Re: vector quantities and energy

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 21 Jan 1999, GARY HEMMINGER wrote:

> Since we study momentum before energy I've had kids ask me the
> question - why isn't energy (particulary kinetic energy)  a vector?
> It strikes me that this is a great question because it can be
> addressed at so many levels.  Feynman would no doubt say something
> rather different to his colleagues than I would to my weakest 10th
> graders and so on.     How would you answer this?

I love this kind of "Why ..." question.  I'd begin my answer as I always
do to such questions by simply saying, "Because *we* say so."  This answer
helps to emphasize that the theories of physics are pure fabrications of
the human mind, that physics is about constructing mathematical algorithms
("models") that mimic the behavior of nature.

I would go on to point out that we would *not* say so, indeed, that
energy--defined as *we* have defined it--would simply not appear in the
lexicon of physics, if we had not found it to be supremely "useful." Its
"usefulness" is judged by its prominence and the frequency with which it
appears in our mathematical models and, most importantly, the extent to
which those models make predictions that are borne out by the verdict of
nature itself in experiments.

No answer could *really* be complete, however, without engaging in
something along the lines suggested by John Denker.  It is our nature as
human beings to want more than purely pragmatic "natural outcome
prediction algorithms." When a concept is as useful as energy, we just
can't help but suspect that there has to be a more fundamental "reason"
lurking in the background, that our "creation" is *really* a "discovery."

Looking for such reasons is, in some sense, nothing more than engaging in
metaphysical speculation; we don our philosopher hats and wrap our
mathematical models in the magnificent robes of "theories" that provide a
unifying viewpoint and a motivation for the math. Nevertheless, we can't
test our "theories" (in the sense I have used the word here), because we
can't tug on those robes; we can only test the algorithms around which the
robes are wrapped.

We have found, however, that the robes are *themselves* very "useful" for
they have served to guide our attention, to point in directions that are
likely to be fruitful for further, more careful analysis.  And, of course,
the usefulness of the robes (which are, again, a creation of the human
mind) serves only to strengthen our conviction that they "really exist."

John
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