Dynamic Equilibrium

We characterize Newtonian particles as being in some kind of steady balance with their environment. They are presumably interacting with countless photons, bouncing around a lot, and colliding with other particles. But despite much agitation, there is still a central tendency that might be called realistic motion, or perhaps naturalistic movement. Particles that depart too far from the mean may be called non-Newtonian, or even unphysical. To be more exact about this we define the kinetic and potential energy.

Kinetic Energy

//Tampan//, Paminggir people. Lampung region of Sumatra, 19th century, 77 x 70 cm. Photograph by D Dunlop.
Tampan, Paminggir people. Lampung region of Sumatra, 19th century, 77 x 70 cm. Photograph by D Dunlop.

Consider a material particle P, described by its rest mass $m$ and momentum $p$. The kinetic energy of P is

$\begin{align} K \equiv \frac{\, p^{ 2}}{2m} \end{align}$

Since $m > 0$ for material particles, $K$ is never negative. And in an inertial frame, momentum is proportional to the wavenumber ${\kappa}$. So $K$ is proportional to $\kappa ^{2}$. Then recall that the wavenumber depends only on the coefficients of dynamic quarks. So the kinetic energy depends strongly on P's dynamic quark content. Sensory interpretation: Dynamic quarks and the wavenumber have already been interpreted as representations of somatic and visual sensations. So the kinetic energy depends mostly on audio-visual sensations.

Potential Energy

Let us also include the mechanical energy $\, E$ in the description of P. The difference between $E$ and the kinetic energy defines another number $\mathcal{U}$ called the potential energy

$\mathcal{U} \equiv E - K$

And recall that if the motion of a material particle is not relativistic, then

$\begin{align} E \simeq m c^{2} \left( 1 + \frac{p^{2}}{2m^{2}c^{2}} \right) = m c^{2} \left( 1 + \frac{K}{mc^{2}} \right) = m c^{2} +K \end{align}$

So the potential energy may be approximated as

$\mathcal{U} \simeq m c^{2}$

For slowly moving Newtonian particles, the potential energy depends strongly on the mass. Then remember that for heavy particles, a sensory interpretation of the mass relates mainly to thermal sensations. And so for Newtonian particles, the potential energy is mostly associated with thermal sensations too.

Dynamic Equilibrium

Definition: When the kinetic and potential energies are equal to each other

$K = \mathcal{U}$

and we say that P is in dynamic equilibrium. But the potential energy is defined by $E$ less $K \,$. So for a particle in dynamic equilibrium

$E=K+ \mathcal{U} =2K =2 \mathcal{U}$

and there is an equal sharing, or equipartition, of mechanical energy between kinetic and potential types. Sensory interpretation: As noted above, in an ideal reference frame the kinetic energy characterizes the sensory magnitude of visual stimuli, whereas the potential energy depends more on thermal perception. So for sensations objectified as particles in dynamic equilibrium, there must be a balanced experience of both thermal and visual sensation. The requirement for eyes-open visual awareness means that, for example, a dream about flying while asleep cannot be considered equilibrium. And neither can watching cartoons on TV, because television only represents audio-visual sensations, not thermal sensations. So dynamic equilibrium is like experiencing ordinary circumstances in classrooms and laboratories on Earth. Unlike many movies, dreams and hallucinations.

Right.png Next step: characteristics of Newtonian Particles.

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