Re: [Phys-l] energy is well defined

[John Denker <jsd@av8n.com>]

On 02/23/2008 08:08 AM, Jeffrey Schnick wrote:

> You make good points here.  

:-)



Some additional supporting points:

In the context of a batted ball:

> Insofar as we can neglect Oscillation and rotation of the ball,

In general the rotation of the ball is not negligible.
And the rotation of the bat is not at all negligible;  it
is expected that the bat is /swung/ not pushed.

A heretical reformulation of physics that can't handle 
rotation is not ready for prime time.

=======

In the context of fluid dynamics, with N parcels of fluid:

> There is no reason to choose N different reference frames.  

Agreed!

> Pick the
> center of mass frame for the entire system and stick with it.  There is
> no problem with focusing your attention on one "blob" of the fluid,

Well, then, if it is OK to have N parcels with nonzero CM
motion, because the reference frame is not attached to the
parcel, why not go the last step and drop the requirement
that the reference frame be attached to the "entire system"???

BTW, in the case of flow of an infinite fluid, the CM of
the "entire system" is undefined.  In conventional physics,
this is not a problem.  It would be a step in the wrong
direction to reformulate physics in such a way that this
becomes a problem.

  In aeronautical engineering, it is convenient to attach
  the reference frame to the airframe, not to the fluid.
  In principle you could do it the other way, but the 
  result would be a mess of epic proportions.

  Conventional physics allows the reference frame to be
  attached to anything, or to nothing in particular.  This is
  Galileo's principle of relativity.  You are free to choose
  whatever frame you like, but others may choose differently.
  Any theory that restricts this choice is a Bad Idea.
 
Also, more importantly:  As soon as you allow a parcel to have
nonzero KE, the previous assertion that "energy is mass" goes
out the window.  The quantity mc^2 is equal to the rest energy,
not the total energy.  For details, see
  http://www.av8n.com/physics/mass.htm
and references therein (especially Oas).

> I tell the students that the gravitational potential energy associated
> with the configuration of the earth plus ball system is energy of the
> system as a whole and is not energy of the ball itself, but for
> accounting purposes, I am going to assign that energy to the ball and
> call it the gravitational potential energy of the ball because it is
> easier to talk about it that way.  

That's fine.  There is good physics to justify that approach.
The justification is nontrivial, because the fundamental
equation 
     Φ = G M m / r
is symmetric under the interchange of M and m, so in some superficial
sense it might seem OK to assign the energy to the earth rather than 
to the particle.  But I wouldn't recommend it.

The rationale for the recommended assignment goes like this:
  a) The energy "really" belongs to the system (or to the field).
  b) We make a negligible mistake in assigning the energy to the 
   particle, in the limit that the particle is verrry small compared 
   to the earth.  We can transfer momentum to/from the earth, but
   we cannot transfer significant KE.  A glance at the formula 
   p^2/2M explains why.

Going through this rationale is important, for some audiences, 
because it communicates something about the _limits of validity_.  
For a gravitating system where the two masses are comparable, 
such as the earth/moon system, it is not generally valid to 
assign the gravitational energy to one mass or the other.

If you want additional counterexamples, the idea of assigning 
gravitational energy to "the" particle is DoA when there are 
multiple sources of the gravitational field.

> then, for case after case I use the
> expression "the gravitational potential mgh of the object," every once
> in a while earnestly reminding the students that the energy is really
> the energy of the earth-plus-object system--not the object.

I agree with both parts there:
 -- Most students can handle the idea that "mgh" is exceedingly
  accurate over laboratory length scales but not cosmological
  length scales.  
 -- They do need to be "reminded" now and then.