## Newtonian Particles are Heavy

Let P be in an excited state characterized by $\left\| \, \overline{\rho} \, \right\|$, the norm of its radius vector, and $m$, the rest mass. The density is defined such that $\, \left\| \, \overline{\rho} \, \right\| = m c^{2} / \, \varrho \,$. So the Newtonian condition that $k_{\sf{F}} \ll \varrho$ implies that

$\begin{align} k_{\sf{F}} \left\| \, \overline{\rho} \, \right\| \ll m c^{2} \end{align}$

From the previous theorem about the enthalpy of a Newtonian particle we have

$m c^{2} \simeq \left| \, H \, \right|$

Eliminating the mass from the last two equations yields

$k_{\sf{F}} \left\| \, \overline{\rho} \, \right\| \ll \left| \, H \, \right|$

But the work required to assemble the quarks in P is $W \equiv k_{\sf{F}} \left\| \, \overline{\rho} \, \right\|$. So for Newtonian particles

$W \ll \left| \, H \, \right|$

Then squaring both sides shows that P satisfies the definition for being a heavy particle