Re: [Phys-L] heat content

[John Denker <jsd@av8n.com>]

On 02/16/2014 08:09 PM, Jeffrey Schnick wrote:

> Let me try to explain what my point here is.  I think it will take 
> some doing.  I'll start with an assertion and try to back it up. What
> we refer to as the kinetic energy of a particle is not really energy
> of that particle but rather energy of a system whose center of mass
> is at rest relative to the inertial reference frame in which the 
> particle is said to have that kinetic energy.  As far as the 
> explanatory and predictive power of the concept, what we call the 
> kinetic energy of a particle only matters insofar as it is the 
> kinetic energy of a system consisting of that particle and something 
> else with which that particle is interacting, will interact, or could
> conceivably interact.

That's an awfully narrow definition of KE.  For your own use, you 
are free to define it that way if you wish ... but beware that 
other folks define it differently.

> For instance, if we have two elementary particles on a collision 
> course with each other and you want to know what set of elementary 
> particles there might be after the collision, what matters is the 
> energy in the center of mass frame

That's the only thing that matters /for some purposes/ ... but for
other purposes there are other things that matter.

Even in something as prosaic as baseball, we routinely calculate the
KE of the ball in the spectators' frame ... without regard to all the 
stuff with which it "could conceivably interact".

> It is in this sense that I say that, for any control mass system, all
> energy of the system is internal energy.

But not every interesting system is a control-mass system.

Even for something relatively prosaic like a wave packet moving 
along a string, we can Fourier analyze the modes.  Neither the 
packet nor the modes are control-mass systems.

As another example: In aerodynamics, it is exceedingly common (and 
useful) to define the KE of a parcel of fluid in the frame comoving 
with the aircraft ... which is not even remotely the center-of-mass 
frame.

================

> I think it would be inconsistent for someone to consider the mass of 
> a particle to be invariant but to consider what we generally refer to
> as the kinetic energy of a particle to actually belong to that 
> particle.  If it were to belong to that particle then it would 
> contribute to the mass of the particle.

Lost me there.  I don't see any inconsistency.

Mass is invariant.  Energy is not.  Therefore obviously there is no 
way the KE could contribute to the mass.  KE contributes to the total
energy, not to the mass.  mc^2 is the rest energy, not the total energy.

> I think the notion that what we call the kinetic energy of a particle
> does not really belong to the particle eliminates what I perceive to
> be a problem, namely that the energy of a particle depends on the
> inertial reference frame from which we view that particle.

We agree that E and KE are frame-dependent.  I just don't see it as
being a problem.

E is invariant with respect to /spacelike/ rotations.  It is not
invariant with respect to boosts, i.e. rotations in any timelike
direction.

E is the timelike component of the [energy,momentum] 4-vector.
Just as X is invariant w.r.t rotations in the YZ plane, E is
invariant to rotations in the XY, YZ, and ZX planes.  Meanwhile,
as soon as we consider more general rotations, these things become
non-invariant.

=======================

New topic, I think:

> What I do with the fact that the gravitational potential energy 
> associated with the interaction between a baseball and the earth is 
> energy of the earth+ball system, not energy of the ball, is to say 
> that for such cases the energy is really energy of the
> earth/baseball system but for accounting purposes I am going to
> assign it to the baseball.

That's traditional and harmless ... as far as it goes.

Things get a little bit murkier when we talk about the moon in the
gravitational field of the earth, which is the same as the earth in
the gravitational field of the moon.  If you're not careful, you 
might double-count the energy.

Things get even murkier when we consider the electromagnetic field
instead of the gravitational field.  It is not hard to store a
nontrivial amount of energy in the field.  An example is posed as
a question here:
   http://www.feynmanlectures.caltech.edu/II_17.html#Ch17-S4
and answered here:
   http://www.feynmanlectures.caltech.edu/II_27.html#Ch27-S6-p10

I reckon that at some point (not necessarily in the introductory 
course) you have to say that the energy is in the field.