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Re: Energy, etc



At 12:40 PM -0700 8/5/99, Inge H. A. Pettersen wrote:

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.

I agree. I said those abstract quantities are not real or substantial.
My hobby horse is the suppression of reification whenever it occurs.
It appears you feel that way too.

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 ?

I'm sorry that there is such a focus on this Lorentz invariance
business. The disagreement of observers is merely an aspect of
unreality; it is not the keystone in my cosmology of the real*.

Lorentz invariance is probably a necessary condition for my kind
of reality, but it is not sufficient. For example, the interval
is Lorentz invariant but it is not real or substantial. It is an
abstract construct that is useful, that's all. Nature doesn't
take notice of the interval when she schedules two events. We've
just noticed that the interval is the same for all observers.
That's akin to noticing that all the blocks in a city core have
the same length. It may be true, and that may be useful, but
there is no underlying substantial entity.

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.

Yes, I'll agree to that, but one must have a complete algorithm
for calculating energy. I hope that I haven't mislead anyone by
implying otherwise.

Thus the energy concept is useful for predictions due to this property.

Utility should not be mistaken for reality; that is a common and
serious cognitive error.

Leigh

*Weltanschauung