, \right\| is the norm of the radius vector of P. Then the density of P is defined as

\varrho \equiv \dfrac{ \, m c^{2} }{ \left\| \, \overline{\rho} \, \right\|  }

Particles and anti-particles have the same mass as each other. We have already seen how  H \! ( \mathsf{P} ) = - H \! ( \overline{\mathsf{P}} ) and  W \! ( \mathsf{P} ) = W \! ( \mathsf{\overline{P}} ) when conjugate symmetry is assumed. But the mass depends on these quantities squared. So

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

Photons are ethereal because they are mostly phase anti-symmetric. The radius vector of a photon  \overline{\rho}  (  \boldsymbol{\gamma} ) is null, and so no work is required to assemble the quarks in a photon,  W \! ( \boldsymbol{\gamma} )=0. Phase anti-symmetry also means that the net number of quarks is nil. Substituting this  \Delta n = 0 condition into the definition of enthalpy shows that  H \! ( \boldsymbol{\gamma} ) =0 as well. Then the definition of mass given above implies that

  m ( \boldsymbol{\gamma} ) =0

Sensory Interpretation

Temporal orientation is a binary description of thermal sensations like those shown in this icon.

Enthalpy characterizes the magnitude of all classes of sensation, whereas the work represents just somatic and visual sensations. The mass is established by their difference, which is mostly due to thermal sensation. So for heavy particles, thermal perceptions are more important than visual sensations. And for particles with an imaginary mass, audio-visual sensations dominate awareness. Next we consider the lifetime of a nuclear particle.

The mass depends on a difference between two quantities in tension with each other, somewhat like the warp and weft of this weaving from Indonesia.
Tampan, Paminggir people. Sumatra 19th century, 58 x 66 cm. Kota Agung style. Photograph by D Dunlop.
References
1The term imaginary is used here with its mathematical meaning . Particles with an imaginary mass are no more fictitious than any other sort of nuclear particle. They carry momentum and transmit forces like other particles. The main thing about having an imaginary mass is that it puts a particle in a logical category that is different from Newtonian particles. So they are not necessarily required to follow Newtonian laws of motion.