Re: the energy

[John Denker <jsd@AV8N.COM>]

Hugh Logan wrote:

> There is a nice article reflecting the view of the Modeling people on
> the teaching of  energy by Mark Schober at
> <http://www.jburroughs.org/science/mschober/physteach/energy03/index.html>
> (Then click on "a handout... .") In this article, Mark promotes the idea
> of energy flowing as a substance.

Note this should not be misinterpreted as suggesting that this
view is unique to or original to the Modeling people.  This
view was conventional long, long before the Modeling movement
got under way.

> Quantities are said to be
> subtance-like if they have density and flow through space. Such
> quantities are supposed to obey conservation laws as in the case of
> charge. Their are other abstract quantites in physics that can be
> described using the idea of flow and density such as probability density
> in quantum mechanics. Texts on quantum mechanics (_Quantum Mechanics_,
> Schiff, 3rd ed., p. 26-27 derive an equation analogous to the equation
> of continuity in fluid mechanics and for charge in electricity and
> magnetism. This equation states
>
> DP(_r_, t)/Dt + div _S(_r_, t)=0,
>
> where "D" denotes partial differentiation, _P(_r_, t) =probability
> density=(psi(_r_, t)*)(psi(_r_, t)), and _S_(_r_,t)=probability current
> density. As Schiff points out, it would be misleading to reify _S(_r_,
> t) as the average particle flux at (_r_, t) as that would be
> inconsistent with the uncertainty principle.

Two quibbles:
  a) As I understand the word "average", S is exactly the
average particle flux.  I don't see anything misleading about
it.  Because of the averaging, uncertainty-principle issues
become percentagewise insignificant.

  b) As mentioned below, reification is _exactly_ what is
happening here, by definition:
  http://www.yourdictionary.com/ahd/r/r0130600.html
which is fine with me.

> Still physicists do not
> hesitate to speak of the flow of probability, an abstract man-made
> mathematical quantity. It is not "stuff" in any physical sense.

It depends on what you mean by "stuff".  Energy is a _thing_,
according to any reasonable definition of "thing".  It is not
a concrete, material, tangible thing.  It is an abstract thing.
As I have pointed out elsewhere,
  http://www.av8n.com/physics/reality-reductionism.htm
my dictionary (Random House) gives 21 definitions for the
word ``thing''. Of these, items 3, 4, 5, 6, 7, 8, 11, 13,
15, 16, 18, 19, 20, and 21 clearly refer to abstract and/or
intangible things.

> I do not see any objection to using the idea of flow of energy on the
> grounds that energy is a man-made concept that cannot be reified as a
> substance. The question, for me, is whether or not
> the idea of energy flow makes the teaching and learning of energy
> conservation easier or better.

Is there a choice?  I don't see an alternative.  The statement
of local conservation of energy is a statement about flow.

....
> It seems to me that the use of the word "flow" is a little
> ambiguous Is it a flow of a substance (or the flow of of something that
> behaves analogously to a substance as in the case of probability in QM),
> or rather is it a figurative
> use of the word "flow" such as used in a "flow chart."

I use the term "conservative flow" in situations where I need
to exclude the figurative notions of flow.

....
> It is
> analogous to the idea that money is essentially the same thing wherever
> it is stored. I like the money transfer analogy better than the substnce
> flow idea.

I prefer the flow idea.  There is some limited value in using
money as a loose analogy, but it shouldn't be taken too seriously.
Money is much less strictly conserved than energy is.  At the
unsophisticated level, if I burn a ten-dollar bill, there is a
non-conservative loss of money.  At a more sophisticated level,
macroeconomic factors change the "money supply" in ways that
governments are hard-pressed to measure, let alone control.
Also it depends on whether your notion of conservation is based
on single-entry bookkeeping (where you just keep track of the
money per se) or double-entry bookkeeping (where if you pay
money to buy a non-monetary asset, you carry the asset on you
books).  Most importantly, money ought to be considered as a
proxy, as a symbol for value, not to be confused with value
itself.
 -- Money itself is not conserved.
 -- Value is certainly not conserved.  Mutually-profitable
  transactions are the norm, not the exception.
 -- The connection between money and value is a very dodgy
  thing, based on government policy, speculator activity,
  public perceptions, etc. etc. etc.


> It puts a strain on my intuition to think of
> energy flowing into a system consisting of a spring as a consequence of
> work done on it by an external force if the flow is like that of a
> substance.

What kind of strain?  What's the alternative?

> However, it does not bother me to think of the energy
> transfer diagrams as flow charts in which the word "flow" is not taken
> too literally.

Why not 100% literally?

Why is not the statement of local conservation of energy
indistinguishable from the equation for conservative flow?
  http://www.av8n.com/physics/conservative-flow.htm

....
>  mass (rest mass) and rest energy. They are essentially the
> same according to E_0=mc^2 or E=m in units in which c=1.

Right.

The pedagogical difficulty here is that some students arrive
with the notion that E=m is some sort of 11th commandment,
not realizing that it is only a special case, valid when the
3-momentum is zero (i.e. in the rest-frame if such exists).

> m is mass (which used to be called "rest mass."

According to one school of thought, "rest mass" has always
been a pleonasm.  That is, m stands for mass, and always
has.  If additional description is required, I prefer to
call it the invariant mass.  It's not just the rest mass;
it is the same in the rest frame or any other.

> Any energy transferred to a system in its rest frame will increase its
> inertial mass by that amount of energy if c=1 (or that amount divided by
> c^2 if conventional units are used) no matter what storage mechanism is
> used for the energy in the system. (Einstein is explicit about this on
> pp. 46-47 of _Relativity, The Special and the General Theory_, 15th ed.)
> In that sense, energy has inertia because it is the same as inertial
> mass. By the principle of equivalence, inertial mass implies a
> proportional gravitational mass -- equal if the same standard is used
> for each. Mass is something like a common measure of energy no matter
> what the storage mechanism.

OK.

> Unfortunately, the change of mass with
> change in rest energy cannot be measured except in a thought experiment,
> since the change is too small to be measurable.

It is distinctly measurable in the case of nuclear reactions.

> The Modelers (following Dr. Arnold Arons) emphasize enlarging the system
> to avoid using the work-energy theorem,

Strictly speaking, there is no work-energy theorem.  There
is a work-KE theorem, or rather a bevy of work-KE theorems,
depending on what sorts of KE you wish to talk about.
  http://www.av8n.com/physics/kinetic-energy.htm

....
> [frictional] heating Q across the boundary in the
> context of the first law of thermodynamics.

Friction is tricky.  One can easily get into trouble, because
of inconsistencies in the way thermodyanmics is usually
formulated.  A way out of the quagmire is described in:
  http://www.av8n.com/physics/thermo-laws.htm#sec-grind

> As I see it, E_0=m is the conserved quantity in an isolated physical
> system.

That's not wrong ... but to do physics we need a more-robust
notion of what conservation means, one that can handle a
non-isolated system.  That is where the idea of conservative
flow comes in.


On 19-Oct-04 Michael D. Edmiston wrote:

>>And what exactly does E=mc2 mean?  Doesn't it mean mass and energy are
>>equivalent?

No, because the equation is not valid in general.  It is only
valid when the 3-momentum is zero.