Re: Energy, etc

["Inge H. A. Pettersen" <ingep@ONLINE.NO>]

Leigh Palmer wrote:

> John Denker has asked if I consider everyone who speaks of energy
> density to be in error. Of course I do not; figures of speech and
> conventional conveniences are useful. Energy density is a useful
> concept. John, please tell me how you view the energy density in a
> gravitational field.
>
> There are many conservation laws in Nature. Is linear momentum a
> substantial entity? Angular momentum? No, neither is real.

I am confused by your term "real" and "substantial" as I personally
consider them as philosophical terms, not physical ones. I guess we are
victims of the Pygmalion effect if we identify our theories and concepts
with nature itself.

> When a
> gravitational system contains just two bodies we know the familiar
> conserved quantities serve well. There are *ten* known scalar
> quantities that are conserved in celestial mechanical systems.
> Three are linear momentum components, three angular momentum
> components, total energy, and three others called "integrals of
> area". All are invariant, and none is substantial.

I do not agree on the use of the term invariant here: all these
quantities are *conserved* as measured by any inertial observer within
the context of Special Relativity; however by making suitable
contraction of these tensors it is possible to get a scalar that is an
invariant, i.e. of same value for all inertial observers. Am I missing
something here ?
It seems to me that you imply that a physical quantity from your
philosophical point of view is "real"/"substantial" only if it is
Lorentz-invariant ?
What we can agree on (I guess :-), irrespectively of any philosopical
prejudices, is that even though energy is not a Lorentz invariant, it is
a conserved quantity for all inertial observers (within the limits of
the uncertainty principle) even though they in general disagree on what
the constant value is. Thus the energy concept is useful for predictions
due to this property.

> Why must energy be special?
>
> Leigh
>
> ...*there are no blocks*      -Feynman