Re: Continuum Mechanics as a 'Principle' Theory (was: Is QM a principle theory?)

[EMAIL PROTECTED] (Ken S. Tucker) wrote:
> >The quantity T is identitied as the stress tensor of the system,
> >and e as the system's internal energy.  They are related by:
> >                   1/2 trace(T) = rho e.
> >
> >In fact, this is true for monoatomic gases.  For diatomic and
> >polyatomic gases, there is an additional component to e that
> >does not arise from the 1/2 the trace of T.
> 
> Agreed, would you say these "additional components" 
> are  antisymmetric and or nonorthogonal components 
> off the trace, where the trace T solves only mono's?

e and trace(T) are invariant under Galilean transformations, and
under the "scale" or "additivity" transformation.  So, the
difference (e - 1/2 trace(T)) persists at all levels: microscopic
and macroscopic, and is intrinsic.

So, if the continuum decomposes into fundamental subsystems (the
"particles") the difference (e - 1/2 trace(T)) for that
subsystem represents a source of energy arising from intrinsic
degrees of freedom OTHER than the translational degrees.

It's direct evidence of the existence of non-translational
degrees of freedom in particles (i.e., spin); and is entirely
non-classical in origin.

In fact, for polyatomic gases, the e WILL actually be
1/2 trace(T) at low enough temperatures; because the other
degrees of freedom are frozen out.  For diatomic gases, it pushes
up to 5/6 trace(T) past a certain critical temperature, as the
other degrees of freedom "thaw" out; and for polyatomic gases,
up to trace(T).