Conservation of Energy and Mass Baby Collar, Dong people. China, Yunnan province, 20th century 38 x 19 cm. From the collection of Tan Tim Qing, Kunming. Photograph by D Dunlop.

Newtonian particles are dense and heavy. And we regularly assume that they are in dynamic equilibrium with their surroundings. Then as discussed earlier, their enthalpy $H$, is related to their mass $m$, by the approximation

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

But the mechanical energy $E$ of any material particle is approximately $E \simeq \gamma m c^{2}$ where $\gamma$ is the Lorentz factor. Then

$E \simeq \gamma \, \left| \, H \, \right|$

For particles in slow motion, $\gamma \simeq 1$ so that $E \simeq \, \left| \, H \, \right|$. But the absolute-value signs can usually be ignored because ordinary particles are composed from electrons, neutrons and protons which all have positive enthalpy. So if we exclude anti-particles and processes like annihilation, then we usually have

$H \simeq E \simeq m c^{2}$

Thus the mechanical energy and the enthalpy are almost interchangeable for slow Newtonian particles made of ordinary matter. But enthalpy is conserved for all particles and conditions. So the energy and mass must also be approximately conserved for slow Newtonian particles too. This idea is honoured as an energy conservation law because it is so important in classical mechanics. Moreover, a conservation law for mass is a basic principle in benchtop chemistry. These excellent approximations are used everyday. Together with the routine assumption of dynamic equilibrium they typify Newtonian particles.