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$           All sub-SYSTEMs have "surroundings", duh.
   Sub-SYSTEMs are "submerged" in SYSTEM "working fluid" AMBiENT.
   Sub-SYSTEMs ONLY EXCHANGE energy with "working fluid" AMBiENT.

   Go-go Google GROUP SEARCH: < My BiGGER bang > ..My REAL STUFF.

   TOTAL LaGrangian h*f Dis-iNFORMATiON follows with Tom Roberts.

                                   brian a m stuckless
    >><> >><> >><> >><> >><>
Tom Roberts wrote: > > Koobee Wublee wrote:
> > "Tom Roberts" <tjroberts@lucent.com> wrote in message
> > news:dlidra$cvs@netnews.net.lucent.com...
> >>    L = \integral g_ij (dx^i/d\tau) (dx^j/d\tau) d\tau
> 
> Yes, the Lagrangian is buried inside there; the integral itself is
> called the action.
> 
> > we can discuss logically and clearly how Noether's Theorem applies to
> > indicate a universal phenomenon to the conservation of observed energy.
> 
> Except, of course, that Noether's theorem states quite explicitly that
> energy is conserved ONLY for systems with a Lagrangian that is invariant
> under time translations. <shrug>
> 
> And you never responded to the fact that for two interacting subsystems,
>   if conservation of energy is "universal", why isn't energy conserved
> in each subsystem? The answer is, of course, that as long as the
> interactions between a subsystem and its surroundings are independent of
> time then energy will be conserved in the subsystem; but if the
> interactions vary over time then the subsystem's Lagrangian won't be
> time independent and energy in the subsystem won't be conserved. That
> _IS_ what Noether's theorem says about such a case. <shrug>
> 
>         As I said before, before Noether this was a puzzle[#], and
>         ad hoc rules had to be established to save energy
>         conservation. So "... for an isolated system that does
>         not interact with its surroundings" had to be added to
>         the "principle of conservation of energy".
>         Not very "universal" is it?
> 
>         [#] Admitedly one that not many people worried about. It
>         was considered self-evident that energy won't be conserved
>         in a subsystem that interacts with its surroundings.
> 
>  > [...]
> 
> Tom Roberts     tjroberts@lucent.com